diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..e63f7d5 --- /dev/null +++ b/.gitignore @@ -0,0 +1,11 @@ +/Notes +main* +.ipynb_checkpoints +*__pycache__ +*temp* +/datasets/* +/analysis/workspace/*/data_files +/analysis/workspace/*/*npz +/analysis/*signac* +/deprecated/* +*Untitled* diff --git a/README.md b/README.md index ce51401..58d615c 100644 --- a/README.md +++ b/README.md @@ -1,2 +1 @@ -# kernel-tutorials -A set of utilities and pedagogic notebooks for the use of linear and kernel methods in atomistic modeling +# kernel_project diff --git a/TestingNewClasses.ipynb b/TestingNewClasses.ipynb new file mode 100644 index 0000000..003cd76 --- /dev/null +++ b/TestingNewClasses.ipynb @@ -0,0 +1,546 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#%load_ext autoreload\n", + "#%autoreload 2\n", + "\n", + "import numpy as np\n", + "\n", + "from utilities.classes import *\n", + "from utilities.general import FPS\n", + "from utilities.plotting import plot_regression, plot_projection\n", + "from utilities.kernels import center_kernel\n", + "from matplotlib import pyplot as plt\n", + "\n", + "from utilities.kernels import linear_kernel, gaussian_kernel" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "training = np.load('../KernelPCovR/analysis/workspace/44510f9e5dec42b711c1467f03f7e504/training.npz')\n", + "testing = np.load('../KernelPCovR/analysis/workspace/44510f9e5dec42b711c1467f03f7e504/testing.npz')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X = training[\"X\"][:2000] * training['Xs'] + training['Xc']\n", + "Y = training[\"Y\"][:2000] * training['Ys'] + training['Yc']\n", + "Xt = testing[\"X\"][:2000] * testing['Xs'] + testing['Xc'] # Same as training\n", + "Yt = testing[\"Y\"][:2000] * testing['Ys'] + testing['Yc'] # Same as training\n", + "\n", + "fps, _ = FPS(X.T, 200)\n", + "X = X[:, fps]\n", + "Xt = Xt[:, fps]\n", + "\n", + "# Mess with some shit\n", + "#X += np.random.uniform(-0.5, 0.5, X.shape[1])\n", + "#Y += np.random.uniform(-0.5, 0.5, Y.shape[1])\n", + "\n", + "#Xt += np.random.uniform(-0.5, 0.5, Xt.shape[1])\n", + "#Yt += np.random.uniform(-0.5, 0.5, Yt.shape[1])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "scp = {\"linewidth\": 0.5, \"edgecolor\":\"k\", \"cbar\": False}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pca_uncentered = PCA(n_PC=2, scale=False, center=False)\n", + "pca_uncentered.fit(X)\n", + "\n", + "pca_centered = PCA(n_PC=2, scale=True, center=True)\n", + "pca_centered.fit(X)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1,2, figsize=(12,5))\n", + "plot_projection(Yt, pca_uncentered.transform(Xt), \n", + " fig=fig, title='Uncentered', ax=ax[0], **scp)\n", + "plot_projection(Yt, pca_centered.transform(Xt), \n", + " fig=fig, title='Centered', ax=ax[1], **scp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "lr_centered = LR(center=True, scale=True, regularization=1.0E-15)\n", + "lr_centered.fit(X, Y)\n", + "print('finished centered fit')\n", + "\n", + "lr_uncentered = LR(center=False, scale=False, regularization=1.0E-15)\n", + "lr_uncentered.fit(X, Y)\n", + "print('finished uncentered fit')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1,2, figsize=(12,5))\n", + "plot_regression(Yt, lr_uncentered.transform(Xt), \n", + " fig=fig, title='Uncentered', ax=ax[0], **scp)\n", + "print('done with uncentered')\n", + "plot_regression(Yt, lr_centered.transform(Xt), \n", + " fig=fig, title='Centered', ax=ax[1], **scp)\n", + "print('done with centered')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#K = linear_kernel(X, X)\n", + "#Kt = linear_kernel(Xt, X)\n", + "K = gaussian_kernel(X, X)\n", + "Kt = gaussian_kernel(Xt, X)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "kpca_uncentered = KPCA(n_PC=2, kernel_type='linear', scale=False, center=False)\n", + "kpca_uncentered.fit(K=K)\n", + "\n", + "kpca_centered = KPCA(n_PC=2, kernel_type='linear', scale=True, center=True)\n", + "kpca_centered.fit(K=K)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1,2, figsize=(12,5))\n", + "plot_projection(Yt, kpca_uncentered.transform(K=Kt), \n", + " fig=fig, title='Uncentered', ax=ax[0], **scp)\n", + "plot_projection(Yt, kpca_centered.transform(K=Kt), \n", + " fig=fig, title='Centered', ax=ax[1], **scp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "krr_centered = KRR(kernel_type='linear', center=True, scale=True)\n", + "krr_centered.fit(K=K, Y=Y)\n", + "\n", + "krr_uncentered = KRR(kernel_type='linear', center=False, scale=False)\n", + "krr_uncentered.fit(K=K, Y=Y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1,2, figsize=(12,5))\n", + "plot_regression(Yt, krr_uncentered.transform(K=Kt), \n", + " fig=fig, title='Uncentered', ax=ax[0], **scp)\n", + "plot_regression(Yt, krr_centered.transform(K=Kt), \n", + " fig=fig, title='Centered', ax=ax[1], **scp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "n_active = 50\n", + "fps_sparse, _ = FPS(X, n_active)\n", + "X_sparse = X[fps_sparse]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Knm = linear_kernel(X, X_sparse)\n", + "#Knmt = linear_kernel(Xt, X_sparse)\n", + "#Kmm = linear_kernel(X_sparse, X_sparse)\n", + "Knm = gaussian_kernel(X, X_sparse)\n", + "Knmt = gaussian_kernel(Xt, X_sparse)\n", + "Kmm = gaussian_kernel(X_sparse, X_sparse)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "skpca_uncentered = SparseKPCA(kernel_type='linear', n_PC=2, n_active=n_active,\n", + " scale=False, center=False)\n", + "skpca_uncentered.fit(X=X, Knm=Knm, Kmm=Kmm)\n", + "\n", + "skpca_centered = SparseKPCA(kernel_type='linear', n_PC=2, n_active=n_active,\n", + " scale=True, center=True)\n", + "skpca_centered.fit(X=X, Knm=Knm, Kmm=Kmm)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1,2, figsize=(12,5))\n", + "plot_projection(Yt, skpca_uncentered.transform(X=Xt, Knm=Knmt), \n", + " fig=fig, title='Uncentered', ax=ax[0], **scp)\n", + "plot_projection(Yt, skpca_centered.transform(X=Xt, Knm=Knmt), \n", + " fig=fig, title='Centered', ax=ax[1], **scp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "skrr_centered = SparseKRR(kernel_type='linear', n_active=n_active,center=True, scale=True)\n", + "skrr_centered.fit(X=X, Knm=Knm, Kmm=Kmm, Y=Y)\n", + "\n", + "skrr_uncentered = SparseKRR(kernel_type='linear', n_active=n_active, center=False, scale=False)\n", + "skrr_uncentered.fit(X=X, Knm=Knm, Kmm=Kmm, Y=Y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1,2, figsize=(12,5))\n", + "plot_regression(Yt, skrr_uncentered.transform(X=Xt, Knm=Knmt), \n", + " fig=fig, title='Uncentered', ax=ax[0], **scp)\n", + "plot_regression(Yt, skrr_centered.transform(X=Xt, Knm=Knmt), \n", + " fig=fig, title='Centered', ax=ax[1], **scp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "alpha = 1.0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PCovR_uncentered = PCovR(alpha=alpha, n_PC=2, scale=False, center=False)\n", + "PCovR_uncentered.fit(X, Y)\n", + "\n", + "PCovR_centered = PCovR(alpha=alpha, n_PC=2, scale=True, center=True)\n", + "PCovR_centered.fit(X, Y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_unc, Yp_unc, Xr_unc = PCovR_uncentered.transform(Xt)\n", + "T_c, Yp_c, Xr_c = PCovR_centered.transform(Xt)\n", + "\n", + "\n", + "fig, ax = plt.subplots(2,2, figsize=(12,12))\n", + "plot_projection(Yt, T_unc, \n", + " fig=fig, title='Uncentered', ax=ax[0][0], **scp)\n", + "plot_projection(Yt, T_c,\n", + " fig=fig, title='Centered', ax=ax[0][1], **scp)\n", + "plot_regression(Yt, Yp_unc, \n", + " fig=fig, ax=ax[1][0], **scp)\n", + "plot_regression(Yt, Yp_c,\n", + " fig=fig, ax=ax[1][1], **scp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "KPCovR_uncentered = KPCovR(kernel_type='linear', alpha=alpha, n_PC=2, scale=False, center=False, regularization=1.0E-15)\n", + "KPCovR_uncentered.fit(X, Y, K=K)\n", + "\n", + "KPCovR_centered = KPCovR(kernel_type='linear', alpha=alpha, n_PC=2, scale=True, center=True)\n", + "KPCovR_centered.fit(X, Y, K=K)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_unc, Yp_unc, Xr_unc = KPCovR_uncentered.transform(K=Kt)\n", + "T_c, Yp_c, Xr_c = KPCovR_centered.transform(K=Kt)\n", + "\n", + "\n", + "fig, ax = plt.subplots(2,2, figsize=(12,12))\n", + "plot_projection(Yt, T_unc, \n", + " fig=fig, title='Uncentered', ax=ax[0][0], **scp)\n", + "plot_projection(Yt, T_c,\n", + " fig=fig, title='Centered', ax=ax[0][1], **scp)\n", + "plot_regression(Yt, Yp_unc, \n", + " fig=fig, ax=ax[1][0], **scp)\n", + "plot_regression(Yt, Yp_c,\n", + " fig=fig, ax=ax[1][1], **scp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "skpcovr_uncentered = SparseKPCovR(kernel_type='linear', alpha=alpha, n_PC=2, \n", + " n_active=n_active,\n", + " scale=False, center=False)\n", + "skpcovr_uncentered.fit(X, Y, Knm=Knm, Kmm=Kmm)\n", + "\n", + "skpcovr_centered = SparseKPCovR(kernel_type='linear', alpha=alpha, n_PC=2, \n", + " n_active=n_active,\n", + " scale=True, center=True)\n", + "skpcovr_centered.fit(X, Y, Knm=Knm, Kmm=Kmm)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_unc, Yp_unc, Xr_unc = skpcovr_uncentered.transform(X=Xt, Knm=Knmt)\n", + "T_c, Yp_c, Xr_c = skpcovr_centered.transform(X=Xt, Knm=Knmt)\n", + "\n", + "\n", + "fig, ax = plt.subplots(2,2, figsize=(12,12))\n", + "plot_projection(Yt, T_unc, \n", + " fig=fig, title='Uncentered', ax=ax[0][0], **scp)\n", + "plot_projection(Yt, T_c,\n", + " fig=fig, title='Centered', ax=ax[0][1], **scp)\n", + "plot_regression(Yt, Yp_unc, \n", + " fig=fig, ax=ax[1][0], **scp)\n", + "plot_regression(Yt, Yp_c,\n", + " fig=fig, ax=ax[1][1], **scp)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Check centering of Kmm\n", + "Knm = gaussian_kernel(X, X_sparse)\n", + "Kmnt = gaussian_kernel(Xt, X_sparse)\n", + "Kmm = gaussian_kernel(X_sparse, X_sparse)\n", + "Kmmc = center_kernel(Kmm)/1.0E5\n", + "Kmmcc = Kmm - np.mean(Knm, axis=0)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(np.linalg.pinv(Kmm))\n", + "print(np.linalg.pinv(Kmmc))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(np.linalg.eigvalsh(Kmm))\n", + "print(np.linalg.eigvalsh(Kmmc))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "skpca_uncentered_Kmm = SparseKPCA(kernel_type='linear', n_PC=2, n_active=n_active,\n", + " scale=True, center=True)\n", + "skpca_uncentered_Kmm.fit(X=X, Knm=Knm, Kmm=Kmm)\n", + "\n", + "skpca_centered_Kmm = SparseKPCA(kernel_type='linear', n_PC=2, n_active=n_active,\n", + " scale=True, center=True)\n", + "skpca_centered_Kmm.fit(X=X, Knm=Knm, Kmm=Kmmc)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(skpca_uncentered_Kmm.transform(X=Xt, Knm=Knmt))\n", + "print(skpca_centered_Kmm.transform(X=Xt, Knm=Knmt))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "skrr_uncentered_Kmm = SparseKRR(kernel_type='linear', n_active=n_active, center=True, scale=True)\n", + "skrr_uncentered_Kmm.fit(X=X, Knm=Knm, Kmm=Kmm, Y=Y)\n", + "\n", + "skrr_centered_Kmm = SparseKRR(kernel_type='linear', n_active=n_active,center=True, scale=True)\n", + "skrr_centered_Kmm.fit(X=X, Knm=Knm, Kmm=Kmmc, Y=Y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(skrr_uncentered_Kmm.transform(X=Xt, Knm=Knmt))\n", + "print(skrr_centered_Kmm.transform(X=Xt, Knm=Knmt))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "skpcovr_uncentered_Kmm = SparseKPCovR(kernel_type='linear', alpha=1.0, n_PC=2, \n", + " n_active=n_active,\n", + " scale=True, center=True)\n", + "skpcovr_uncentered_Kmm.fit(X, Y, Knm=Knm, Kmm=Kmm)\n", + "\n", + "skpcovr_centered_Kmm = SparseKPCovR(kernel_type='linear', alpha=1.0, n_PC=2, \n", + " n_active=n_active,\n", + " scale=True, center=True)\n", + "skpcovr_centered_Kmm.fit(X, Y, Knm=Knm, Kmm=Kmmc)\n", + "\n", + "T_unc, Yp_unc, Xr_unc = skpcovr_uncentered_Kmm.transform(X=Xt, Knm=Knmt)\n", + "T_c, Yp_c, Xr_c = skpcovr_centered_Kmm.transform(X=Xt, Knm=Knmt)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(T_unc)\n", + "print(T_c)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(Yp_unc)\n", + "print(Yp_c)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(Xr_unc)\n", + "print(Xr_c)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.9" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": {}, + "toc_section_display": true, + "toc_window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/datasets/CSD-1000R.xyz b/datasets/CSD-1000R.xyz new file mode 100644 index 0000000..5e5c643 --- /dev/null +++ b/datasets/CSD-1000R.xyz @@ -0,0 +1,131580 @@ +180 +Lattice="4.865228002 0.0 0.0 0.0 7.37224106961 0.0 0.0 0.0 42.2402452141" Properties=species:S:1:pos:R:3:CS_local:R:1:CS_total:R:1 Natoms=180 NAME=IQIZEO ENERGY=-1911.69922393 CS_global=6.23 pbc="T T T" rattling=0.025 +C 1.78046115 0.40103327 12.11874268 87.69000000 93.91000000 +C 0.68785040 7.00457452 33.25904326 84.89000000 91.12000000 +C 3.12469430 4.07198555 8.96284978 87.57000000 93.80000000 +C 4.17280299 3.31374623 30.11339592 84.23000000 90.46000000 +H 2.64677163 0.90201712 11.76903430 20.12000000 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27.32000000 +H 0.83435712 27.58523056 1.60163328 20.08000000 26.95000000 +H 5.81261306 13.05454167 0.77455294 19.77000000 26.64000000 +138 +Lattice="7.951829106 0.0 0.0 2.0034474396 12.6621268843 0.0 2.80216891415 3.29743268636 12.2183034945" Properties=species:S:1:pos:R:3:CS_local:R:1:CS_total:R:1 Natoms=138 NAME=HUVPAR ENERGY=-1245.37041595 CS_global=6.29 pbc="T T T" rattling=0.025 +O 2.76937887 9.27591033 4.58478108 183.22000000 189.52000000 +O 10.02113869 6.71707256 7.57688526 182.02000000 188.31000000 +C 8.94910577 7.90934462 3.56570746 64.76000000 71.05000000 +C 3.81060452 8.06376226 8.68277925 56.86000000 63.15000000 +H 9.42690057 6.98501250 3.74483278 18.92000000 25.21000000 +H 3.31753874 8.97184681 8.48256488 18.58000000 24.87000000 +C 9.51221082 9.08738345 3.95737215 -10.38000000 -4.09000000 +C 3.23876376 6.85184070 8.27110436 -13.60000000 -7.31000000 +C 8.75933582 10.33584003 3.86211369 41.32000000 47.61000000 +C 4.06114388 5.65875391 8.37399864 48.74000000 55.03000000 +H 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5.66486091 34.46000000 40.91000000 +C 1.19183531 2.05720085 0.46881392 33.43000000 39.88000000 +H 4.96186015 2.19737478 5.76536151 16.38000000 22.82000000 +H 11.96137304 6.22717540 0.18749225 18.33000000 24.77000000 +H 4.28907256 5.76220879 6.26846568 18.01000000 24.45000000 +H -2.65012056 1.86359012 11.88033531 17.88000000 24.33000000 +48 +Lattice="6.436257586 0.0 0.0 1.9974796693 7.51182702745 0.0 0.331409339361 -0.00258093929199 8.94854775457" Properties=species:S:1:pos:R:3:CS_local:R:1:CS_total:R:1 Natoms=48 NAME=ALOSEZ ENERGY=-603.10317472 CS_global=6.46 pbc="T T T" rattling=0.05 +N 7.10327539 4.83293200 5.95601992 -87.47000000 -81.01000000 +N 1.72803135 2.74315128 2.87925354 -73.69000000 -67.24000000 +N 1.70344326 4.44770023 6.73703251 22.82000000 29.27000000 +N 7.06624891 3.08863103 2.27188168 24.02000000 30.47000000 +C 2.51565567 3.43590044 6.25517420 135.62000000 142.08000000 +C 6.22349452 4.06792924 2.71156191 143.57000000 150.03000000 +C 1.90838005 5.10924639 7.79677971 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Modelling\n", + "\n", + "These notebooks provide a hands-on introduction to linear and kernel methods, with applications to chemical and materials modelling. The notebooks provide a rather complete discussion of the theoretical foundations of supervised and unsupervised learning techniques, starting from principal component analysis and linear regression, and continuing to rather advanced techniques based on the kernel trick. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Dataset\n", + "A dataset composed of molecular materials extracted from the Cambridge Structural Database, and optimized at the DFT-PBE level is used as a demonstrative example. For each atom, the nuclear magnetic shielding has been computed with the GIPAW method, and so exercises aim to reveal the relation between local chemical environments and the value of the [chemical shielding](https://en.wikipedia.org/wiki/Chemical_shift). Both \"local\" and \"total\" chemical shieldings (that also contain terms related to the macroscopic magnetism of the material) are included, to demonstrate the simultaneous description of multiple properties. The two properties are nearly identical, and we include them just to show how regression methods can be applied to multiple properties at once.\n", + "\n", + "**Note**: for pedagogic purposes, all chemical elements are considered together, even though from an applicative (and physical) point of view it does not make sense to compare shielding values for different elements. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The atom-centred environments are represented in terms of 2 and 3-body correlations, described by the [SOAP](https://doi.org/10.1063/1.5090481) power spectrum, and can be computed using the `librascal` library, following the procedure in [Importing Data](X_ImportingData.ipynb). For ease of use, pre-computed features can be downloaded from [here](https://www.dropbox.com/s/itokckbbkvxaqsk/precomputed.npz?dl=0). The file `precomputed.npz` should be copied to the `datasets/` folder." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# How to Use These Notebooks\n", + "\n", + "Notebooks are meant to be read and executed sequentially, and should function without the need of writing any code. However, for best learning outcomes, more Python-savvy readers are encouraged to experiment with modifying the code, printing and visualizing intermediate values, or even just changing the input files to correspond to a different chemical system. The package also contains a set of utility functions that can be used to perform analyses using a scikit-learn-style syntax, that are demonstrated at the end of each notebook, and that are used when demonstrating the behavior of different methods when their hyperparameters are changed. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. `LinearMethods` delves into linear regression (LR), principal component analysis (PCA), and multidimensional scaling (MDS).\n", + "\n", + "2. `PrincipalCovariatesRegression` demonstrates a method, PCovR, which combines the power of unsupervised (PCA) and supervised (LR) learning.\n", + "\n", + "3. In `KernelMethods`, we introduce versions of the previous models which take advantage of the **kernel trick**.\n", + "\n", + "4. In `SparseKernelMethods`, we demonstrate methods which use the kernel trick, but with lower computational cost, working with few samples.\n", + "\n", + "5. In `CUR`, we explain a matrix decomposition strategy to approximate input data or select features for ML models, and extend this method using PCovR.\n", + "\n", + "* There are also a few appendices, denoted `X_Appendix.ipynb`, which contain information on importing data and the notation used throughout the tutorial.\n", + "\n", + "These notebooks have the following dependencies: `ase`, `json`, `matplotlib`, `numpy`, `scipy`, `sklearn`, and `tqdm`. We also suggest to enable the Jupyter Notebook `Python Markdown` extension.\n", + "\n", + "Furthermore, many new methods require the `scikit-cosmo` package, which can be downloaded from ." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.11" + }, + "toc": { + "base_numbering": 1, + "nav_menu": { + "height": "210px", + "width": "289px" + }, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "186.914px" + }, + "toc_section_display": true, + "toc_window_display": true + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/notebooks/1_LinearMethods.ipynb b/notebooks/1_LinearMethods.ipynb new file mode 100644 index 0000000..af398f6 --- /dev/null +++ b/notebooks/1_LinearMethods.ipynb @@ -0,0 +1,1392 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction and Background\n", + "\n", + "In this notebook we demonstrate how to use learning models to correlate atomic structures with materials properties. We cover two standard linear methods: linear regression (LR) and principal components analysis (PCA). If you are already familiar with LR and PCA, you can continue onto [Principal Covariates Regression](2_PrincipalCovariatesRegression.ipynb).\n", + "\n", + "For each model, we first go step-by-step through the derivation, with equations, embedded links, and citations supplied where useful. Second, we demonstrate a \"Utility Class\" for the models, which can be found in the utilities folder and contains all necessary functions.\n", + "\n", + "The input data is stored in a $n_{samples}\\times n_{features}$ feature matrix $\\mathbf{X}$, and the properties one might want to correlate structural features within a $n_{samples}\\times n_{properties}$ matrix $\\mathbf{Y}$. \n", + "\n", + "Note that, as discussed in [Importing Data](X_ImportingData.ipynb), features and properties are centered and normalized. They have also been split into training and testing sets, denoted ($\\mathbf{X}_{train}$, $\\mathbf{Y}_{train}$) and ($\\mathbf{X}_{test}$, $\\mathbf{Y}_{test}$)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python3\n", + "\n", + "import sys, os\n", + "\n", + "# Maths things\n", + "import numpy as np\n", + "\n", + "# Plotting\n", + "import matplotlib as mpl\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Local Utilities for Notebook\n", + "sys.path.append(\"../\")\n", + "from utilities.general import load_variables, get_stats\n", + "from utilities.plotting import (\n", + " plot_projection,\n", + " plot_regression,\n", + " plot_simple,\n", + " get_cmaps,\n", + " table_from_dict,\n", + " check_mirrors,\n", + ")\n", + "from skcosmo.preprocessing import KernelFlexibleCenterer as KFC\n", + "\n", + "cmaps = get_cmaps()\n", + "plt.style.use(\"../utilities/kernel_pcovr.mplstyle\")\n", + "dbl_fig = (2 * plt.rcParams[\"figure.figsize\"][0], plt.rcParams[\"figure.figsize\"][1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we must load the data. For a step-by-step explanation of this, please see [Importing Data](X_ImportingData.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var_dict = load_variables()\n", + "locals().update(var_dict)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have these variables at our disposal:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x=%who_ls ndarray float64 list int str\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Where $X$ is the feature matrix, $Y$ is the property matrix, $K$ is the kernel matrix, $n_{PC}$ is the number of principal components, and $n_{train}$ and $n_{test}$ are the number of samples in the training sets and test sets." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Principal Component Analysis (PCA)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In principal component analysis (PCA), we seek to reduce the dimensionality of the input data $\\mathbf{X}$ such that the first few dimensions, which are easiest for humans to visualize, account for as much of the [variance](https://en.wikipedia.org/wiki/Variance) in the input data as possible. In this way, we reduce the dimensionality of the input data while retaining and enhancing the natural diversity in the data. In order to accomplish this, the input data are projected onto a subset of the eigenvectors of the covariance matrix of the data, namely the eigenvectors corresponding to the $n_{PCA}$ largest eigenvalues\n", + "[(Pearson, 1901)](http://doi.org/10.1080/14786440109462720), \n", + "[(Hotelling, 1936)](https://www.jstor.org/stable/2333955),\n", + "[(Wikipedia)](https://en.wikipedia.org/wiki/Principal_component_analysis).\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reconstruction Error of a Projection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "PCA is the attempt to find an approximation of the $n_{samples}\\times n_{features}$ feature matrix in terms of a $n_{samples}\\times n_{PCA}$ **latent space** matrix, that we define as $\\mathbf{T} =\\mathbf{X} \\mathbf{P}_{XT}$.\n", + "\n", + "The matrix $\\mathbf{P}_{XT}$ projects between feature space and latent space. The approximation of the feature matrix in terms of latent space coordinates can be written in terms of another linear projection $\\mathbf{P}_{TX}$ as $\\mathbf{X}_{PCA} = \\mathbf{T} \\mathbf{P}_{TX}$. \n", + "\n", + "Requiring that $\\mathbf{X}_{PCA} \\mathbf{P}_{XT} = \\mathbf{T} $ (i.e. that $\\mathbf{X}_{PCA}$ is a perfect approximation of the portion of the feature space that is projected to the latent space) implies that $\\mathbf{P}_{TX}\\mathbf{P}_{XT}=\\mathbf{I}$. Without loss of generality, we take the projection matrix to the latent space to contain orthonormal column vectors, which implies that $\\mathbf{P}_{TX}=\\mathbf{P}_{XT}^T$.\n", + "\n", + "The **reconstruction error** is defined as the difference between the original feature matrix and that approximated using only latent-space information, \n", + "\n", + "\\begin{equation}\n", + "\\ell=\\lVert\\mathbf{X}-\\mathbf{X}_{PCA}\\rVert^2 = \n", + "\\lVert\\mathbf{X}-\\mathbf{X}\\mathbf{P}_{XT}\\mathbf{P}_{XT}^T\\rVert^2\n", + "\\end{equation}\n", + "\n", + "where $\\lVert \\cdot \\rVert$ denotes the [Frobenius norm](http://mathworld.wolfram.com/FrobeniusNorm.html). \n", + "\n", + "Using the orthonormality of the column vectors in $\\mathbf{P}_{XT}$, $\\mathbf{P}_{XT}^T\\mathbf{P}_{XT} = \\mathbf{I}$, and the [matrix relations](https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf):\n", + "\n", + "\\begin{align}\n", + "(1) & \\quad\\left\\lVert\\mathbf{A}\\right\\rVert^2=\\operatorname{Tr}(\\mathbf{A}\\mathbf{A}^T) \\\\\n", + "(2) & \\quad\\left(\\mathbf{I}-\\mathbf{P}_{XT} \\mathbf{P}_{XT}^T\\right)^2 = \\left(\\mathbf{I}-\\mathbf{P}_{XT} \\mathbf{P}_{XT}^T\\right)\\\\\n", + "(3) & \\quad\\operatorname{Tr}(\\mathbf{A B C}) = \\operatorname{Tr}(\\mathbf{B C A})\n", + "\\end{align}\n", + "\n", + "we write\n", + "\n", + "\\begin{equation}\n", + "\\ell=\\operatorname{Tr}\\left(\\mathbf{X} \\left(\\mathbf{I}-\\mathbf{P}_{XT} \\mathbf{P}_{XT}^T\\right) \\mathbf{X}^T \\right).\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Principal Components" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finding the optimal projection to the latent space amounts to minimizing the loss $\\ell$ within the space spanned by the orthogonal basis of the projection matrix. Using another time the fact that the trace of a product is invariant to circular permutations of the factors (Eq. (3) above), and given that $\\operatorname{Tr}\\left(\\mathbf{X}\\mathbf{X}^T\\right)$ is a constant, minimizing $\\ell$ is equivalent to _maximising_ the similarity $\\rho$,\n", + "\n", + "\\begin{equation}\n", + "\\rho=\\operatorname{Tr}\\left(\\mathbf{P}_{XT}^T \\mathbf{X}^T \\mathbf{X} \\mathbf{P}_{XT}\\right).\n", + "\\end{equation}\n", + "\n", + "By recognizing that the equation for $\\mathbf{\\rho}$ can be written in terms of a [Rayleigh Quotient](https://en.wikipedia.org/wiki/Rayleigh_quotient#Special_case_of_covariance_matrices), we note that $\\rho$ is maximised when $\\mathbf{P}_{XT}$ is the matrix built out of the $n_{PCA}$ principal eigenvectors of $\\mathbf{X}^T\\mathbf{X}=\\mathbf{C}$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Covariance and Eigendecomposition\n", + "\n", + "To perform PCA in practice, we first compute the covariance matrix $\\mathbf{C}=\\mathbf{X}^T\\mathbf{X}$ and its eigendecomposition,\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{C} = \\mathbf{U}_C \\mathbf{\\Lambda}_C \\mathbf{U}_C^T,\n", + "\\end{equation}\n", + "\n", + "where $\\mathbf{\\Lambda}_C$ is a matrix with the eigenvalues of $\\mathbf{C}$ on the diagonal in decreasing order (top left to bottom right), and $\\mathbf{U}_C$ is a matrix containing the corresponding eigenvectors as columns.\n", + "\n", + "Note that, when divided by the number of samples, the inner product of the training feature matrices only corresponds to an estimator of the covariance of the data when the feature matrix has been previously centered, which it has been here. [(Wikipedia)](https://en.wikipedia.org/wiki/Covariance#Relationship_to_inner_products)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "C = X_train.T @ X_train\n", + "\n", + "v_C, U_C = np.linalg.eigh(C)\n", + "\n", + "# U_C/v_C are already sorted, but in *increasing* order, so reverse them\n", + "U_C = np.flip(U_C, axis=1)\n", + "v_C = np.flip(v_C, axis=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The computation and sorting of the eigenvalues can also be performed using the `eig_solver(matrix, n_components, tol)` function in `skcosmo/utils`.\n", + "\n", + "Given that we have scaled the features to have unit variance, the magnitude of the eigenvalues, relative to the sum of the eigenvalues, indicates the fraction of the variance associated with each principal component." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.loglog(np.asarray(range(len(v_C))) + 1, v_C / n_train, marker=\"o\")\n", + "plt.title(r\"Size of $n^{th}$ Eigenvalue $v_n$\")\n", + "plt.xlabel(\"n\")\n", + "plt.ylabel(r\"$v_n$\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Low-Dimensional Projection and Approximation\n", + "\n", + "As discussed above, the projection matrix on the PCA latent space corresponds to the orthonormal basis defined by the eigenvectors $\\mathbf{P}_{XT}= \\hat{\\mathbf{U}}_C$, where $\\hat{\\mathbf{U}}_C$ includes only the first $n_{PCA}$ eigenvectors of the covariance ($\\mathbf{U}_C$) as columns and is therefore of size $n_{features}\\times n_{PCA}$. The resulting projection yields the low-dimensional representation,\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{T} = \\mathbf{X}\\hat{\\mathbf{U}}_C,\n", + "\\end{equation}\n", + "\n", + "PCA projections give a simplified representation of the data that may (or may not!) correlate with the property of interest, but should include most of the variance in the feature space." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PXT = U_C[:, :n_PC]\n", + "PTX = PXT.T\n", + "\n", + "T = X_train @ PXT\n", + "\n", + "plot_projection(Y_train, T, **cmaps)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Where the chemical shielding values are denoted by the marker color." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As mentioned previously, the low-dimensional projections can also be used to construct a low-rank approximant of the input space, \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{X}_{PCA} = \\mathbf{T} \\mathbf{P}_{XT}^T = \\mathbf{T}\\hat{\\mathbf{U}}_C^T,\n", + "\\end{equation}\n", + "\n", + "i.e., vectors that have the same dimensionality of the initial features, but actually are just lying in a $n_{PCA}$-dimensional subspace. This yields our original projection equation $\\mathbf{X}_{PCA} = \\mathbf{X}\\mathbf{P}_{XT}\\mathbf{P}_{XT}^T$.\n", + "\n", + "In the plot below, we represent the first two components of the feature space for $\\mathbf{X}$ and $\\mathbf{X}_{PCA}$. Given the high dimensionality of the feature space, the figure cannot quantitatively represent the accuracy of the reconstruction." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X_PCA = T @ PTX" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=dbl_fig)\n", + "plot_simple(X_train, fig=fig, ax=ax[0], title=\"Original Data\", **cmaps)\n", + "plot_simple(\n", + " X_PCA,\n", + " fig=fig,\n", + " ax=ax[1],\n", + " title=\"Best Reconstruction with {} PCs\".format(n_PC),\n", + " **cmaps\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Out-of-sample projection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once PCA has been performed on a **training set** and the eigenvectors have been found, it is possible to find low-dimensional projections (and reconstructed approximants) of other data points (the **test set**), which is approximately optimal in the same sense as the PCA loss." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If $\\mathbf{X}_{test}$ is the feature matrix of the test points, their latent-space projection can be obtained as $\\mathbf{T}_{test}=\\mathbf{X}_{test}\\mathbf{P}_{XT}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_PCA_test = X_test @ PXT\n", + "X_test_PCA = T_PCA_test @ PTX" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot_projection(Y_test, T_PCA_test, **cmaps)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Error and Loss" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We compute errors for the out-of-sample projections based on the same expression for the loss that we used to build the PCA projection for the training set:\n", + "\n", + "\\begin{equation}\n", + "\\ell_{proj}=\\lVert\\mathbf{X}_{test}-\\mathbf{X}_{PCA, test}\\rVert^2 = \\lVert\\mathbf{X}_{test}-\\mathbf{X}_{test}\\mathbf{P}_{XT}\\mathbf{P}_{TX}\\rVert^2 \n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have supplied a utility `get_stats` and a markdown table converter for statistics in `utilities/plotting.py`, which can be called to compare or print statistics:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "table_from_dict([get_stats(x=X_train, y=Y_train, t=T, xr=X_PCA), \n", + " get_stats(x=X_test, y=Y_test, t=T_PCA_test, xr=X_test_PCA)], \n", + " headers = [\"Training\", \"Testing\"], \n", + " title=\"PCA\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you may assume, the error in the projection decreases as we include more components. Here we show the decrease in the approximation error, and show how the first two features in $\\mathbf{X}_{PCA}$ converge to the exact value as the number of selected components approaches the number of features of $\\mathbf{X}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "trials = range(X_test.shape[1])[::5]\n", + "\n", + "n_plot = 4\n", + "fsize = (3 * n_plot, 3)\n", + "\n", + "fig, ax = plt.subplots(1, n_plot + 1, figsize=fsize, sharex=True, sharey=True)\n", + "\n", + "for i, n in enumerate(trials[:: int(len(trials) / n_plot)]):\n", + " n = max(n, 2)\n", + " PXT = U_C[:, :n]\n", + " PTX = PXT.T\n", + "\n", + " X_r = X_test @ PXT @ PTX\n", + "\n", + " ax[i].scatter(X_r[:, 0], X_r[:, 1], c=Y_test[:, 0], linewidth=0.5, edgecolor=\"k\")\n", + " ax[i].set_title(f\"{n} Comp.\")\n", + " ax[i].set_xlabel(r\"$X_1$\")\n", + "\n", + "ax[-1].scatter(X_test[:, 0], X_test[:, 1], c=Y_test[:, 0], linewidth=0.5, edgecolor=\"k\")\n", + "ax[-1].set_title(\"Original Test Data\")\n", + "ax[-1].set_xlabel(r\"$X_1$\")\n", + "ax[0].set_ylabel(r\"$X_2$\")\n", + "\n", + "fig.suptitle(\"Reconstructed Data\", y=1.1)\n", + "fig.subplots_adjust(wspace=0.1)\n", + "\n", + "plt.figure(figsize=fsize)\n", + "plt.loglog(\n", + " trials,\n", + " [\n", + " ((X_test - X_test @ U_C[:, 0:n] @ U_C[:, :n].T) ** 2).mean(axis=0).sum()\n", + " for n in trials\n", + " ],\n", + " \"b-\",\n", + " marker=\"o\",\n", + ")\n", + "plt.title(r\"Representation Error for n Components\")\n", + "plt.xlabel(\"n\")\n", + "plt.ylabel(\"Error\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Classical Multidimensional Scaling (MDS)\n", + "\n", + "A reduction in the dimension of the feature space is also achieved with a different logic that underlies several dimensionality reduction techniques known as [multidimensional scaling (MDS)](https://en.wikipedia.org/wiki/Multidimensional_scaling) [(Torgerson1952)](https://doi.org/10.1007/BF02288916).\n", + "In MDS, the projected feature space is chosen to preserve the _pairwise distances_ of the original space, defining the loss (in MDS known as the $\\textit{strain}$):\n", + "\n", + "\\begin{equation}\n", + " \\ell = \\sum_{j}\\sum_{i0]\n", + "v_K = v_K[v_K>0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The resulting projection is might seem a bit familiar (more on this in Sec. 3.3)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T = U_K[:, :n_MDS] @ np.diagflat(np.sqrt(v_K[:n_MDS]))\n", + "plot_projection(Y_train, T, title=\"Multidimensional Scaling of Training Data\", **cmaps)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Projecting New Data\n", + "\n", + "Given that our latent-space projection is not given as a function of the input space, how do we project new data? First, we reconstruct $\\mathbf{T}$ as a function of $\\mathbf{X}$ by solving for $\\mathbf{P}_{XT}$\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{T} = \\mathbf{X}\\mathbf{P}_{XT}.\n", + "\\end{equation}\n", + "\n", + "We solve by multiplying both sides by the [pseudo-inverse](https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse) of $\\mathbf{X}$\n", + "\n", + "\\begin{equation}\n", + "(\\mathbf{X}^T\\mathbf{X})^{-1}\\mathbf{X}^T\\mathbf{T} = \\mathbf{P}_{XT}.\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PXT = np.linalg.solve(X_train.T @ X_train, X_train.T @ T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".... or as a least-square problem, which is faster and more stable" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PXT = np.linalg.lstsq(X_train, T, rcond=None)[0]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_test = X_test @ PXT\n", + "\n", + "fig, ax = plt.subplots(1, 2, figsize=dbl_fig)\n", + "plot_projection(\n", + " Y_train,\n", + " T,\n", + " fig=fig,\n", + " ax=ax[0],\n", + " title=\"Multidimensional Scaling of Training Data\",\n", + " **cmaps\n", + ")\n", + "plot_projection(\n", + " Y_test,\n", + " T_test,\n", + " fig=fig,\n", + " ax=ax[1],\n", + " title=\"Multidimensional Scaling of Testing Data\",\n", + " **cmaps\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Connection with PCA, and with the SVD of $\\mathbf{X}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can take advantage of the relationship between the eigenvectors and eigenvalues of the covariance $\\mathbf{C} = \\mathbf{X}^T\\mathbf{X}$ and those of the Gram matrix $\\mathbf{K} = \\mathbf{X}\\mathbf{X}^T$.\n", + "\n", + "In fact, it is possible to show that the singular-value decomposition of \n", + "$\\mathbf{X}$ can be written as $\\mathbf{X}=\\mathbf{U_K}\\mathbf{\\Sigma}\\mathbf{U_C}^T$, where $\\mathbf{\\Sigma}$ is a rectangular matrix that is full of zeros, except for having the square root of the non-zero eigenvalues of $\\mathbf{C}$ or $\\mathbf{K}$ (that are the same) on the diagonal.\n", + "\n", + "Then, one sees that \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\hat{U}_K} = \\mathbf{X}\\mathbf{\\hat{U}_C}\\mathbf{\\hat{\\Lambda}_C}^{-1/2}\n", + "\\end{equation}\n", + "\n", + "Where the matrices have shapes:\n", + "\n", + "| Matrix | Shape |\n", + "| :-: | :- |\n", + "|$\\mathbf{\\hat{U}_K}$ | $n_{samples}\\times n_{PCA}$ |\n", + "|$ \\mathbf{X}$ | $n_{samples}\\times n_{features}$ |\n", + "|$\\mathbf{\\hat{U}_C}$ | $n_{features}\\times n_{PCA}$ |\n", + "|$\\mathbf{\\hat{\\Lambda}_C}$ | $n_{PCA}\\times n_{PCA}$ |" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "C = X_train.T @ X_train\n", + "\n", + "v_C, U_C = np.linalg.eigh(C)\n", + "\n", + "# U_C/v_C are already sorted, but in *increasing* order, so reverse them\n", + "U_C = np.flip(U_C, axis=1)\n", + "v_C = np.flip(v_C, axis=0)\n", + "\n", + "U_C = U_C[:,v_C>0]\n", + "v_C = v_C[v_C>0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we see that the largest eigenvalues of $\\mathbf{C}$ and $\\mathbf{K}$ are the same." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.loglog(v_K, \"b-\", marker=\"o\", label=r\"$\\Lambda_K$\")\n", + "plt.loglog(v_C, \"r-\", marker=\"o\", label=r\"$\\Lambda_C$\")\n", + "plt.title(r\"Size of $n^{th}$ Eigenvalue $v_n$\")\n", + "plt.legend()\n", + "plt.xlabel(\"n\")\n", + "plt.ylabel(r\"$v_n$\")\n", + "\n", + "np.linalg.norm(v_K[: v_C.shape[0]] - v_C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using these relationships we obtain MDS\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{T}=\\mathbf{\\hat{U}_K}\\mathbf{\\hat{\\Lambda}_K}^{1/2} = \\mathbf{X}\\mathbf{\\hat{U}_C}\\mathbf{\\hat{\\Lambda}_C}^{-1/2}\\mathbf{\\hat{\\Lambda}_K}^{1/2}= \\mathbf{X}\\hat{\\mathbf{U}}_\\mathbf{C}\n", + "\\end{equation}\n", + "\n", + "which shows that MDS and PCA yield the same projection." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.decomposition import PCA\n", + "\n", + "T = X_test @ PXT\n", + "\n", + "ref = PCA(n_components=n_MDS)\n", + "ref.fit(X_train)\n", + "T_ref = ref.transform(X_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=dbl_fig)\n", + "plot_projection(Y_test, T, fig=fig, ax=ax[0], title=\"Multidimensional Scaling\", **cmaps)\n", + "plot_projection(\n", + " Y_test, check_mirrors(T_ref, T), fig=fig, ax=ax[1], title=\"PCA\", **cmaps\n", + ")\n", + "fig.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Error and Variance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As for the case of PCA, we see how the error decreases as the number of components is increased" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K = X_test @ X_test.T\n", + "ns = range(X_train.shape[1])\n", + "ns = [*ns[:20], *ns[20::10]]\n", + "\n", + "PXT = np.linalg.lstsq(X_train, U_K @ np.diagflat(np.sqrt(v_K)), rcond=None)[0]\n", + "T = X_test @ PXT\n", + "strains = [\n", + " (np.linalg.norm(K) - np.linalg.norm(T[:, :n] @ T[:, :n].T)) / np.linalg.norm(K)\n", + " for n in ns\n", + "]\n", + "\n", + "\n", + "plt.semilogy(ns, strains, marker=\"o\")\n", + "plt.xlabel(\"Number of MDS Components\")\n", + "plt.ylabel(\"Strain\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Linear Regression" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Finding Weights which Minimize Loss\n", + "In [linear regression](https://en.wikipedia.org/wiki/Linear_regression#Estimation_methods) (LR), we aim to find a linear relationship between the features (inputs) and target(s) that minimizes the error of the reconstruction of the target variable. In other words, we seek a model \n", + "\n", + "\\begin{equation}\n", + "\\hat{\\mathbf{Y}} = \\mathbf{X}\\mathbf{P}_{XY},\n", + "\\end{equation}\n", + "\n", + "where the weights $\\mathbf{P}_{XY}$ minimize the loss,\n", + "\n", + "\\begin{align}\n", + "\\ell &= \\left\\lVert \\mathbf{Y} - \\hat{\\mathbf{Y}}\\right\\rVert^2\\\\\n", + "&=\\left\\lVert \\mathbf{Y} - \\mathbf{X}\\mathbf{P}_{XY}\\right\\rVert^2.\n", + "\\end{align}\n", + "\n", + "By minimizing the loss function with respect to $\\mathbf{P}_{XY}$ using the [matrix relations](https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf)\n", + "\n", + "\\begin{align}\n", + "(1) & \\quad\\left\\lVert\\mathbf{A}\\right\\rVert^2=\\operatorname{Tr}(\\mathbf{A}\\mathbf{A}^T) \\\\\n", + "(2) & \\quad (\\mathbf{A}+\\mathbf{B})^T = \\mathbf{A}^T + \\mathbf{B}^T\\\\\n", + "(3) & \\quad \\operatorname{Tr}(\\mathbf{A} + \\mathbf{B}) = \\operatorname{Tr}(\\mathbf{A}) + \\operatorname{Tr}(\\mathbf{B})\\\\\n", + "(4) & \\quad\\operatorname{Tr}(\\mathbf{A B C}) = \\operatorname{Tr}(\\mathbf{B C A})\\\\\n", + "(5) & \\quad \\frac{\\partial}{\\partial\\mathbf{B}} \\operatorname{Tr} (\\mathbf{AB}^T) = \\mathbf{A}\\\\\n", + "(6) & \\quad \\frac{\\partial}{\\partial\\mathbf{B}} \\operatorname{Tr} (\\mathbf{ABB}^T\\mathbf{A}^T) = 2\\mathbf{A}^T\\mathbf{AB},\\\\\n", + "\\end{align}\n", + "\n", + "one obtains\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{XY} = (\\mathbf{X}^T \\mathbf{X} + \\lambda \\mathbf{I})^{-1} \\mathbf{X}^T \\mathbf{Y}.\n", + "\\end{equation}\n", + "\n", + "where $\\lambda$ is the small regularization parameter. When $\\lambda$ is greater than zero, the model is known as *ridge regression*, corresponding to a $\\mathcal{L}^2$ regularization of the loss, i.e. a penalty that is associated with models with large weights\n", + "\n", + "\\begin{equation}\n", + "\\ell = \\left\\lVert \\mathbf{Y} - \\mathbf{X}\\mathbf{P}_{XY}\\right\\rVert^2 + \\lambda \\left\\lVert \\mathbf{P}_{XY}\\right\\rVert^2.\n", + "\\end{equation}\n", + "\n", + "We look at the effect of this regularization parameter in Section 4.3." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "regularization=1e-16\n", + "\n", + "XTX = X_train.T @ X_train + regularization*np.eye(X_train.shape[1])\n", + "PXY = np.linalg.pinv(XTX) @ X_train.T @ Y_train" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The prediction for the train (or test) set $\\mathbf{X}$ is easily obtained multiplying the features by the weights." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Y_lr_train = X_train @ PXY\n", + "Y_lr_test = X_test @ PXY\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "plot_regression(\n", + " Y_train[:, 0],\n", + " Y_lr_train[:, 0],\n", + " title=\"Linear Regression: Training Set\",\n", + " fig=fig,\n", + " ax=axes[0],\n", + " **cmaps\n", + ")\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " Y_lr_test[:, 0],\n", + " title=\"Linear Regression: Testing Set\",\n", + " fig=fig,\n", + " ax=axes[1],\n", + " **cmaps\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Error and Loss\n", + "\n", + "We then go back and calculate the loss functions from earlier." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "table_from_dict(\n", + " [\n", + " get_stats(x=X_train, y=Y_train, yp=Y_lr_train),\n", + " get_stats(x=X_test, y=Y_test, yp=Y_lr_test),\n", + " ],\n", + " headers=[\"Training\", \"Testing\"],\n", + " title=\"LR\",\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Choosing a Regularization\n", + "\n", + "Adding small amounts of noise to data in regressions leads to a more robust model [(Marquardt 1970)](https://www.tandfonline.com/doi/pdf/10.1080/00401706.1970.10488699?casa_token=ZAXSZfnnkGsAAAAA:aji-q3QyTuSZRkBTTx1k_Z4Fnc3YQimEvJHxSQPzfTwoF6ksV0tbXb06TmP08__yalTAkQpbEszS1co), [(Koistinen 1992)](http://papers.nips.cc/paper/459-kernel-regression-and-backpropagation-training-with-noise.pdf), [(Gupta 2017)](https://towardsdatascience.com/regularization-in-machine-learning-76441ddcf99a) by reducing the [overfitting](https://en.wikipedia.org/wiki/Overfitting). \n", + "A similar result is achieved by setting an appropriate value for the parameter $\\lambda$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.linear_model import Ridge\n", + "\n", + "regularizations = np.linspace(-10, 0, 24)\n", + "lrs = [Ridge(alpha=10 ** i) for i in regularizations]\n", + "\n", + "for lr in lrs:\n", + " lr.fit(X_train, Y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ell = np.array(\n", + " [\n", + " np.linalg.norm(Y_test - lr.predict(X_test)) ** 2.0\n", + " / np.linalg.norm(Y_test) ** 2.0\n", + " for lr in lrs\n", + " ]\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even small values of the regularization lead to an increase in the fit of the model." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.semilogx(10 ** regularizations, ell, marker=\"o\")\n", + "\n", + "best_regularization = 10 ** regularizations[ell.argmin()]\n", + "plt.scatter([best_regularization], [ell.min()], c=\"r\", zorder=3)\n", + "\n", + "print(\n", + " f\"The ideal value of $\\lambda$ for this LR (with respect to $R^2$) is {round(best_regularization,4)}.\"\n", + ")\n", + "\n", + "plt.xlabel(r\"$\\lambda$\")\n", + "plt.ylabel(r\"$\\ell$\")\n", + "\n", + "plt.title(r\"Effect of $\\lambda$ on $R^2$ for Linear Regression\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Principal Covariates Regression: Predicting Properties with our Low-Dimensional Projection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It's possible to use the projection determined by PCA to regress properties in a manner similar to linear regression. For this, we determine a weight $\\mathbf{P}_{TY}$ which minimizes\n", + "\n", + "\\begin{equation}\n", + "\\ell = \\lVert\\mathbf{Y}-\\mathbf{T}\\mathbf{P}_{TY}\\rVert^2 + \\lambda \\lVert \\mathbf{P}_{TY} \\rVert^2\n", + "\\end{equation}\n", + "\n", + "Analogous to LR, we find this weight to be:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{TY} = (\\mathbf{T}^T \\mathbf{T} + \\lambda \\mathbf{I})^{-1} \\mathbf{T}^T \\mathbf{Y}.\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pca = PCA(n_components=2)\n", + "pca.fit(X_train)\n", + "T_train = pca.transform(X_train)\n", + "T_test = pca.transform(X_test)\n", + "\n", + "PTY = T_train.T @ T_train + best_regularization * np.eye(T_train.shape[1])\n", + "PTY = np.linalg.pinv(PTY)\n", + "PTY = PTY @ T_train.T @ Y_train\n", + "\n", + "Y_pca = T_test @ PTY\n", + "plot_regression(Y_test[:, 0], Y_pca[:, 0], **cmaps)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Look at how bad that is! As one can imagine, including more components gives a better prediction of the properties." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Next: Combining LR and PCA\n", + "\n", + "In the next notebook, we show how PCA and LR can be combined into a new model. [Continue on -->](2_PrincipalCovariatesRegression.ipynb)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Implementation in `scikit-learn`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The classes covered in this notebook are available through [scikit-learn](scikit-learn.org), more commonly referred to as `sklearn`. Here we'll review the basics of their usage; readers are encouraged to refer to sklearn documentation for further detail." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## PCA" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.decomposition import PCA" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pca = PCA(n_components=n_PC)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `pca.fit(X)` computes the covariance $\\mathbf{C}$ of $\\mathbf{X}$ and internally stores the eigenvectors/values." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pca.fit(X_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `pca.transform(X)` computes and returns the PCA projection $\\mathbf{T}$. We can also use the eigenvectors from the PCA fit to project new data that was not used to originally construct $\\mathbf{P}_{XT}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_test = pca.transform(X_test)\n", + "T_train = pca.transform(X_train)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "plot_projection(\n", + " Y_train, T_train, title=\"Projection of Training Data\", fig=fig, ax=axes[0], **cmaps\n", + ")\n", + "plot_projection(\n", + " Y_test, T_test, title=\"Projection of Testing Data\", fig=fig, ax=axes[1], **cmaps\n", + ")\n", + "\n", + "fig.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `pca.inverse_transform(X)` will provide the approximation of $\\mathbf{X}$ from the latent space projection." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Xr_train = pca.inverse_transform(T_train)\n", + "Xr_test = pca.inverse_transform(T_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "table_from_dict(\n", + " [\n", + " get_stats(x=X_train, y=Y_train, t=T_train, xr=Xr_train),\n", + " get_stats(x=X_test, y=Y_test, t=T_test, xr=Xr_test),\n", + " ],\n", + " headers=[\"Training\", \"Testing\"],\n", + " title=\"PCA\",\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## LR\n", + "\n", + "Unlike PCA, which takes the number of PCA components in the constructor, the linear regression class takes the regularization as a parameter.\n", + "\n", + "In `sklearn`, we can use either linear_models.LinearRegression or linear_models.Ridge to compute a linear regression. However, only Ridge will allow the inclusion of the regularization parameter, by definition." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.linear_model import LinearRegression as LR\n", + "from sklearn.linear_model import Ridge as Ridge" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "lr = Ridge(alpha=best_regularization)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `lr.fit(X,Y)` computes the weights $\\mathbf{P}_{XY}$ and internally stores them." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "lr.fit(X_train, Y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `lr.predict(X)` computes and returns the predicted $\\hat{\\mathbf{Y}}$ values from $\\hat{\\mathbf{Y}}_{LR} = \\mathbf{X}\\mathbf{P}_{XY}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Y_lr_train = lr.predict(X_train)\n", + "Y_lr_test = lr.predict(X_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "plot_regression(\n", + " Y_train[:, 0],\n", + " Y_lr_train[:, 0],\n", + " title=\"Linear Regression of Training Data\",\n", + " fig=fig,\n", + " ax=axes[0],\n", + " **cmaps\n", + ")\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " Y_lr_test[:, 0],\n", + " title=\"Linear Regression of Testing Data\",\n", + " fig=fig,\n", + " ax=axes[1],\n", + " **cmaps\n", + ")\n", + "\n", + "fig.subplots_adjust(wspace=0.25)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "table_from_dict(\n", + " [\n", + " get_stats(x=X_train, y=Y_train, yp=Y_lr_train),\n", + " get_stats(x=X_test, y=Y_test, yp=Y_lr_test),\n", + " ],\n", + " headers=[\"Training\", \"Testing\"],\n", + " title=\"Linear Regression\",\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chemiscope visualization\n", + "\n", + "We can use the `chemiscope_input` function from `utilities/chemiscope.py` to generate an input file for the [chemiscope](https://chemiscope.org/) interactive visualiser. This allows showing how different atomic environments are projected with PCA, or how the predicted properties relate to the structures." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "## Download chemiscope from https://github.com/cosmo-epfl/chemiscope/\n", + "from chemiscope import write_input\n", + "\n", + "import ase\n", + "from ase import io\n", + "import json" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "frames = ase.io.read(\"../datasets/CSD-1000R.xyz\", \":10\")\n", + "\n", + "# We want to have prediction and projection for all the environments\n", + "lr = Ridge(alpha=best_regularization)\n", + "lr.fit(X_train, Y_train)\n", + "Y_lr_full_scaled = lr.predict(X)\n", + "\n", + "# we have to rescale the properties back to be able to compare them to the actual values\n", + "Y_lr_full = Y_scale * Y_lr_full_scaled + Y_center\n", + "\n", + "pca = PCA(n_components=n_PC)\n", + "pca.fit(X_train)\n", + "T = pca.transform(X)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "data = write_input(\n", + " # File to write \n", + " path=\"../CSD-1000R.json\",\n", + " \n", + " # Dataset name\n", + " meta={\"name\": \"CSD-1000R\"},\n", + " \n", + " # Structures in the dataset\n", + " frames=frames,\n", + " \n", + " # projection of the dataset, and properties predictions\n", + " properties={\n", + " **{f\"PCA_{i+1}\": {\"target\": \"atom\", \"values\": T[:, i]} for i in range(n_PC)},\n", + " \"chemical_shieldings\": {\n", + " \"target\": \"atom\",\n", + " \"values\": np.array(Y[:, 0]).reshape(len(Y[:, 0]), 1),\n", + " },\n", + " \"predicted_chemical_shieldings\": {\n", + " \"target\": \"atom\",\n", + " \"values\": np.array(Y_lr_full[:, 0]).reshape(len(Y_lr_full[:, 0]), 1),\n", + " },\n", + " \"atomic_species\": {\n", + " \"target\": \"atom\",\n", + " \"values\": np.concatenate([frame.numbers for frame in frames])\n", + " },\n", + " },\n", + " \n", + " # This should be the same cutoff used to generate the features\n", + " cutoff=3.5,\n", + ")" + ] + }, + { + "attachments": { + "screenshot.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Loading `CSD-1000R.json` at https://chemiscope.org/ should give you something that looks like the screenshot below. On the left, you can change what is displayed to look at PCA projection or LR regressions variables; and on the right, you can see the corresponding atomic environment.\n", + "\n", + "![Chemiscope visualizer screenshot](attachment:screenshot.png)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.11" + }, + "toc": { + "base_numbering": 1, + "nav_menu": { + "height": "210px", + "width": "289px" + }, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "165px" + }, + "toc_section_display": true, + "toc_window_display": true + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/notebooks/2_PrincipalCovariatesRegression.ipynb b/notebooks/2_PrincipalCovariatesRegression.ipynb new file mode 100644 index 0000000..76aa435 --- /dev/null +++ b/notebooks/2_PrincipalCovariatesRegression.ipynb @@ -0,0 +1,1142 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction and Background\n", + "\n", + "In [the previous notebook](1_LinearMethods.ipynb), we showed linear methods for learning atomic structures. In this notebook, we combine these supervised (LR) and unsupervised (PCA) models into one. \n", + "\n", + "As before, for each model, we first go step-by-step through the derivation, with equations, embedded links, and citations supplied where useful. At the end of the notebook, we demonstrate a \"Skcosmo Class\" for the model, which is found in the skcosmo module and contains all necessary functions." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python3\n", + "\n", + "import sys\n", + "\n", + "# Maths things\n", + "import numpy as np\n", + "\n", + "# Plotting\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Local Utilities for Notebook\n", + "sys.path.append(\"../\")\n", + "from utilities.general import load_variables\n", + "from utilities.plotting import (\n", + " plot_projection,\n", + " plot_regression,\n", + " check_mirrors,\n", + " get_cmaps,\n", + ")\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.decomposition import PCA\n", + "\n", + "from skcosmo.pcovr import PCovR\n", + "\n", + "\n", + "cmaps = get_cmaps()\n", + "plt.style.use(\"../utilities/kernel_pcovr.mplstyle\")\n", + "dbl_fig = (2 * plt.rcParams[\"figure.figsize\"][0], plt.rcParams[\"figure.figsize\"][1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we must load the data. For a step-by-step explanation of this, please see [Importing Data](X_ImportingData.ipynb).\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var_dict = load_variables()\n", + "locals().update(var_dict)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Fundamentals of Principal Covariates Regression (PCovR)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constructing the Loss and Similarity Functions\n", + "\n", + "Principal Covariates Regression (PCovR) is a mathematical model that combines principal component analysis and linear regression (or more specifically, \n", + "[principal components regression](https://en.wikipedia.org/wiki/Principal_component_regression)), with a parameter $\\alpha$ that is used to \n", + "tune the relative weight of each of the two tasks and their corresponding losses [(de Jong, 1992)](https://www.doi.org/10.1016/0169-7439(92)80100-I), \n", + "[(Vervloet, 2015)](https://www.doi.org/10.18637/jss.v065.i08). \n", + "\n", + "\\begin{equation}\n", + "\\ell =\n", + "\\alpha {\\left\\lVert \\mathbf{X} - \\mathbf{X}\\mathbf{P}_{XT}\\mathbf{P}_{TX}\\right\\rVert^2}\n", + " +\n", + "(1-\\alpha){\\left\\lVert \\mathbf{Y} - \\mathbf{X}\\mathbf{P}_{XT}\\mathbf{P}_{TY}\\right\\rVert^2}.\n", + "\\end{equation}\n", + "\n", + "It is easier to minimize this by looking for a projection $\\tilde{\\mathbf{T}}$ in a latent space if we require $\\tilde{\\mathbf{T}}^T\\tilde{\\mathbf{T}} = \\mathbf{I}$, i.e. for the the column vectors in $\\tilde{\\mathbf{T}}$ to be orthonormal. \n", + "\n", + "\\begin{equation}\n", + "\\ell =\n", + "\\alpha {\\left\\lVert \\mathbf{X} - \\mathbf{X}\\mathbf{P}_{X\\tilde{T}}\\mathbf{P}_{\\tilde{T}X}\\right\\rVert^2}\n", + " +\n", + "(1-\\alpha){\\left\\lVert \\mathbf{Y} - \\mathbf{X}\\mathbf{P}_{X\\tilde{T}}\\mathbf{P}_{\\tilde{T}Y}\\right\\rVert^2}.\n", + "\\end{equation}\n", + "\n", + "where $\\tilde{\\mathbf{T}}$ is the [whitened](https://en.wikipedia.org/wiki/Whitening_transformation) version of our earlier projection $\\mathbf{T}$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By definition, $\\mathbf{X}\\mathbf{P}_{X\\tilde{T}} = \\tilde{\\mathbf{T}}$. Due to orthonormality, the definition $\\tilde{\\mathbf{T}}\\mathbf{P}_{\\tilde{T}X} = \\mathbf{X}$ implies that $\\mathbf{P}_{\\tilde{T}X} = \\tilde{\\mathbf{T}}^T\n", + " \\mathbf{X}$. Similarly, we find $\\mathbf{P}_{\\tilde{T}Y} = \\tilde{\\mathbf{T}}^T\\mathbf{Y}$, leading to\n", + "\n", + "\\begin{equation}\n", + " \\ell = \\alpha\\lVert\\mathbf{X} - \\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T\\mathbf{X}\\rVert^2 + (1 - \\alpha)\\lVert\\mathbf{Y} - \\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T\\mathbf{Y}\\rVert^2.\n", + "\\end{equation}\n", + "\n", + "**Note**: if the features and the properties were not normalized, it would be advisable to do so here, by dividing the first term by ${\\lVert \\mathbf{X} \\rVert^2}$ and the second by ${\\Vert \\mathbf{Y} \\rVert^2}$, to make sure that the two components are compared on equal footings, without introducing a dependence on their absolute magnitude.\n", + "\n", + "\n", + "Just like with [PCA](1_LinearMethods.ipynb), instead of minimizing loss, we maximize the similarity measure, leading to:\n", + "\n", + "\\begin{equation}\n", + "\\rho = \\operatorname{Tr}\\left(\\alpha \\cdot \\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T\\mathbf{X}\\mathbf{X}^T + \\left(1-\\alpha\\right)\\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T\\mathbf{Y}\\mathbf{Y}^T\\right),\n", + "\\end{equation}\n", + "\n", + "where $\\rho$ is obtained from $\\ell$ by exploiting the invariance of the trace to circular permutations, and dropping constant terms. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Combining X- and Y-Space\n", + "\n", + "An important detail to consider is that we are looking for an approximation of the properties based on a reduced-dimensional latent space that depends only on the $\\mathbf{X}$ features. In order to avoid considering components of the properties that cannot be represented even in the full feature space, we must first project our properties onto $\\mathbf{X}$.\n", + "\n", + "For this, we use the least-squares approximation of $\\mathbf{Y}$ as found in [linear regression](1_LinearMethods.ipynb).\n", + "\n", + "\\begin{equation}\n", + "\\hat{\\mathbf{Y}} = \\mathbf{X}\\mathbf{P}_{XY} = \\mathbf{X}\\left(\\mathbf{X}^T\\mathbf{X} + \\lambda \\mathbf{I}\\right)^{-1}\\mathbf{X}^T \\mathbf{Y}\n", + "\\end{equation}\n", + "\n", + "where $\\lambda$ is the regularization parameter." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "regularization = 1e-6\n", + "\n", + "lr = Ridge(alpha=regularization)\n", + "lr.fit(X_train, Y_train)\n", + "Yhat_train = lr.predict(X_train).reshape((-1, Y_train.shape[1]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When when $\\lambda$ is small, $\\operatorname{Tr}(\\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T\\mathbf{Y}\\mathbf{Y}^T) = \\operatorname{Tr}(\\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T\\mathbf{\\hat{Y}}\\mathbf{\\hat{Y}}^T)$ we write the similarity function as\n", + "\n", + "\\begin{equation}\n", + "\\rho = \\operatorname{Tr}\\left(\\alpha \\cdot \\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T\\mathbf{X}\\mathbf{X}^T + \\left(1-\\alpha\\right)\\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T\\mathbf{\\hat{Y}}\\mathbf{\\hat{Y}}^T\\right),\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Formulations of PCovR\n", + "\n", + "In the similarity measure we have the matrix product $\\mathbf{XX}^T$. This matrix becomes too large to handle if $\\mathbf{X}$ has many more rows (samples) than columns (features). Therefore, two formulations of PCovR have been proposed: one for cases where $n_{samples} \\gg n_{features}$, and the other for cases where $n_{features} \\gg n_{samples}$. The former we refer to as **feature space PCovR** (which is analogous to PCA), and we refer to the latter as **sample space PCovR** (which is analogous to MDS).\n", + "We begin by discussing sample space PCovR." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Sample-Space PCovR" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To compute PCovR using the all $n_{samples}$ components of our Sample Space, we must combine the sample-space kernel ($\\mathbf{X}\\mathbf{X}^T$) and the outer product of the regressed properties ($\\hat{\\mathbf{Y}}\\hat{\\mathbf{Y}}^T$). " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We define the modified [Gram matrix](https://en.wikipedia.org/wiki/Gramian_matrix)\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{\\tilde{K}} = \\alpha {\\mathbf{X} \\mathbf{X}^T}\n", + " + (1 - \\alpha) {\\hat{\\mathbf{Y}} \\hat{\\mathbf{Y}}^T},\n", + "\\end{equation}\n", + "\n", + "Since the trace of the matrix is invariant under cyclic permutation ($\\operatorname{Tr}(\\mathbf{A B C}) = \\operatorname{Tr}(\\mathbf{B C A}) = \\operatorname{Tr}(\\mathbf{C A B})$), we can write \n", + "$\\rho = \\operatorname{Tr}\\left(\\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T\\mathbf{\\tilde{K}}\\right) = \\operatorname{Tr}\\left(\\tilde{\\mathbf{T}}^T\\mathbf{\\tilde{K}}\\tilde{\\mathbf{T}}\\right)$, that is maximized when $\\tilde{\\mathbf{T}}$ contains the principal eigenvectors of $\\mathbf{\\tilde{K}}$ (i.e., the eigenvectors associated with the largest eigenvalues). " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "alpha = 0.5\n", + "\n", + "K_pca = X_train @ X_train.T\n", + "K_lr = Yhat_train @ Yhat_train.T\n", + "\n", + "K = (alpha * K_pca) + (1.0 - alpha) * K_lr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What follows is analogous to multi-dimensional scaling, with $\\mathbf{\\tilde{K}}$ acting as the Gram matrix, modified to weight structural and property correlations. \n", + "First, we diagonalize $\\mathbf{\\tilde{K}}=\\mathbf{U_\\tilde{K}}\\mathbf{\\Lambda_\\tilde{K}}\\mathbf{U_\\tilde{K}}^T$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v_Kt, U_Kt = np.linalg.eigh(K)\n", + "\n", + "# U_Kt/v_Kt are already sorted, but in *increasing* order, so reverse them\n", + "U_Kt = np.flip(U_Kt, axis=1)\n", + "v_Kt = np.flip(v_Kt, axis=0)\n", + "\n", + "U_Kt = U_Kt[:,v_Kt>0]\n", + "v_Kt = v_Kt[v_Kt>0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\tilde{\\mathbf{T}} = \\mathbf{\\hat{U}_\\tilde{K}}$, where $\\mathbf{\\hat{U}_\\tilde{K}}$ contains the first $n_{PCA}$ components of $\\mathbf{U_\\tilde{K}}$.\n", + "\n", + "While it is useful to construct our loss and similarity using the whitened matrix $\\tilde{\\mathbf{T}}$, in doing so we lose information on the relative variance of the different components of the input space. To recover the MDS limit when $\\alpha=1$, we build projections by \"de-whitening\" the principal eigenvectors by multiplying by a factor of $\\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{1/2}$, i.e.\n", + "$\\mathbf{T} = \\tilde{\\mathbf{T}} \\hat{\\mathbf{\\Lambda_\\tilde{K}}}^{1/2} = \\mathbf{X} \\mathbf{P}_{X\\tilde{T}}\\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{1/2}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T = U_Kt[:, :n_PC] @ np.diagflat(np.sqrt(v_Kt[:n_PC]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Determining the Projector $\\mathbf{P}_{XT}$\n", + "\n", + "We also derive a projector from $X$ space directly to the latent space in the form of $\\mathbf{T} = \\mathbf{XP}_{XT}$ (and vice versa). For that we need to solve \n", + "\\begin{equation}\n", + "\\mathbf{X}\\mathbf{P}_{XT} = \\tilde{\\mathbf{T}} \\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{1/2} = \\mathbf{\\tilde{K}}\\mathbf{\\hat{U}_\\tilde{K}}\\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{-1/2}\n", + "\\end{equation}\n", + "\n", + "where we used the fact that $\\tilde{\\mathbf{T}}$ is built from columns of $\\mathbf{\\hat{U}_{\\tilde{K}}}$.\n", + "Writing explicitly $\\mathbf{\\tilde{K}}$ and $\\hat{\\mathbf{Y}}$,\n", + "\n", + "\\begin{align}\n", + "\\mathbf{X}\\mathbf{P}_{XT} &= \\left( \n", + "\\alpha \\color{red}{\\mathbf{X}} \\mathbf{X}^T\n", + "+ (1 - \\alpha) \n", + "\\color{red}{\\mathbf{X}}\\left(\\mathbf{X}^T\\mathbf{X}\\right)^{-1}\\mathbf{X}^T \\mathbf{Y}\n", + "\\hat{\\mathbf{Y}}^T\n", + "\\right) \\mathbf{\\hat{U}_\\tilde{K}}\\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{-1/2} \\\\\n", + "&= \\color{red}{\\mathbf{X}} \\left( \n", + "\\alpha \\mathbf{X}^T\n", + "+ (1 - \\alpha) \n", + "\\left(\\mathbf{X}^T\\mathbf{X}\\right)^{-1}\\mathbf{X}^T \\mathbf{Y}\n", + "\\hat{\\mathbf{Y}}^T\n", + "\\right) \\mathbf{\\hat{U}_\\tilde{K}} \\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{-1/2}.\n", + "\\end{align}\n", + "\n", + "we obtain the projector from feature to latent space $\\mathbf{P}_{XT}$ explicitly \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{XT} = \\left(\n", + "\\alpha{\\mathbf{X}^T}\n", + "+ (1 - \\alpha)\n", + "\\left(\\mathbf{X}^T\\mathbf{X}\\right)^{-1}\\mathbf{X}^T \\mathbf{Y}\n", + "\\hat{\\mathbf{Y}}^T\n", + "\\right) \\mathbf{\\hat{U}_\\tilde{K}}\\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{-1/2}.\n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P_lr = X_train.T @ X_train + np.eye(X_train.shape[1]) * regularization\n", + "P_lr = np.linalg.pinv(P_lr)\n", + "P_lr = (P_lr @ X_train.T @ Y_train).reshape((-1, Y_train.shape[1])) @ Yhat_train.T\n", + "\n", + "P_pca = X_train.T\n", + "\n", + "P = (alpha * P_pca) + (1.0 - alpha) * P_lr\n", + "PXT = P @ U_Kt[:, :n_PC] @ np.diag(1 / np.sqrt(v_Kt[:n_PC]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We verify that $\\mathbf{T}\\approx \\mathbf{X}\\mathbf{P}_{XT}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(np.linalg.norm(X_train @ PXT - T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And plot the projection. Note how the position of points in latent space correlates much better with the properties than they do in PCA latent space." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_pcovr_test = X_test @ PXT" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "ref = PCA(n_components=n_PC)\n", + "ref.fit(X_train)\n", + "t_ref = ref.transform(X_test)\n", + "\n", + "plot_projection(\n", + " Y_test,\n", + " check_mirrors(T_pcovr_test, t_ref),\n", + " fig=fig,\n", + " ax=axes[0],\n", + " title=r\"PCovR (Sample Space, $\\alpha={}$)\".format(alpha),\n", + " **cmaps\n", + ")\n", + "plot_projection(Y_test, t_ref, fig=fig, ax=axes[1], title=\"PCA\", **cmaps)\n", + "\n", + "fig.suptitle(\n", + " r\"These are not the same unless $\\alpha = 1.0.$\",\n", + " y=0.0,\n", + " fontsize=plt.rcParams[\"font.size\"] + 6,\n", + ")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The image on the left (PCovR) is the 2D projected that is weighted by a factor of (1-$\\alpha$) towards those axes which best discern the property vector $\\mathbf{Y}$. Note how the color of the points changes with the position of the points.\n", + "\n", + "The image to the right (PCA) is the 2D projection which best preserves the variance of the feature matrix $\\mathbf{X}$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Predicting the Properties\n", + "Now how do we get the weights to predict the properties? Basically we need to \n", + "solve the linear regression problem in the projected space, i.e., solve for the weights $\\mathbf{P}_{TY}$ such that:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{Y_{PCovR}} = \\mathbf{T} \\mathbf{P}_{TY} = \\mathbf{X} \\mathbf{P}_{XT} \\mathbf{P}_{TY}. \n", + "\\end{equation}\n", + "\n", + "We determine the regression parameter $\\mathbf{P}_{TY}$ by applying the usual LR expression using the projections $\\mathbf{T}$.\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{TY} = (\\mathbf{T}^T\\mathbf{T})^{-1}\\mathbf{T}^T\\mathbf{Y} = \n", + " \\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{-1}\\mathbf{T}^T\\mathbf{Y},\n", + "\\end{equation}\n", + "\n", + "Where the factor of $\\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{-1}$ arises from the fact that\n", + "$\\mathbf{T}^T\\mathbf{T}=\\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{1/2}\\mathbf{\\hat{U}_\\tilde{K}}^T\\mathbf{\\hat{U}_\\tilde{K}}\\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}^{1/2}=\n", + "\\hat{\\mathbf{\\Lambda}}_\\mathbf{\\tilde{K}}$. Note that $\\mathbf{Y}$ corresponds to the property vector for the train set.\n", + "\n", + "**Note:** this differs from the expression in [2015 paper on PCovR](https://www.doi.org/10.18637/jss.v065.i08), which uses the whitened PCA projections $\\tilde{\\mathbf{T}}=\\mathbf{U_\\tilde{K}}$ with variance 1. Here, we construct our PCA projections without this normalization, so we must divide by the eigenvalue matrix to compute regression weights." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PTY = np.diagflat(1 / (v_Kt[:n_PC])) @ T.T @ Y_train\n", + "Y_pcovr_test = X_test @ PXT @ PTY\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "ref_lr = Ridge(alpha=regularization)\n", + "ref_lr.fit(X_train, Y_train)\n", + "yref = lr.predict(X_test)\n", + "\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " Y_pcovr_test[:, 0],\n", + " fig=fig,\n", + " ax=axes[0],\n", + " title=r\"PCovR (Sample Space, $\\alpha={}$)\".format(alpha),\n", + " **cmaps\n", + ")\n", + "plot_regression(Y_test[:, 0], yref[:, 0], fig=fig, ax=axes[1], title=\"LR\", **cmaps)\n", + "\n", + "fig.suptitle(\n", + " r\"These become more dissimilar as $\\alpha \\to 1.0.$\",\n", + " y=0.01,\n", + " fontsize=plt.rcParams[\"font.size\"] + 6,\n", + ")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Feature-Space PCovR" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Similarity Function in Feature-Space\n", + "\n", + "In the case where the number of samples is greater than the number of features ($n_{samples} >> n_{features}$), computing the eigenvectors of $\\mathbf{\\tilde{K}}$ may be undesirable. In this case, we instead compute the eigenvectors of the $n_{features} \\times n_{features}$ matrix, i.e., the feature space. In order to formulate a feature-space version of PCovR we again consider how PCovR maximises the similarity ($\\rho$) between our projection and the original data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\\begin{equation}\n", + "\\rho = \\operatorname{Tr}\\left(\\tilde{\\mathbf{T}}^T\\mathbf{\\tilde{K}}\\tilde{\\mathbf{T}}\\right)\n", + "\\end{equation}\n", + "\n", + "and rewrite it in terms of the decomposition $\\tilde{\\mathbf{T}} = \\mathbf{X}\\mathbf{P}_{X\\tilde{T}}$\n", + "\n", + "\\begin{align}\n", + "\\rho &= \\operatorname{Tr}\\left(\\mathbf{P}_{X\\tilde{T}}^T\\mathbf{X}^T\\mathbf{\\tilde{K}}\\mathbf{X}\\mathbf{P}_{X\\tilde{T}}\\right)\n", + "\\end{align}\n", + "\n", + "$\\mathbf{X}^T\\mathbf{\\tilde{K}}\\mathbf{X}$ is a $n_{features}\\times n_{features}$ matrix, so why not solve for $\\mathbf{P}_{X\\tilde{T}}$ through an eigendecomposition of $\\mathbf{X}^T\\mathbf{\\tilde{K}}\\mathbf{X}$?\n", + "\n", + "For this trick to work, we need to work with an matrix whose column vectors are orthonormal, but $\\mathbf{P}_{X\\tilde{T}}^T\\mathbf{P}_{X\\tilde{T}} \\neq \\mathbf{I}$! However, \n", + "\\begin{equation}\n", + "\\mathbf{P}_{X\\tilde{T}}^T\\mathbf{C}\\mathbf{P}_{X\\tilde{T}} = \\mathbf{P}_{X\\tilde{T}}^T\\mathbf{X}^T\\mathbf{X}\\mathbf{P}_{X\\tilde{T}} = \\tilde{\\mathbf{T}}^T\\tilde{\\mathbf{T}} = \\mathbf{I}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "C = X_train.T @ X_train\n", + "\n", + "PXV = PXT @ np.diagflat(1.0/np.sqrt(v_Kt[:n_PC]))\n", + "\n", + "print(np.linalg.norm(PXV.T @ C @ PXV - \n", + " np.eye(PXV.shape[1])))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Therefore $\\mathbf{C}^{1/2}\\mathbf{P}_{X\\tilde{T}}$ contains orthonormal column vectors! \n", + "\n", + "We calculate $\\mathbf{C}^{1/2}$ and $\\mathbf{C}^{-1/2}$ using the eigendecomposition of $\\mathbf{C}$, given\n", + "\n", + "\\begin{align}\n", + "& \\mathbf{C}^{1/2} = \\mathbf{U}_C \\mathbf{\\Lambda}^{1/2} \\mathbf{U}_C^T\\\\\n", + "& \\mathbf{C}^{-1/2} = \\mathbf{U}_C \\mathbf{\\Lambda}^{-1/2} \\mathbf{U}_C^T\\\\\n", + "\\end{align}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v_C, U_C = np.linalg.eigh(C)\n", + "\n", + "# U_C/v_C are already sorted, but in *increasing* order, so reverse them\n", + "U_C = np.flip(U_C, axis=1)\n", + "v_C = np.flip(v_C, axis=0)\n", + "\n", + "U_C = U_C[:,v_C>0]\n", + "v_C = v_C[v_C>0]\n", + "\n", + "Csqrt = U_C @ np.diagflat(np.sqrt(v_C)) @ U_C.T\n", + "iCsqrt = U_C @ np.diagflat(1.0 / np.sqrt(v_C)) @ U_C.T" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then write\n", + "\n", + "\\begin{align}\n", + "\\rho &= \\operatorname{Tr}\\left(\\mathbf{P}_{X\\tilde{T}}^T\\mathbf{C}^{1/2}\\mathbf{C}^{-1/2}\\mathbf{X}^T\\mathbf{\\tilde{K}}\\mathbf{X}\\mathbf{C}^{-1/2}\\mathbf{C}^{1/2}\\mathbf{P}_{X\\tilde{T}}\\right)\n", + "\\end{align}\n", + "\n", + "and introduce a modified covariance matrix $\\tilde{\\mathbf{C}}$\n", + "\n", + "\\begin{equation}\n", + "\\tilde{\\mathbf{C}} = \\mathbf{C}^{-1/2}\\mathbf{X}^T\\mathbf{\\tilde{K}}\\mathbf{X}\\mathbf{C}^{-1/2}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Ct = iCsqrt @ X_train.T\n", + "Ct = Ct @ K @ Ct.T\n", + "\n", + "v_Ct, U_Ct = np.linalg.eigh(Ct)\n", + "U_Ct = np.flip(U_Ct, axis=1)\n", + "v_Ct = np.flip(v_Ct, axis=0)\n", + "\n", + "U_Ct = U_Ct[:,v_Ct>0]\n", + "v_Ct = v_Ct[v_Ct>0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We verify that $\\mathbf{\\tilde{C}}$ and $\\mathbf{\\tilde{K}}$ have the same eigenvalues, as they're connected to each other by the same relation that links the covariance and the Gram matrix. As such, the blue and red lines in the figure below should be indistinguishable." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1)\n", + "ax.set_yscale(\"log\")\n", + "ax.plot(v_Kt, marker=\"o\", c=\"b\", label=r\"$\\mathbf{\\tilde{K}}$\")\n", + "ax.plot(v_Ct, marker=\"o\", c=\"r\", label=r\"$\\mathbf{\\tilde{C}}$\")\n", + "ax.set_xlabel(\"n\")\n", + "ax.set_ylabel(\"$\\lambda_n$\")\n", + "ax.set_title(\n", + " r\"Eigenvalues of $\\mathbf{\\tilde{C}}$ and $\\mathbf{\\tilde{K}}$ as a function of n\"\n", + ")\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computing the Projectors\n", + "\n", + "The similarity is maximized when the orthonormal column vectors in matrix $\\mathbf{C}^{1/2}\\mathbf{P}_{X\\tilde{T}}$ match the principal eigenvalues of $\\mathbf{\\tilde{C}}$, i.e. $\\mathbf{P}_{X\\tilde{T}} = \\mathbf{C}^{-1/2}\\hat{\\mathbf{U}}_{\\mathbf{\\tilde{C}}}$. Similar to [PCA](1_LinearMethods.ipynb), we require that $\\mathbf{X}_{PcovR} = \\mathbf{\\tilde{T}}\\mathbf{P}_{\\tilde{T}X}$ approximates the portion of the feature space projected to the potential space, i.e., $\\mathbf{X}_{PcovR} \\mathbf{P}_{X\\tilde{T}} = \\mathbf{\\tilde{T}} $, which implies that $\\mathbf{P}_{\\tilde{T}X}\\mathbf{P}_{X\\tilde{T}}=\\mathbf{I}$ and $\\mathbf{P}_{\\tilde{T}X}=\\hat{\\mathbf{U}}_{\\mathbf{\\tilde{C}}}^T \\mathbf{C}^{1/2}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PXV = iCsqrt @ U_Ct[:, :n_PC]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In general\n", + "$\\mathbf{P}_{X\\tilde{T}} \\mathbf{P}_{\\tilde{T}X} = \\mathbf{C}^{-1/2}\\hat{\\mathbf{U}}_{\\mathbf{\\tilde{C}}}\\hat{\\mathbf{U}}_{\\mathbf{\\tilde{C}}}^T \\mathbf{C}^{1/2}$ is not a symmetric matrix, and so it is not possible to define an $\\mathbf{P}_{XT}$ such that $\\mathbf{P}_{TX}=\\mathbf{P}_{XT}^{T}$. \n", + "Consistently with the case of sample-space PCovR, we define \n", + "\n", + "\\begin{equation}\n", + "\\begin{split}\n", + "\\mathbf{P}_{XT} =& \\mathbf{C}^{-1/2}\\hat{\\mathbf{U}}_{\\mathbf{\\tilde{C}}}\\hat{\\mathbf{\\Lambda}}_{\\mathbf{\\tilde{C}}}^{1/2} \\\\\n", + "\\mathbf{P}_{TX} =& \\hat{\\mathbf{\\Lambda}}_{\\mathbf{\\tilde{C}}}^{-1/2} \\hat{\\mathbf{U}}_{\\mathbf{\\tilde{C}}}^T \\mathbf{C}^{1/2} \\\\\n", + "\\mathbf{P}_{TY} =&(\\mathbf{T}^T\\mathbf{T})^{-1}\\mathbf{T}^T\\mathbf{Y} \\\\\n", + " =&\\hat{\\mathbf{\\Lambda}}_{\\mathbf{\\tilde{C}}}^{-1/2} \\hat{\\mathbf{U}}_{\\mathbf{\\tilde{C}}}^T \\mathbf{C}^{-1/2} \\mathbf{X}^T \\mathbf{Y} \\\\\n", + "\\end{split}\n", + "\\label{eq:pcovr-projectors}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PXT = PXV @ np.diagflat(np.sqrt(v_Ct[:n_PC]))\n", + "PTX = np.diagflat(1.0 / np.sqrt(v_Ct[:n_PC])) @ U_Ct[:, :n_PC].T, Csqrt\n", + "PTY = (\n", + " np.diagflat(1.0 / np.sqrt(v_Ct[:n_PC]))\n", + " @ U_Ct[:, :n_PC].T\n", + " @ iCsqrt\n", + " @ X_train.T\n", + " @ Y_train\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Projecting the Data\n", + "Projecting and regressing in feature-space PCovR proceeds similarly to Sample Space PCovR:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_fspcovr_test = X_test @ PXT\n", + "\n", + "Y_fspcovr_test = T_fspcovr_test @ PTY" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We compare with the Sample Space PCovR and see that the results are essentially identical:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "ref = PCovR(mixing=alpha, n_components=2, space=\"sample\")\n", + "ref.fit(X_train, Y_train)\n", + "tref = ref.transform(X_test)\n", + "yref = ref.predict(X_test)\n", + "xref = ref.inverse_transform(tref)\n", + "\n", + "plot_projection(\n", + " Y_test,\n", + " check_mirrors(T_fspcovr_test, tref),\n", + " fig=fig,\n", + " ax=axes[0],\n", + " title=\"PCovR (Feature Space)\",\n", + " **cmaps\n", + ")\n", + "plot_projection(\n", + " Y_test, tref, fig=fig, ax=axes[1], title=\"PCovR (Sample Space)\", **cmaps\n", + ")\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " Y_fspcovr_test[:, 0],\n", + " fig=fig,\n", + " ax=axes[0],\n", + " title=r\"PCovR (Feature Space, $\\alpha={}$)\".format(alpha),\n", + " cbar=False,\n", + " **cmaps\n", + ")\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " yref[:, 0],\n", + " fig=fig,\n", + " ax=axes[1],\n", + " title=r\"PCovR (Sample Space, $\\alpha={}$)\".format(alpha),\n", + " cbar=False,\n", + " **cmaps\n", + ")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you find a mirror reflection between the upper-left and upper-right subfigures, it is because the signs of the eigenvectors are not fixed. Their second principal components $PC_2$ may have the opposite signs." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PCovR Performance\n", + "\n", + "To determine the sensitivity of PCovR to the value of $\\alpha$ and the number of PCA components, it is instructive to visualize the dependence of the projections and to the different components of the loss on these parameters. We do so using the skcosmo classes." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "n_alphas = 11\n", + "alphas = np.linspace(0.0, 1.0, n_alphas)\n", + "components = np.arange(0, 5, 1, dtype=np.int)[2::]\n", + "n_components = components.size\n", + "\n", + "pcovr_calculators = np.array(\n", + " [\n", + " [PCovR(mixing=a, n_components=c, space=\"feature\") for a in alphas]\n", + " for c in components\n", + " ]\n", + ")\n", + "\n", + "for cdx, c in enumerate(components):\n", + " for adx, a in enumerate(alphas):\n", + " pcovr_calculators[cdx][adx].fit(X_train, Y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison of PCovR Projections and Regressions\n", + "\n", + "To use PCovR, it's useful to get an intuitive sense for the change in the projections and regressions across $\\alpha$, and see the trade-off. Below we plot both projections and regressions for $n_{\\alpha}$ different values of $\\alpha$.\n", + "\n", + "**Note**: Remember that in PCA-like projection, sometimes projections of the same data may be related by mirror reflection. For these projections, this may also occur." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "n_plots = int(n_alphas ** 0.5)\n", + "scale = 3\n", + "\n", + "t_ref = pcovr_calculators[0][-3].transform(X_test)\n", + "y_ref = pcovr_calculators[0][-3].predict(X_test)\n", + "x_ref = pcovr_calculators[0][-3].inverse_transform(tref)\n", + "\n", + "pfig, pax = plt.subplots(\n", + " n_plots,\n", + " int(np.ceil(n_alphas / n_plots)),\n", + " figsize=(\n", + " scale * int(np.ceil(n_alphas / n_plots)),\n", + " scale * n_plots,\n", + " ),\n", + ")\n", + "\n", + "rfig, rax = plt.subplots(\n", + " n_plots,\n", + " int(np.ceil(n_alphas / n_plots)),\n", + " figsize=(\n", + " scale * int(np.ceil(n_alphas / n_plots)),\n", + " scale * n_plots,\n", + " ),\n", + ")\n", + "for p, r, pcovr in zip(pax.flatten(), rax.flatten(), pcovr_calculators[0]):\n", + "\n", + " t = pcovr.transform(X_test)\n", + " y = pcovr.predict(X_test)\n", + " x = pcovr.inverse_transform(t)\n", + "\n", + " plot_projection(\n", + " Y_test, check_mirrors(t, t_ref), fig=pfig, ax=p, alpha=1.0, s=20, **cmaps\n", + " )\n", + "\n", + " plot_regression(\n", + " Y_test[:, 0],\n", + " y[:, 0],\n", + " fig=pfig,\n", + " ax=r,\n", + " cbar=False,\n", + " vmin=0,\n", + " vmax=5,\n", + " alpha=1.0,\n", + " s=20,\n", + " **cmaps,\n", + " )\n", + "\n", + " p.set_title(r\"$\\alpha=$\" + str(round(pcovr.mixing, 3)))\n", + " r.set_title(r\"$\\alpha=$\" + str(round(pcovr.mixing, 3)))\n", + "\n", + "\n", + "for p, r in zip(pax.flatten()[n_alphas:], rax.flatten()[n_alphas:]):\n", + " p.axis(\"off\")\n", + " r.axis(\"off\")\n", + "\n", + "pfig.subplots_adjust(wspace=0.6, hspace=0.6)\n", + "pfig.suptitle(r\"Projections across $\\alpha$\")\n", + "rfig.subplots_adjust(wspace=0.6, hspace=0.6)\n", + "rfig.suptitle(r\"Regressions across $\\alpha$\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison of PCovR Loss Terms\n", + "To get a more quantitative assessment of the behavior of PCovR as a function of $\\alpha$, we plot the errors from the linear regression and PCA terms of the PCovR. The linear regression loss is calculated as the RMSE between our known and predicted properties\n", + "\n", + "\\begin{align}\n", + "\\ell_{regr} = \n", + " {\\left\\lVert \\mathbf{Y} - \\mathbf{X}\\mathbf{P}_{XT}\\mathbf{P}_{TY}\\right\\rVert^2} \\\\\n", + "\\end{align}\n", + "\n", + "and the variance loss from the reconstruction of the input features\n", + "\n", + "\\begin{equation}\n", + "\\ell_{proj}=\n", + " {\\left\\lVert \\mathbf{X} - \\mathbf{X}\\mathbf{P}_{XT}\\mathbf{P}_{TX}\\right\\rVert^2}. \\\\\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "L_pca = np.zeros((n_components, n_alphas))\n", + "L_lr = np.zeros((n_components, n_alphas))\n", + "\n", + "for cdx, c in enumerate(components):\n", + " for adx, a in enumerate(alphas):\n", + " calculator = pcovr_calculators[cdx][adx]\n", + " \n", + " # TODO: remove except when score is merged into skcosmo\n", + " try:\n", + " L_pca[cdx, adx], L_lr[cdx, adx] = calculator.score(X_test, Y_test)\n", + " except:\n", + " xr = calculator.inverse_transform(calculator.transform(X_test))\n", + " yp = calculator.predict(X_test)\n", + "\n", + " L_pca[cdx, adx] = (\n", + " np.linalg.norm(X_test - xr) ** 2.0 / np.linalg.norm(X_test) ** 2.0\n", + " )\n", + " L_lr[cdx, adx] = (\n", + " np.linalg.norm(Y_test - yp) ** 2.0 / np.linalg.norm(Y_test) ** 2.0\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, [axsLR, axsPCA] = plt.subplots(1, 2, figsize=dbl_fig, sharex=True)\n", + "\n", + "for cdx, c in enumerate(components):\n", + " axsLR.plot(alphas, L_lr[cdx, :], marker=\"o\", label=\"{:d} PCs\".format(c))\n", + " axsPCA.plot(alphas, L_pca[cdx, :], marker=\"o\", label=\"{:d} PCs\".format(c))\n", + "\n", + "axsLR.set_ylabel(r\"$\\ell_{LR}$\")\n", + "axsLR.set_xlabel(r\"$\\alpha$\")\n", + "axsPCA.set_ylabel(r\"$\\ell_{PCA}$\")\n", + "axsPCA.set_xlabel(r\"$\\alpha$\")\n", + "\n", + "fig.subplots_adjust(wspace=0.3)\n", + "axsLR.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Given that the two terms vary in opposite directions (which is obvious, since $\\alpha$ changes the way they contribute to the total loss), choosing a value implies making a tradeoff between LR and PCA performance. The least biased choice is then to look for the value that minimizes the (non-weighted) sum of the PCA and LR terms. \n", + "\n", + "This is the optimal choice if one gives equal importance to the two tasks, and is (roughly) equivalent to plotting a $\\lambda$ curve -- i.e. a plot of $\\ell_{LR}$ against $\\ell_{PCA}$ for different values of the mixing $\\alpha$ -- and looking for the elbow of the curve, that gives the value at which the improvement in the accuracy of one of the losses balance the degradation of the other." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = plt.figure(figsize=dbl_fig)\n", + "axsLoss = fig.add_subplot(1, 2, 1)\n", + "axsSum = fig.add_subplot(1, 2, 2)\n", + "\n", + "for cdx, c in enumerate(components):\n", + " axsLoss.loglog(L_pca[cdx, :], L_lr[cdx, :], marker=\"o\", label=\"{:d} PCs\".format(c))\n", + "\n", + "axsLoss.set_xlabel(r\"$\\ell_{PCA}$\")\n", + "axsLoss.set_ylabel(r\"$\\ell_{LR}$\")\n", + "axsLoss.legend()\n", + "\n", + "for cdx, c in enumerate(components):\n", + " loss_sum = L_lr[cdx, :] + L_pca[cdx, :]\n", + " axsSum.semilogy(alphas, loss_sum, marker=\"o\", label=\"{:d} PCs\".format(c))\n", + " print(\"Optimal alpha for {:d} PCs = {:.2f}\".format(c, alphas[np.argmin(loss_sum)]))\n", + "\n", + "axsSum.set_xlabel(r\"$\\alpha$\")\n", + "axsSum.set_ylabel(r\"$\\ell_{LR} + \\ell_{PCA}$\")\n", + "\n", + "fig.subplots_adjust(wspace=0.5, hspace=0.3)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Next: Kernel Methods\n", + "\n", + "Continue on to the [next notebook](3_KernelMethods.ipynb)!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Implementation in `skcosmo`\n", + "\n", + "Classes from the skcosmo module enable computing PCovR with a scikit.learn-like syntax. \n", + "\n", + "The PCovR class takes a parameter `space` to designate whether projectors should be computed in structure or feature space. If the parameter is not supplied, the class detects the shape of the input data when `pcovr.fit(X,Y)` is called and chooses the most efficient method." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from skcosmo.pcovr import PCovR" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***To avoid confusion with scikit-learn naming conventions, where `alpha` is a regularization parameter, the keyword `mixing` is used to specify the PCovR $\\alpha$.***" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "alpha = 0.5\n", + "pcovr = PCovR(mixing=alpha, n_components=2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pcovr.fit(X_train, Y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`pcovr.transform(X)` returns the projection $\\mathbf{T}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "t = pcovr.transform(X_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`pcovr.predict(X)` returns the regressed properties $\\mathbf{Y}_p$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "y = pcovr.predict(X_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`pcovr.predict(T)` returns the reconstructed input data $\\mathbf{X}_r$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x = pcovr.inverse_transform(t)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=dbl_fig)\n", + "plot_projection(\n", + " Y_test, t, title=r\"PCovR ($\\alpha$={})\".format(alpha), fig=fig, ax=ax[0], **cmaps\n", + ")\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " y[:, 0],\n", + " title=r\"PCovR ($\\alpha$={})\".format(alpha),\n", + " fig=fig,\n", + " ax=ax[1],\n", + " **cmaps\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.11" + }, + "toc": { + "base_numbering": 1, + "nav_menu": { + "height": "210px", + "width": "289px" + }, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "186.934px" + }, + "toc_section_display": true, + "toc_window_display": true + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/notebooks/3_KernelMethods.ipynb b/notebooks/3_KernelMethods.ipynb new file mode 100644 index 0000000..2b80d02 --- /dev/null +++ b/notebooks/3_KernelMethods.ipynb @@ -0,0 +1,1597 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction and Background\n", + "\n", + "In this notebook, we introduce kernel-based versions of the models covered in the [Linear Methods](1_LinearMethods.ipynb) and [PCovR](2_PrincipalCovariatesRegression.ipynb) notebooks.\n", + "\n", + "As always, for each model, we first go step-by-step through the derivation, with equations, embedded links, and citations supplied where useful. Second, we will employ a \"Sklearn/Skcosmo Class\" for the models, which can be found in the skcosmo/sklearn mudule and contains all necessary functions.\n", + "\n", + "**Note**: To display values of variables in the markdown cells, you should [enable the jupyter contrib nbextension](https://stackoverflow.com/questions/52812231/print-variable-in-jupyter-notebook-markdown-cell-python)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python3\n", + "\n", + "import sys\n", + "\n", + "# Maths things\n", + "import numpy as np\n", + "\n", + "# Plotting\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Local Utilities for Notebook\n", + "sys.path.append(\"../\")\n", + "from utilities.general import load_variables, sorted_eig, get_stats\n", + "from utilities.plotting import (\n", + " plot_projection,\n", + " plot_regression,\n", + " check_mirrors,\n", + " get_cmaps,\n", + " table_from_dict,\n", + ")\n", + "from sklearn.metrics.pairwise import linear_kernel, rbf_kernel\n", + "from sklearn.decomposition import PCA, KernelPCA\n", + "from sklearn.linear_model import Ridge\n", + "from sklearn.kernel_ridge import KernelRidge\n", + "from functools import partial\n", + "\n", + "from skcosmo.pcovr import KPCovR\n", + "from skcosmo.preprocessing import KernelFlexibleCenterer\n", + "\n", + "cmaps = get_cmaps()\n", + "plt.style.use(\"../utilities/kernel_pcovr.mplstyle\")\n", + "dbl_fig = (2 * plt.rcParams[\"figure.figsize\"][0], plt.rcParams[\"figure.figsize\"][1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we must load the data. For a step-by-step explanation of this, please see [Importing Data](X_ImportingData.ipynb). As mentioned in the [foreword notebook](0_Foreword.ipynb), pre-computed features should be downloaded from [here](https://www.dropbox.com/s/itokckbbkvxaqsk/precomputed.npz?dl=0) and the file `precomputed.npz` should be copied to the `datasets/` folder." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var_dict = load_variables()\n", + "locals().update(var_dict)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Constructing Kernels\n", + "\n", + "## The Kernel Trick\n", + "\n", + "Many kernel methods are similar to linear methods,\n", + "except that we take advantage of the [**kernel trick**](https://en.wikipedia.org/wiki/Kernel_method#Mathematics:_the_kernel_trick) in order to \n", + "introduce a non-linear transformation of the feature space.\n", + "\n", + "The kernel trick consists in introducing a [**positive definite**](https://en.wikipedia.org/wiki/Positive-definite_kernel) function of pairs of samples, $ k(\\mathbf{x}, \\mathbf{x}^{\\prime})$, that defines implicitly a higher (possibly infinite) dimensional feature space, in which one can apply linear analysis methods. \n", + "\n", + "There are [many](https://en.wikipedia.org/wiki/Positive-definite_kernel#Examples_of_p.d._kernels) positive definite kernels. Common kernels are the linear (dot product) kernel,\n", + "\\begin{equation}\n", + " k(\\mathbf{x}, \\mathbf{x}^{\\prime}) = \\mathbf{x}^T \\mathbf{x},\n", + "\\end{equation}\n", + "and the Gaussian kernel,\n", + "\\begin{equation}\n", + " k(\\mathbf{x}, \\mathbf{x}^{\\prime}) = \\exp{\\left(-\\gamma\\lVert \\mathbf{x} - \\mathbf{x}^{\\prime}\\rVert^2\\right)}.\n", + "\\end{equation}\n", + "\n", + "In this notebook we use the gaussian kernel (```rbf_kernel(XA, XB, gamma=1.0)```), however, we have also included the linear kernel function (```linear_kernel(XA, XB)```) in ```sklearn```. You can check rather easily that if you use a linear kernel all of the kernel methods reduce explicitly to linear regression or principal component analysis in the original feature space." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Changing the kernels in this cell will change them throughout the notebook tutorial.\n", + "# The function variable designates the kernel function to use throughout the notebook.\n", + "# The string variable is used to pass to the utility classes.\n", + "kernel_params = {\"kernel\": \"rbf\", \"gamma\": 1.0}\n", + "kernel_func = partial(rbf_kernel, gamma=1.0)\n", + "kernel_type = \"gaussian\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [representer theorem](https://en.wikipedia.org/wiki/Representer_theorem) guarantees that if the kernel is a positive definite function (both these two examples are) there is a Hilbert space with elements $\\phi(\\mathbf{x})$ whose dot product reproduces the kernel, i.e.\n", + "\n", + "\\begin{equation}\n", + " k(\\mathbf{x}, \\mathbf{x}^{\\prime}) = \\phi(\\mathbf{x})^T\\phi(\\mathbf{x}^{\\prime}).\n", + "\\end{equation}\n", + "\n", + "This Hilbert space is known as the [**reproducing kernel Hilbert space**](https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space), or RKHS. If one builds a kernel matrix $\\mathbf{K}$ whose elements contain the kernel computed between the corresponding pair of samples, \n", + "For simple kernels, such as the linear kernel shown above, the RKHS is intuitive: $\\phi(\\mathbf{x}) = \\mathbf{x}$.\n", + "However, for even slightly more complex kernel functions, the RKHS may be infinitely dimensional, such as the [RBF kernel](https://en.wikipedia.org/wiki/Radial_basis_function_kernel).\n", + "If one builds a kernel matrix $\\mathbf{K}$ whose elements contain the kernel computed between the corresponding pair of samples, \n", + "\n", + "\\begin{equation}\n", + " K_{ij} = k(\\mathbf{x}_i, \\mathbf{x}_j)\n", + "\\end{equation}\n", + "\n", + "the formal relation with the reproducing features can be written in a matrix notation\n", + "\n", + "\\begin{equation}\n", + "\\quad \\mathbf{K} = \\mathbf{\\Phi_X\\Phi_X^T}.\n", + "\\end{equation}\n", + "\n", + "$\\mathbf{\\Phi_X}$ indicates a matrix that holds the values of the RKHS features for each sample in $\\mathbf{X}$, which means that $\\mathbf{X}$and $\\mathbf{\\Phi_X}$ have the same number of samples, but different numbers of features. To simplify the notation, in this notebook we drop the $\\mathbf{X}$ subscript and refer to this matrix simply as $\\mathbf{\\Phi}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K_train_raw = kernel_func(X_train, X_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is important to realize that even if in general $\\phi(\\mathbf{x})$ is not known, _for a given data set_ the representer theorem provides an explicit construction for an approximation of the RKHS features. The construction is very closely related to the KPCA method that we discuss below. \n", + "\n", + "Start by writing an eigendecomposition of the kernel matrix, \n", + "\n", + "\\begin{equation}\n", + " \\mathbf{K} = \\mathbf{U_K} \\mathbf{\\Lambda_K} \\mathbf{U_K}^T.\n", + "\\end{equation}\n", + "\n", + "If one defines \n", + "\\begin{equation}\n", + "\\mathbf{\\Phi} = \\mathbf{U_K} \\mathbf{\\Lambda_K}^{1/2} = \\mathbf{K} \\mathbf{U_K} \\mathbf{\\Lambda_K}^{-1/2}\n", + "\\end{equation}\n", + "one sees that $\\mathbf{\\Phi}\\mathbf{\\Phi}^T = \\mathbf{K}$: the eigenvectors of the kernel matrix make it possible to construct a set of features whose scalar product reproduces exactly the values of the kernel for the dataset. \n", + "\n", + "The second equality is important because it provides a recipe to build an _approximate_ set of RKHS features for a _new_ set of points. If $\\mathbf{K}_{NN}$ indicates the kernel matrix for the train set, and the matrix $\\mathbf{K}_{N'N}$ contains the kernels between some new (e.g. test-set) samples and the train samples, which means the size of $\\mathbf{K}_{N'N}$ is $n_{new\\ samples}\\times n_{train\\ sample}$, one can compute \n", + "\\begin{equation}\n", + "\\mathbf{\\Phi}_{N'N} = \\mathbf{K}_{N'N} \\mathbf{U} \\mathbf{\\Lambda}^{-1/2},\n", + "\\end{equation}\n", + "where $\\mathbf{U}$ and $\\mathbf{\\Lambda}$ refer to the eigendecomposition of the square $\\mathbf{K}_{NN}$.\n", + "Then, $\\mathbf{\\Phi}_{N'N}$ is a matrix whose entries approximate the RKHS features for the new set of points. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v_K, U_K = np.linalg.eigh(K_train_raw)\n", + "\n", + "# U_K/v_K are already sorted, but in *increasing* order, so reverse them\n", + "U_K = np.flip(U_K, axis=1)\n", + "v_K = np.flip(v_K, axis=0)\n", + "\n", + "U_K = U_K[:, v_K > 0]\n", + "v_K = v_K[v_K > 0]\n", + "\n", + "Phi = U_K @ np.diag(np.sqrt(v_K))\n", + "\n", + "print(np.linalg.norm((K_train_raw - Phi @ Phi.T)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Kernel Centering" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as it is often convenient to center features for linear methods, it is often beneficial to work with kernels that are also \"centered\". Centering a kernel can be understood in terms of centering of the associated RKHS features. \n", + "\n", + "Let us first introduce the centering matrix $\\mathbf{1}_{N'N}$, which is just is a $N'\\times N$ matrix for which each element takes value $1/N$. \n", + "\n", + "Using the expression above for $\\mathbf{\\Phi}$, one can compute \n", + "\n", + "\\begin{equation}\n", + "\\bar{\\mathbf{\\Phi}}_{N'N} = \\mathbf{1}_{N'N} \\mathbf{K}_{NN} \\mathbf{U} \\mathbf{\\Lambda}^{-1/2}\n", + "\\end{equation}\n", + "\n", + "A similar centering matrix can be built for $\\mathbf{\\Phi}_{NN}$\n", + "\n", + "\\begin{equation}\n", + "\\bar{\\mathbf{\\Phi}}_{NN} = \\mathbf{1}_{NN} \\mathbf{K}_{NN} \\mathbf{U} \\mathbf{\\Lambda}^{-1/2}\n", + "\\end{equation}\n", + "\n", + "The centered kernel $\\tilde{\\mathbf{K}}_{N'N}$ reads\n", + "\n", + "\\begin{equation}\n", + "\\tilde{\\mathbf{K}}_{N'N} = (\\mathbf{\\Phi}_{N'N} - \\bar{\\mathbf{\\Phi}}_{N'N})(\\mathbf{\\Phi}_{NN}-\\bar{\\mathbf{\\Phi}}_{NN})^T = \n", + "\\mathbf{K}_{N'N} - \\mathbf{1}_{N'N} \\mathbf{K}_{NN} - \\mathbf{K}_{N'N}\\mathbf{1}_{NN}\n", + "+ \\mathbf{1}_{N'N} \\mathbf{K}_{NN} \\mathbf{1}_{NN}.\n", + "\\end{equation}\n", + "\n", + "which can be computed without the need of ever evaluating explicitly the RKHS features.\n", + "This is a common pattern in kernel methods: RKHS features allow casting problems in a linear\n", + "language, but eventually the linear problem can yield an equation in which one only needs to evaluate the kernel function." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this notebook, we center the kernels, which can be done with a utility function" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "k_centerer = KernelFlexibleCenterer()\n", + "K_train = k_centerer.fit_transform(K_train_raw)\n", + "K_scale = k_centerer.scale_" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Testing Set Kernel\n", + "\n", + "For new data, we must generate a new kernel. Notice that a kernel takes *two* sets of data as arguments, one of which can be our testing $\\mathbf{X}_{N'}$ and the other the training $\\mathbf{X}_N$. This contains the kernels computed between all of the test set samples $N'$ and the train set samples $N$. This can be computed as " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K_test = kernel_func(X_test, X_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We center with the training kernel as reference, as discussed above" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# centering relative to the approximate RHKS defined by\n", + "# the training kernel matrix can be achieved specifying\n", + "# K_train as the reference kernel matrix\n", + "\n", + "K_test = k_centerer.transform(K_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Kernel PCA (KPCA)\n", + "\n", + "In [kernel principal component analysis](https://en.wikipedia.org/wiki/Kernel_principal_component_analysis)\n", + "(KPCA) we take advantage of the kernel in order to \n", + "introduce a non-linear transformation of the feature space \n", + "[(Scholkopf 1996)](http://www.face-rec.org/algorithms/Kernel/kernelPCA_scholkopf.pdf), \n", + "[(Scholkopf 1998)](http://www.doi.org/10.1162/089976698300017467), and then proceed to single out the largest-variance directions in RKHS. \n", + "\n", + "With the linear (dot product) kernel, performing KPCA with a linear kernel is equivalent to performing standard PCA." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Principal Components\n", + "\n", + "KPCA proceeds analogously to PCA. First, the eigenvalues and eigenvectors of $\\mathbf{K}$ are computed:\n", + "\\begin{equation}\n", + " \\mathbf{K} = \\mathbf{U_K} \\mathbf{\\Lambda_K} \\mathbf{U_K}^T\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v_K, U_K = np.linalg.eigh(K_train)\n", + "\n", + "# U_K/v_K are already sorted, but in *increasing* order, so reverse them\n", + "U_K = np.flip(U_K, axis=1)\n", + "v_K = np.flip(v_K, axis=0)\n", + "\n", + "U_K = U_K[:, v_K > 0]\n", + "v_K = v_K[v_K > 0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The KPCA Projection\n", + "\n", + "The KPCA projection may then be computed taking the first $n_{PCA}$ components \n", + "\\begin{equation}\n", + "\\mathbf{T}=\\mathbf{\\hat{U}_K}\\mathbf{\\hat{\\Lambda}_K}^{1/2} = \\mathbf{\\hat{U}_K}\\mathbf{\\hat{\\Lambda}_K} (\\mathbf{\\hat{U}_K}^T\\mathbf{\\hat{U}_K}) \\mathbf{\\hat{\\Lambda}_K}^{-1/2} = \\mathbf{K} \\mathbf{\\hat{U}_K} \\mathbf{\\hat{\\Lambda}_K}^{-1/2}\n", + "\\end{equation}\n", + "\\begin{equation}\n", + " \\mathbf{T} = \\mathbf{K}\\mathbf{P}_{KT} = \\mathbf{K} \\mathbf{\\hat{U}_K} \\mathbf{\\hat{\\Lambda}_K}^{-1/2}.\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Remember that in PCA, the projection $\\mathbf{T} = \\mathbf{X}\\mathbf{U}_C$. So why the factor of $\\mathbf{\\Lambda}_K^{-1/2}$?**\n", + "\n", + "The eigenvectors of $\\mathbf{K} = \\mathbf{\\Phi}\\mathbf{\\Phi}^T$ are in fact analogous to the eigenvectors of the Gram matrix $\\mathbf{X}\\mathbf{X}^T$ and thereby related to those of the covariance $\\mathbf{C} = \\mathbf{X}^T\\mathbf{X} = \\mathbf{U}_C \\mathbf{\\Lambda}_C \\mathbf{U}_C^T$ by $\\mathbf{X}\\mathbf{U_C}$, which is not normalized. In essence, the $\\mathbf{\\Lambda}_K^{-1/2}$ factor serves to normalize our projection matrix. [(Tipping 2001)](https://papers.nips.cc/paper/1791-sparse-kernel-principal-component-analysis.pdf) \n", + "\n", + "Note also that the KPCA latent space corresponds to the highest-variance components in the RKHS: if one does not truncate the latent space, $\\mathbf{T}=\\mathbf{\\Phi}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "n_PC = 2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PKT = U_K[:, :n_PC] @ np.diagflat(1.0 / np.sqrt(v_K[0:n_PC]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The expression for the testing data is then identical to that for the projection of the train set:\n", + "\\begin{equation}\n", + " \\mathbf{T} = \\mathbf{K}_{N'N} \\mathbf{P}_{KT}\n", + "\\end{equation}\n", + "$\\mathbf{P}_{KT}$ is the projection obtained during training, while the $\\mathbf{K}_{N'N}$ indicates the kernel between the test set and the training points." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_KPCA_train = K_train @ PKT\n", + "T_KPCA_test = K_test @ PKT" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note**: if we used a linear kernel, the projection would be identical to the PCA projection (modulo reflection, since the sign of the eigenvectors is not defined), and it would likewise correspond to the Classical MDS solution." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "plot_projection(\n", + " Y_train, T_KPCA_train, fig=fig, ax=axes[0], title=\"KPCA of Training Data\", **cmaps\n", + ")\n", + "plot_projection(\n", + " Y_test, T_KPCA_test, fig=fig, ax=axes[1], title=\"KPCA of Testing Data\", **cmaps\n", + ")\n", + "fig.subplots_adjust(wspace=0.4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even though this is not done very often (because the kernel acts in a different space than the original feature space) it is possible to reconstruct an approximation of the feature vector based on the KPCA latent space. Consider this like \"predicting\" $\\mathbf{X}$, similar to predicting $\\mathbf{Y}$ in linear regression. The projection matrix $\\mathbf{P}_{TX}$ corresponds to the least-square weights\n", + " \n", + "\\begin{equation} \n", + "\\mathbf{P}_{TX} = (\\mathbf{T}\\mathbf{T}^T)^{-1}\\mathbf{T}^T \\mathbf{X} = \\mathbf{\\hat{\\Lambda}}_K^{-1} \\mathbf{T}^T \\mathbf{X}\n", + "\\end{equation}\n", + "\n", + "Where the factor of $\\mathbf{\\Lambda_K}^{-1}$ arises from the fact that\n", + "$\\mathbf{T}^T\\mathbf{T}=\n", + "\\mathbf{\\Lambda_K}^{-1/2}\\mathbf{U_K}^T\\mathbf{K}^T\\mathbf{K}\\mathbf{U_K}\\mathbf{\\Lambda_K}^{-1/2}=\n", + "\\mathbf{\\Lambda_K}^{1/2}\\mathbf{U_K}^T\\mathbf{U_K}\\mathbf{\\Lambda_K}^{1/2}=\n", + "\\mathbf{\\Lambda_K}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PTX = np.diagflat(1 / ((v_K[:n_PC]))) @ T_KPCA_train.T @ X_train\n", + "\n", + "Xr_train = T_KPCA_train @ PTX\n", + "Xr_test = T_KPCA_test @ PTX" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The KPCA projection approximates the kernel matrix, so one can check for convergence using the [Frobenius norm](https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K_approx_train = T_KPCA_train @ T_KPCA_train.T\n", + "\n", + "K_test_test = kernel_func(X_test, X_test)\n", + "K_test_test = k_centerer.transform(K_test_test)\n", + "K_approx_test = T_KPCA_test @ T_KPCA_test.T\n", + "\n", + "table_from_dict(\n", + " [\n", + " get_stats(\n", + " x=X_train,\n", + " xr=Xr_train,\n", + " y=Y_train,\n", + " t=T_KPCA_train,\n", + " k=K_train,\n", + " kapprox=K_approx_train,\n", + " ),\n", + " get_stats(\n", + " x=X_test,\n", + " xr=Xr_test,\n", + " y=Y_test,\n", + " t=T_KPCA_test,\n", + " k=K_test_test,\n", + " kapprox=K_approx_test,\n", + " ),\n", + " ],\n", + " headers=[\"Training\", \"Testing\"],\n", + " title=\"KPCA\",\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Kernel Ridge Regression (KRR)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Finding the KRR Weights\n", + "Just as in KPCA, in kernel ridge regression (KRR) we can use the kernel trick to make property predictions [(Saunders 1998)](https://eprints.soton.ac.uk/258942/1/Dualrr_ICML98.pdf). In KRR, the model takes the form\n", + "\\begin{equation}\n", + " \\hat{\\mathbf{Y}}_{KRR} = \\mathbf{K} \\mathbf{P}_{KY},\n", + "\\end{equation}\n", + "\n", + "where $\\mathbf{P}_{KY}$ is a vector of regression weights. The regression weights can be computed using\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{P}_{KY} = \\left( \\mathbf{K} + \\lambda \\mathbf{I} \\right)^{-1}\\mathbf{Y}\n", + "\\end{equation}\n", + "\n", + "where $\\lambda$ is the regularization parameter \n", + "[(Girosi 1995)](https://pdfs.semanticscholar.org/96af/5da062cee7ce50fc0624654c61363506772b.pdf),\n", + "[(Smola 2000)](https://pdfs.semanticscholar.org/dd09/78a594290f6dc530e65983d79a056874185c.pdf), \n", + "[(Welling)](https://www.ics.uci.edu/~welling/classnotes/papers_class/Kernel-Ridge.pdf). This parameter can be set to some small fraction of the maximum eigenvalue $\\lambda_{max}$ of $\\mathbf{K}$, e.g., $\\lambda = 10^{-16}\\lambda_{max}$, or it can be determined through cross-validation." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "lambda_max = np.amax(np.linalg.eigvalsh(K_train))\n", + "regularization = 1e-4\n", + "lambda_reg = lambda_max * regularization\n", + "\n", + "PKY_krr = np.linalg.solve(K_train + lambda_reg * np.eye(n_train), Y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our regularization is {{regularization*lambda_max}}." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then predict our properties using the training and testing kernels." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Y_krr_train = K_train @ PKY_krr\n", + "Y_krr_test = K_test @ PKY_krr\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "plot_regression(\n", + " Y_train[:, 0],\n", + " Y_krr_train[:, 0],\n", + " title=\"Kernel Ridge Regression: Training Set\",\n", + " fig=fig,\n", + " ax=axes[0],\n", + " **cmaps\n", + ")\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " Y_krr_test[:, 0],\n", + " title=\"Kernel Ridge Regression: Testing Set\",\n", + " fig=fig,\n", + " ax=axes[1],\n", + " **cmaps\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## KRR as regression in RKHS\n", + "\n", + "It is instructive to see how KRR is equivalent to ridge regression in RKHS features. In other words, the equation for ridge regression is equivalent to the equation for _kernel_ ridge regression when $\\mathbf{X}$ is replaced with $\\mathbf{\\Phi}$.\n", + "\n", + "\\begin{equation}\n", + " \\hat{\\mathbf{Y}}_{KRR} = \\mathbf{\\Phi} (\\mathbf{\\Phi}^T\\mathbf{\\Phi} \n", + " + \\lambda \\mathbf{I})^{-1} \\mathbf{\\Phi}^T \\mathbf{Y} =\n", + " \\mathbf{\\Phi} \\mathbf{\\Phi}^T (\\mathbf{\\Phi}\\mathbf{\\Phi}^T\n", + " + \\lambda \\mathbf{I})^{-1} \\mathbf{Y} = \\mathbf{K} (\\mathbf{K}+\\lambda \\mathbf{I})^{-1} \\mathbf{Y}\n", + "\\end{equation}\n", + "\n", + "where the second step can be proven through a Taylor expansion, where any function $f(A^T A) * A^T$ can be rewritten as $A^T*f(A A^T)$ by expanding it in the form $\\sum_k c_k (A^T A)^k A^T = A^T \\sum_k c_k (A A^T)^k$.\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Error and Loss\n", + "\n", + "Here our loss function is:\n", + "\n", + "\\begin{equation}\n", + "\\ell = \\left\\lVert \\mathbf{Y} - \\mathbf{K}\\mathbf{P}_{KY}\\right\\rVert^2\n", + "\\end{equation}\n", + "\n", + "which we can compare to that of ridge regression. Note how the additional flexibility afforded by the non-linear kernel halves the MSE. By reducing the regularization, one could reduce the train set error essentially to zero: in fact, the best regularization needs to be determined by cross-validation, or by using an external test set. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "lr = Ridge(alpha=regularization)\n", + "\n", + "lr.fit(X_train, Y_train)\n", + "Y_lr = lr.predict(X_test)\n", + "\n", + "table_from_dict([get_stats(x=X_test, \n", + " yp=Y_lr,\n", + " y=Y_test, \n", + " ), \n", + " get_stats(x=X_test, \n", + " yp=Y_krr_test,\n", + " y=Y_test, \n", + " k=K_test)], \n", + " headers = [\"LR\", \"KRR\"]\n", + " )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Choosing a Regularization Parameter\n", + "\n", + "Similar to in linear/ridge regression, including some regularization is equivalent to introducing a $\\mathcal{L}^2$ penalty in the loss, associated to $\\left\\lVert \\mathbf{P}_{KY} \\right\\rVert^2$. Here we express it as a fraction of the maximum eigenvalue. While the regularization is used here just to avoid overfitting, it can also be interpreted -- as it is done in the context of Gaussian process regression -- as a measure of the level of noise that is present in the training data." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "regularizations = np.linspace(-10, -2, 24)\n", + "krrs = [KernelRidge(alpha=10 ** i, **kernel_params) for i in regularizations]\n", + "\n", + "for k in krrs:\n", + " k.fit(X=K_train, y=Y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ell = np.array(\n", + " [\n", + " np.linalg.norm(Y_test - k.predict(K_test)) ** 2.0\n", + " / np.linalg.norm(Y_test) ** 2.0\n", + " for k in krrs\n", + " ]\n", + ")\n", + "best_regularization = 10 ** regularizations[ell.argmin()]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even small regularizations lead to an increase in accuracy for predicting out-of-sample data. The best regularization here is {{round(best_regularization, 8)}}." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.semilogx(10 ** regularizations, ell, marker=\"o\", zorder=-1)\n", + "plt.scatter(\n", + " best_regularization,\n", + " min(ell),\n", + " marker=\"o\",\n", + " color=\"r\",\n", + ")\n", + "\n", + "plt.xlabel(r\"$\\lambda$\")\n", + "plt.ylabel(r\"$\\ell$\")\n", + "\n", + "plt.title(r\"Effect of $\\lambda$ on $\\ell$ for Kernel Ridge Regression\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Kernel PCovR " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Derivation of KPCovR\n", + "Formulating a kernelized version of PCovR is surprisingly simple. One just needs to write formally the expressions using the RKHS features in lieu of the linear features, and combine them into a kernel matrix to obtain the final expression.\n", + "\n", + "As an important reminder, $\\tilde{\\mathbf{K}}$ represents the modified Gram matrix used in PCovR, given by\n", + "\n", + "\\begin{equation}\n", + " \\tilde{\\mathbf{K}} = \\alpha \\mathbf{XX}^T\n", + " + (1 - \\alpha) \\hat{\\mathbf{Y}} \\hat{\\mathbf{Y}}^T,\n", + "\\end{equation}\n", + "\n", + "versus $\\mathbf{K}$, which is our kernel matrix.\n", + "\n", + "To construct a PCovR based upon the kernel matrix, we first need to use the approximate $\\hat{\\mathbf{Y}}$ obtained from (possibly regularized) KRR:\n", + "\n", + "\\begin{equation}\n", + "\\hat{\\mathbf{Y}} = \\mathbf{K}\\left(\\mathbf{K}+\\mathbf{I}\\lambda\\right)^{-1}\\mathbf{Y},\n", + "\\end{equation} \n", + "\n", + "and to substitute $\\mathbf{K} = \\mathbf{\\Phi \\Phi}^T$ for $ \\mathbf{XX}^T$. \n", + "\n", + "We choose to normalize our kernel matrix dividing by the factor $\\operatorname{Tr}(\\mathbf{K})/N$, so as to obtain a similar balancing of the LR and PCA parts of the loss as is used for linear PCovR. Thus we finally get\n", + "\n", + "\\begin{equation}\n", + " \\tilde{\\mathbf{K}} = \\alpha \\frac{\\mathbf{K}} {\\operatorname{Tr}(\\mathbf{K})/N} \n", + " + (1 - \\alpha) \\hat{\\mathbf{Y}} \\hat{\\mathbf{Y}}^T.\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "alpha = 0.5\n", + "\n", + "regularization = 1e-12\n", + "\n", + "krr = KernelRidge(alpha=regularization, **kernel_params)\n", + "krr.fit(K_train, Y_train)\n", + "Yhat_train = krr.predict(K_train).reshape(-1, Y.shape[-1])\n", + "PKY = krr.dual_coef_\n", + "K_pca = K_train / (np.trace(K_train) / n_train)\n", + "K_lr = Yhat_train @ Yhat_train.T\n", + "\n", + "Kt = (alpha * K_pca) + (1.0 - alpha) * K_lr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Projecting into Latent Space\n", + "\n", + "The projection can be obtained as in the linear PCovR case, combining eigenvalues and eigenvectors of $\\tilde{\\mathbf{K}}$\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{T} = \\mathbf{K}\\mathbf{P}_{KT} = \\tilde{\\mathbf{K}}\\mathbf{\\hat{U}_{\\tilde{\\mathbf{K}}}}\\mathbf{\\Lambda_{\\tilde{\\mathbf{K}}}}^{-1/2}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v_Kt, U_Kt= np.linalg.eigh(Kt)\n", + "\n", + "# U_K/v_Ktare already sorted, but in *increasing* order, so reverse them\n", + "U_Kt= np.flip(U_Kt, axis=1)\n", + "v_Kt= np.flip(v_Kt, axis=0)\n", + "\n", + "U_Kt= U_Kt[:,v_Kt>0]\n", + "v_Kt= v_Kt[v_Kt>0]\n", + "\n", + "# note that Kt might have a large null space\n", + "print(\"Size {} vs {}\".format(len(v_Kt),len(Kt)))\n", + "\n", + "T = Kt @ U_Kt[:, :n_PC] @ np.diagflat(1.0/np.sqrt(v_Kt[:n_PC]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Given each portion of $\\tilde{\\mathbf{K}}$ contains a factor of $\\mathbf{K}$\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\tilde{K}} = \\left(\\alpha \\frac{\\mathbf{K}} {\\operatorname{Tr}(\\mathbf{K})/N} + (1 - \\alpha)\n", + "\\mathbf{K}\\left(\\mathbf{K}+\\mathbf{I}\\lambda\\right)^{-1}\\mathbf{YY}^T \\left(\\mathbf{K}+\\mathbf{I}\\lambda\\right)^{-1} \\mathbf{K}\n", + "\\right)\n", + "\\end{equation}\n", + "\n", + "We can find our projector by dividing $\\tilde{\\mathbf{K}}\\mathbf{\\hat{U}_{\\tilde{\\mathbf{K}}}}\\mathbf{\\Lambda_{\\tilde{\\mathbf{K}}}}^{-1/2}$ by $\\mathbf{K}$, \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{KT} = \\left(\n", + " \\alpha\\frac{\\mathbf{I}}{\\operatorname{Tr}{(\\mathbf{K})}/N}\n", + "+ (1 - \\alpha)\n", + "\\left(\\mathbf{K}+\\mathbf{I}\\lambda\\right)^{-1}\\mathbf{YY}^T \\left(\\mathbf{K}+\\mathbf{I}\\lambda\\right)^{-1} \\mathbf{K}\n", + "\\right) \\mathbf{\\hat{U}_{\\tilde{\\mathbf{K}}}}\\mathbf{\\Lambda_{\\tilde{\\mathbf{K}}}}^{-1/2}\n", + "\\end{equation}\n", + "\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{KT} = \\left(\n", + " \\alpha\\frac{\\mathbf{I}}{\\operatorname{Tr}{(\\mathbf{K})}/N}\n", + "+ (1 - \\alpha)\n", + "\\mathbf{P}_{KY}\\mathbf{\\hat{Y}}^T\n", + "\\right) \\mathbf{\\hat{U}_{\\tilde{\\mathbf{K}}}}\\mathbf{\\Lambda_{\\tilde{\\mathbf{K}}}}^{-1/2}\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P_krr = PKY @ Yhat_train.T\n", + "\n", + "P_kpca = np.eye(n_train)/(np.trace(K_train)/n_train)\n", + " \n", + "P = (alpha*P_kpca) + (1.0-alpha)*P_krr\n", + "PKT = P @ U_Kt[:,:n_PC] @ np.diag(1/np.sqrt(v_Kt[:n_PC])) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can confirm that this gives the same $\\mathbf{T}$ as above and similarly project the test kernel." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_kpcovr_train = K_train @ PKT\n", + "T_kpcovr_test = K_test @ PKT\n", + "\n", + "print(np.linalg.norm(T-T_kpcovr_train))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "ref = KernelPCA(n_components=2, **kernel_params)\n", + "ref.fit(K_train)\n", + "T_kpca = ref.transform(K_test)\n", + "\n", + "plot_projection(\n", + " Y_test,\n", + " T_kpcovr_test,\n", + " fig=fig,\n", + " ax=axes[0],\n", + " title=r\"KPCovR ($\\alpha={}$)\".format(alpha),\n", + " **cmaps\n", + ")\n", + "plot_projection(Y_test, T_kpca, fig=fig, ax=axes[1], title=\"KPCA\", **cmaps)\n", + "\n", + "fig.suptitle(\n", + " r\"These will become increasingly different as $\\alpha \\to 0.0.$\",\n", + " y=0.0,\n", + " fontsize=plt.rcParams[\"font.size\"] + 6,\n", + ")\n", + "\n", + "fig.subplots_adjust(hspace=0.3)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The structure-property relationship is revealed more clearly in the result of PCovR." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Predicting Properties \n", + "\n", + "Similar PCovR, to get the KRR prediction we should compute $\\mathbf{P}_{TY}$ such that\n", + "$\\mathbf{Y} = \\mathbf{K}\\mathbf{P}_{KT}\\mathbf{P}_{TY} = \\mathbf{T} \\mathbf{P}_{TY}$. Recall when we derived linear regression, the optimal weights $\\mathbf{P}_{KY}$ were given by the pseudoinverse of our input variable, subject to some regularization. Using this same logic, $\\mathbf{P}_{TY}$ is given by\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{TY}=(\\mathbf{T}^T\\mathbf{T})^{-1}\\mathbf{T}^T \\mathbf{Y}=\n", + "\\mathbf{\\Lambda}_{\\tilde{K}}^{-1}\\mathbf{T}^T \\mathbf{Y}\n", + "\\end{equation}\n", + "\n", + "**Note:** even though $\\mathbf{K}$ must be computed with all the points in the train set, the \n", + "prediction uses only the projections in the KPCA space, so the latent KPCovR variables explain fully \n", + "structure-property relations." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PTY = np.diagflat(1/((v_Kt[:n_PC]))) @ T_kpcovr_train.T @ Y_train\n", + "Ypred = K_test @ PKT @ PTY" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "ref = KernelRidge(alpha=regularization, **kernel_params)\n", + "ref.fit(K_train, Y_train)\n", + "yref = ref.predict(K_test)\n", + "\n", + "errors = np.concatenate((np.abs(Ypred - Y_test), np.abs(yref - Y_test)))\n", + "\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " Ypred[:, 0],\n", + " fig=fig,\n", + " ax=axes[0],\n", + " vmin=errors.min(),\n", + " vmax=errors.max(),\n", + " title=r\"KPCovR ($\\alpha={}$)\".format(alpha),\n", + " **cmaps\n", + ")\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " yref[:, 0],\n", + " fig=fig,\n", + " ax=axes[1],\n", + " vmin=errors.min(),\n", + " vmax=errors.max(),\n", + " title=\"KRR\",\n", + " **cmaps\n", + ")\n", + "\n", + "fig.suptitle(\n", + " r\"These will become increasingly different as $\\alpha \\to 1.0.$\",\n", + " y=0.0,\n", + " fontsize=plt.rcParams[\"font.size\"] + 6,\n", + ")\n", + "\n", + "fig.subplots_adjust(hspace=0.3)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison of KPCovR Performance\n", + "\n", + "We will use the utility class to plot how the method is tuned with changing $\\alpha$ and the number of PCA components. Note: executing this cell can take some time." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "n_alphas = 11\n", + "alphas = np.linspace(0.0, 1.0, n_alphas)\n", + "# a = np.linspace(-5.0,5.0,n_alphas)\n", + "# alphas = np.exp(a)/(np.exp(-a)+np.exp(a))\n", + "components = np.array([2,3,4,8])\n", + "n_components = components.size\n", + "\n", + "kpcovr_calculators = np.array([[KPCovR(mixing=a, n_components=c, \n", + " kernel='precomputed') for a in alphas] \n", + " for c in components])\n", + "\n", + "for cdx, c in enumerate(components):\n", + " for adx, a in enumerate(alphas):\n", + " kpcovr_calculators[cdx][adx].fit(K_train, Y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparison of KPCovR Projections and Regressions\n", + "\n", + "Just like with PCovR, for KPCovR it's useful to get an intuitive sense for the change in the projections and regressions across $\\alpha$, and see the trade-off. Below we plot both projections and regressions for $n_\\alpha$ different values of $\\alpha$:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "n_plots = int(n_alphas ** 0.5)\n", + "scale = 3\n", + "\n", + "t_ref = kpcovr_calculators[0][-3].transform(K_test)\n", + "\n", + "pfig, pax = plt.subplots(\n", + " n_plots,\n", + " int(np.ceil(n_alphas / n_plots)),\n", + " figsize=(\n", + " scale * int(np.ceil(n_alphas / n_plots)),\n", + " scale * n_plots,\n", + " ),\n", + ")\n", + "\n", + "rfig, rax = plt.subplots(\n", + " n_plots,\n", + " int(np.ceil(n_alphas / n_plots)),\n", + " figsize=(\n", + " scale * int(np.ceil(n_alphas / n_plots)),\n", + " scale * n_plots,\n", + " ),\n", + ")\n", + "for p, r, kpcovr in zip(pax.flatten(), rax.flatten(), kpcovr_calculators[0]):\n", + "\n", + " t = kpcovr.transform(K_test)\n", + " y = kpcovr.predict(K_test)\n", + "\n", + " plot_projection(Y_test, check_mirrors(t, t_ref), fig=pfig, ax=p, **cmaps, alpha=1.0)\n", + "\n", + " plot_regression(Y_test[:, 0], y[:, 0], fig=pfig, ax=r, **cmaps, alpha=1.0)\n", + "\n", + " p.set_title(r\"$\\alpha=$\" + str(round(kpcovr.mixing, 6)))\n", + " r.set_title(r\"$\\alpha=$\" + str(round(kpcovr.mixing, 6)))\n", + "\n", + "\n", + "for p, r in zip(pax.flatten()[n_alphas:], rax.flatten()[n_alphas:]):\n", + " p.axis(\"off\")\n", + " r.axis(\"off\")\n", + "\n", + "pfig.subplots_adjust(wspace=0.6, hspace=0.6)\n", + "pfig.suptitle(r\"Projections across $\\alpha$\")\n", + "rfig.subplots_adjust(wspace=0.6, hspace=0.6)\n", + "rfig.suptitle(r\"Regressions across $\\alpha$\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparison of KPCovR Loss Terms\n", + "\n", + "Computing the loss minimised by KPCovR is trivial if one computes explicitly a RKHS approximation of $\\mathbf{\\Phi}$, but it requires some work if one wants to avoid evaluating $\\mathbf{\\Phi}$\n", + "\n", + "Rewriting in terms of the RKHS, we get:\n", + "\n", + "\\begin{equation}\n", + " \\ell = \\alpha\\lVert \\mathbf{\\Phi} - \\mathbf{\\Phi}\\mathbf{P}_{\\Phi T}\\mathbf{P}_{T\\Phi}\\rVert^2 + (1 - \\alpha)\\left\\lVert \\mathbf{Y} - \\mathbf{KP}_{KT}\\mathbf{P}_{TY}\\right\\rVert^2.\n", + "\\end{equation}\n", + "\n", + "In case one wants to avoid evaluating the RKHS, however, $\\ell_\\text{proj}$ may be computed in terms of the kernel.\n", + "\n", + "Indicating the kernel between set $A$ and $B$ as $\\mathbf{K}_{AB}$, the projection of set $A$ as $\\mathbf{T}_A$, and with N and V as the train and validation/test set, one obtains\n", + "\\begin{equation}\n", + "\\begin{split}\n", + "\\ell_\\text{proj}=&\n", + "\\operatorname{Tr}\\left[\n", + "\\mathbf{K}_{VV} - 2\n", + " \\mathbf{K}_{VN} \\mathbf{T}_N (\\mathbf{T}_N^T \\mathbf{T}_N)^{-1} \\mathbf{T}_V^T\\right.\\\\\n", + " +&\\mathbf{T}_V(\\mathbf{T}_N^T \\mathbf{T}_N)^{-1} \\mathbf{T}_N^T \\mathbf{K}_{NN} \\left.\\mathbf{T}_N (\\mathbf{T}_N^T \\mathbf{T}_N)^{-1} \\mathbf{T}_V^T.\n", + "\\right]\n", + "\\end{split}\n", + "\\end{equation}\n", + "When the loss is evaluated on the train set, so that $N\\equiv V$, this expression reduces to\n", + "\\begin{equation}\n", + " \\ell_\\text{proj} = \\operatorname{Tr}\\left(\\mathbf{K}_{NN} - \\mathbf{K}_{NN} \\mathbf{P}_{KT} \\mathbf{P}_{TK} \\right).\n", + "\\end{equation}\n", + "where $\\mathbf{P}_{TK} = (\\mathbf{T}_N^T \\mathbf{T}_N)^{-1} \\mathbf{T}_N^T \\mathbf{K}_{NN}$.\n", + "\n", + "Where $\\operatorname{Tr}{(\\mathbf{K}_{VV})} \\neq 1$, it is necessary to divide the preceding loss equation by $\\operatorname{Tr}{(\\mathbf{K}_{VV})}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K_vv = K_test_test.copy()\n", + "K_vn = K_test.copy()\n", + "K_nn = K_train.copy()\n", + "\n", + "\n", + "def l_proj(my_kpcovr):\n", + " t_n = my_kpcovr.transform(K_train)\n", + " t_v = my_kpcovr.transform(K_test)\n", + "\n", + " w = t_n @ np.linalg.pinv(t_n.T @ t_n) @ t_v.T\n", + " return np.trace(K_vv - 2 * K_vn @ w + w.T @ K_nn @ w) / np.trace(K_vv)\n", + "\n", + "\n", + "def l_y(my_kpcovr):\n", + " return (\n", + " np.linalg.norm(Y_test - my_kpcovr.predict(K_test)) ** 2.0\n", + " / np.linalg.norm(Y_test) ** 2.0\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "L_proj = np.zeros((n_components, n_alphas))\n", + "L_regr = np.zeros((n_components, n_alphas))\n", + "\n", + "for cdx, c in enumerate(components):\n", + " for adx, a in enumerate(alphas):\n", + " L_proj[cdx, adx], L_regr[cdx, adx] = (\n", + " l_proj(kpcovr_calculators[cdx][adx]),\n", + " l_y(kpcovr_calculators[cdx][adx]),\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, [axs_regr, axs_proj] = plt.subplots(1, 2, figsize=(12, 6), sharex=True)\n", + "\n", + "for cdx, c in enumerate(components):\n", + " axs_regr.plot(alphas, L_regr[cdx, :], marker=\"o\", label=\"{:d} PCs\".format(c))\n", + " axs_proj.plot(alphas, L_proj[cdx, :], marker=\"o\", label=\"{:d} PCs\".format(c))\n", + "\n", + "axs_regr.set_ylabel(r\"$\\ell_{regr}$\")\n", + "axs_regr.set_xlabel(r\"$\\alpha$\")\n", + "axs_proj.set_ylabel(r\"$\\ell_{proj}$\")\n", + "axs_proj.set_xlabel(r\"$\\alpha$\")\n", + "\n", + "fig.subplots_adjust(wspace=0.3)\n", + "axs_regr.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By performing KPCovR, the total error is reduced:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = plt.figure(figsize=(14, 6))\n", + "axsLoss = fig.add_subplot(1, 2, 1)\n", + "axsSum = fig.add_subplot(1, 2, 2)\n", + "\n", + "for cdx, c in enumerate(components):\n", + " axsLoss.loglog(\n", + " L_proj[cdx, :], L_regr[cdx, :], marker=\"o\", label=\"{:d} PCs\".format(c)\n", + " )\n", + "\n", + "axsLoss.set_xlabel(r\"$\\ell_{proj}$\")\n", + "axsLoss.set_ylabel(r\"$\\ell_{regr}$\")\n", + "axsLoss.legend()\n", + "\n", + "for cdx, c in enumerate(components):\n", + " loss_sum = L_regr[cdx, :] + L_proj[cdx, :]\n", + " axsSum.semilogy(alphas, loss_sum, marker=\"o\", label=\"{:d} PCs\".format(c))\n", + " print(\"Optimal alpha for {:d} PCs = {:.2f}\".format(c, alphas[np.argmin(loss_sum)]))\n", + "\n", + "axsSum.set_xlabel(r\"$\\alpha$\")\n", + "axsSum.set_ylabel(r\"$\\ell_{regr} + \\ell_{proj}$\")\n", + "\n", + "fig.subplots_adjust(wspace=0.5, hspace=0.3)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Next: Sparse Kernel Methods\n", + "\n", + "Continue on to the [next notebook](4_SparseKernelMethods.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Implementation in `scikit-learn`\n", + "\n", + "Classes from `sklearn` enable computing KPCA and KRR. Here we'll review the basics of their usage; readers are encouraged to refer to sklearn documentation for further detail." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.decomposition import KernelPCA\n", + "from sklearn.kernel_ridge import KernelRidge" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## KPCA" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# We set kernel = 'precomputed' and supply kpca.fit(X) with X = K_train to improve computational efficiency.\n", + "kpca = KernelPCA(n_components=2, **kernel_params)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `kpca.fit(K_train)` will generate the kernel for $\\mathbf{X}$ and compute/internally store the eigenvectors/values." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "kpca.fit(K_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `kpca.transform(K)` will compute and return the KPCA projection $\\mathbf{T}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_KPCA_train = kpca.transform(K_train)\n", + "T_KPCA_test= kpca.transform(K_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "plot_projection(\n", + " Y_train, T_KPCA_train, title=\"KPCA of Training Data\", fig=fig, ax=axes[0], **cmaps\n", + ")\n", + "plot_projection(\n", + " Y_test, T_KPCA_test, title=\"KPCA of Testing Data\", fig=fig, ax=axes[1], **cmaps\n", + ")\n", + "\n", + "fig.subplots_adjust(wspace=0.5)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PTX = np.diagflat(1 / ((v_K[:n_PC]))) @ T_KPCA_train.T @ X_train\n", + "\n", + "Xr_train = T_KPCA_train @ PTX\n", + "Xr_test = T_KPCA_test @ PTX\n", + "\n", + "K_approx_train = T_KPCA_train @ T_KPCA_train.T\n", + "K_test_test = kernel_func(X_test, X_test)\n", + "K_approx_test = T_KPCA_test @ T_KPCA_test.T\n", + "\n", + "table_from_dict(\n", + " [\n", + " get_stats(\n", + " x=X_train,\n", + " xr=Xr_train,\n", + " y=Y_train,\n", + " t=T_KPCA_train,\n", + " k=K_train,\n", + " kapprox=K_approx_train,\n", + " ),\n", + " get_stats(\n", + " x=X_test,\n", + " xr=Xr_test,\n", + " y=Y_test,\n", + " t=T_KPCA_test,\n", + " k=K_test_test,\n", + " kapprox=K_approx_test,\n", + " ),\n", + " ],\n", + " headers=[\"Training\", \"Testing\"],\n", + " title=\"KPCA\",\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## KRR" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# We set kernel = 'precomputed' and supply krr.fit(X,y) with X = K_train to improve computational efficiency.\n", + "krr = KernelRidge(alpha=regularization, **kernel_params)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `krr.fit(X,Y)` will compute the weights $\\mathbf{P}_{KY}$ and internally store them." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "krr.fit(K_train, Y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `krr.predict(X)` will generate the desired kernel from input $\\mathbf{X}$ and compute and return the predicted $\\mathbf{Y}$ values from $\\hat{\\mathbf{Y}}_{KRR} = \\mathbf{K}\\mathbf{P}_{KY}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Y_krr_train = krr.predict(K_train)\n", + "Y_krr_test = krr.predict(K_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "plot_regression(\n", + " Y_train[:, 0],\n", + " Y_krr_train[:, 0],\n", + " title=\"Kernel Ridge Regression of Training Data\",\n", + " fig=fig,\n", + " ax=axes[0],\n", + " **cmaps\n", + ")\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " Y_krr_test[:, 0],\n", + " title=\"Kernel Ridge Regression of Testing Data\",\n", + " fig=fig,\n", + " ax=axes[1],\n", + " **cmaps\n", + ")\n", + "\n", + "fig.subplots_adjust(wspace=0.25)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "table_from_dict([get_stats(x=X_train, yp=Y_krr_train,y=Y_train, k=K_train), \n", + " get_stats(x=X_test, yp=Y_krr_test, y=Y_test, k=K_test)], \n", + " headers = [\"Training\", \"Testing\"], \n", + " title=\"Kernel Ridge Regression\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Implementation in `skcosmo`\n", + "\n", + "Classes from `skcosmo` enable computing KPCovR. Here we'll review the basics of their usage; readers are encouraged to refer to skcosmo documentation for further detail." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from skcosmo.pcovr import KPCovR" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "***To avoid confusion with scikit-learn naming conventions, where `alpha` is a regularization parameter, the keyword `mixing` is used to specify the KPCovR $\\alpha$.***\n", + "\n", + "We will show the function signature using X, but we will also supply our precomputed kernel for computational efficiency." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## KPCovR" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "kp = KPCovR(mixing=0.8, n_components=2, **kernel_params, center=True, alpha=1E-4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Calling `kpcovr.fit(X, Y, K)` will compute the weights $\\mathbf{P}_{KY}$ and internally store them." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "kp.fit(X_train, Y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "kp.alpha" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`kpcovr.transform(X)` returns the projection $\\mathbf{T}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "t = kp.transform(X_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`pcovr.predict(X)` returns the regressed properties $\\mathbf{Y}_p$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "y = kp.predict(X_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "plot_projection(Y_test, t, title=\"KPCovR\", fig=fig, ax=ax[0], **cmaps)\n", + "plot_regression(Y_test[:, 0], y[:, 0], title=\"KPCovR\", fig=fig, ax=ax[1], **cmaps)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.11" + }, + "toc": { + "base_numbering": 1, + "nav_menu": { + "height": "210px", + "width": "289px" + }, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "186.906px" + }, + "toc_section_display": true, + "toc_window_display": true + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/notebooks/4_SparseKernelMethods.ipynb b/notebooks/4_SparseKernelMethods.ipynb new file mode 100644 index 0000000..2425204 --- /dev/null +++ b/notebooks/4_SparseKernelMethods.ipynb @@ -0,0 +1,1118 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction and Background\n", + "\n", + "In this notebook, we demonstrate how to adapt the kernel methods shown in the [previous notebook](3_KernelMethods.ipynb) to use sparse kernels.\n", + "\n", + "As for the previous notebooks, for each model, we first go step-by-step through the derivation, with equations, embedded links, and citations supplied where useful. At the end of the notebook, we employ a \"skcosmo class\" for the model, which is found in the skcosmo module and contains all necessary functions." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python3\n", + "import sys\n", + "\n", + "# Maths things\n", + "import numpy as np\n", + "\n", + "# Plotting\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Local Utilities for Notebook\n", + "sys.path.append('../')\n", + "from utilities.general import load_variables, get_stats\n", + "from utilities.plotting import (\n", + " plot_projection, plot_regression, check_mirrors, get_cmaps, table_from_dict\n", + ")\n", + "from sklearn.metrics.pairwise import linear_kernel, rbf_kernel\n", + "from sklearn.kernel_ridge import KernelRidge\n", + "from sklearn.decomposition import KernelPCA\n", + "from skcosmo.pcovr import KPCovR\n", + "from skcosmo.selection import SampleFPS\n", + "from skcosmo.preprocessing import SparseKernelCenterer\n", + "from functools import partial\n", + "\n", + "cmaps = get_cmaps()\n", + "plt.style.use('../utilities/kernel_pcovr.mplstyle')\n", + "dbl_fig=(2*plt.rcParams['figure.figsize'][0], plt.rcParams['figure.figsize'][1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we must load the data. For a step-by-step explanation of this, please see [Importing Data](X_ImportingData.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var_dict = load_variables()\n", + "locals().update(var_dict)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Constructing a Sparse Kernel" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "## Change this cell to change the kernel function throughout\n", + "kernel_params = {\"kernel\": \"rbf\", \"gamma\": 1.0}\n", + "kernel_func = partial(rbf_kernel, gamma=1.0)\n", + "kernel_type = \"gaussian\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Nyström Approximation\n", + "\n", + "In sparse kernel methods, an approximate kernel is used in place of the full kernel. This approximate kernel is typically constructed according to the [Nyström approximation](https://en.wikipedia.org/wiki/Low-rank_matrix_approximations#Nystr%C3%B6m_approximation) [(Williams 2001)](http://papers.nips.cc/paper/1866-using-the-nystrom-method-to-speed-up-kernel-machines.pdf),\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{K} \\approx \\mathbf{\\hat{K}}_{NN} = \\mathbf{K}_{NM} \\mathbf{K}_{MM}^{-1} \\mathbf{K}_{NM}^T\n", + "\\end{equation}\n", + "\n", + "Here, $M$ represents a subset of the $N$ total rows/columns of the kernel matrix, i.e. the kernel between a small **active set** that is selected with subsampling method, like farthest point sampling (FPS) [(Eldar 1997)](https://doi.org/10.1109/83.623193), or a CUR decomposition [(Imbalzano2018)](https://doi.org/10.1063/1.5024611), that is discussed in the [next notebook](5_CUR.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note**: In our imported data from `load_variables()`, `X_train` and `X_test` are pre-centered and pre-scaled relative to the train set. Additionally, the imported `K_train` and `K_test` kernels have been constructed using uncentered and unscaled $\\mathbf{X}$ data. If we want to compare the sparse kernels that we will soon construct to the imported \"full\" kernels, we also need to build the sparse kernels on uncentered and unscaled $\\mathbf{X}$ data. Therefore, we undo the scaling and centering on the imported $\\mathbf{X}$ data here, and re-center and re-scale the data after building the sparse kernels. In general, centering and scaling the $\\mathbf{X}$ data before building kernels is optional; however, one should be consistent when working with multiple kernels." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X_train = X_train * X_scale + X_center\n", + "X_test = X_test * X_scale + X_center" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "n_active = 20\n", + "\n", + "fps_selector = SampleFPS(mixing=1.0, X=X_train)\n", + "fps_idxs = fps_selector.select(n_active)\n", + "\n", + "Xsparse = X_train[fps_idxs, :]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In other words, $\\mathbf{K}_{NM}$ is the kernel matrix between input data $\\mathbf{X}$ and $\\mathbf{X_{sparse}}$, a version of $\\mathbf{X}$ containing only the active set. $\\mathbf{K}_{MM}$ is the matrix containing the kernel evaluated between the active set samples." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Kmm = kernel_func(Xsparse, Xsparse)\n", + "Knm_train = kernel_func(X_train, Xsparse)\n", + "Knm_test = kernel_func(X_test, Xsparse)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Explicit RKHS\n", + "\n", + "Sometimes, it might be more convenient to explicitly write out the projection of the training points\n", + "on the [RKHS](https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space) defined by the active set.\n", + "This is essentially a KPCA built for the active set, that is not truncated to a few eigenvectors,\n", + "\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{\\Phi}_{NM} = \\mathbf{K}_{NM} \\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{-1/2}.\n", + "\\end{equation}\n", + "\n", + "Using this definition it is easy to derive the Nyström approximation: \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\hat{K}}_{NN} = \\mathbf{\\Phi}_{NM} \\mathbf{\\Phi}_{NM}^T = \n", + "\\mathbf{K}_{NM} \\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{-1} \\mathbf{U}_{MM}^T \\mathbf{K}_{NM}^T\n", + "= \\mathbf{K}_{NM} \\mathbf{K}_{MM}^{-1} \\mathbf{K}_{NM}^T.\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Centering the RKHS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just as the \"full\" kernels in [the previous notebook](3_KernelMethods.ipynb) were centered, sparse kernels must also be centered relative to the train set. The goal is to ensure that the Nyström-approximated kernel $\\mathbf{\\hat{K}}_{NN}$ is centered relative to the training set. This is achieved by centering the approximate RKHS features $\\mathbf{\\Phi}_{NM}$, and we denote the centered version of the RKHS features as $\\mathbf{\\tilde{\\Phi}}_{NM} = \\mathbf{\\Phi}_{NM} - \\mathbf{\\bar{\\Phi}}_{M}$. If we represent each element of $\\mathbf{\\Phi}$ in its summation form\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{\\Phi}_{nm} = \\frac{1}{\\sqrt{\\Lambda_{mm}}}\\sum_{m'}^M \\left(K_{nm'} U_{m'm}\\right), \n", + "\\end{equation}\n", + "\n", + "then the column means are given by\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{\\bar{\\Phi}}_{m} = \\frac{1}{\\sqrt{\\Lambda_{mm}}}\\sum_{m'}^M \\left(\\left(\\frac{1}{N}\\sum_n^N K_{nm'}\\right)U_{m'm} \\right), \n", + "\\end{equation}\n", + "\n", + "so the centered feature matrix is computed by $\\mathbf{K}_{NM}$, centered by the column means of the kernel, as denoted by $\\mathbf{\\bar{K}}_M$.\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{\\tilde{\\Phi}}_{NM} = \\left(\\mathbf{K}_{NM} -\\mathbf{\\bar{K}}_M\\right) \\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{-1/2}.\n", + "\\end{equation}\n", + "\n", + "It is best to keep the column mean $\\mathbf{\\bar{K}}_M$ separate, because it has to be used also when performing out-of-sample embedding, where $\\mathbf{K}_{NM}$ would corresponds to the test set kernel. For consistency, $\\mathbf{\\bar{K}}_M$ must always be the kernel mean associated with the **train set**.\n", + "\n", + "Alternatively, one can store $\\mathbf{\\bar{\\Phi}}_{M}$ and use it for centering.\n", + "\n", + "**Note**: in the following we often use $\\mathbf{\\Phi}_{NM}$ and $\\mathbf{\\tilde{\\Phi}}_{NM}$ without the subscripts to indicate the train set features approximated in the active RKHS.\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The kernel between the active points $\\mathbf{K}_{MM}$ can also be centered independently, though this is optional and can lead to near-zero eigenvalues, as noted below." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K_center = np.mean(Knm_train, axis=0)\n", + "\n", + "Knm_train -= K_center\n", + "Knm_test -= K_center" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition to centering the kernel, one may also want to scale the sparse kernel(s) so that, for example, the trace of the Nyström-approximated train kernel is equal to the number of training points. To achieve this, the sparse kernel $\\mathbf{K}_{NM}$ is divided by\n", + "\n", + "\\begin{equation}\n", + " \\sqrt{\\frac{\\operatorname{Tr}(\\mathbf{K}_{NM}\\mathbf{K}_{MM}^{-1}\\mathbf{K}_{NM}^T)}{n_{train}}}\n", + "\\end{equation}\n", + "\n", + "where $\\mathbf{K}_{NM}$ refers to the kernel between the **train set** and the active points. The same scaling should be applied to both the train and test sets." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K_scale = Knm_train @ np.linalg.pinv(Kmm, rcond=1.0E-12) @ Knm_train.T\n", + "K_scale = np.sqrt(np.trace(K_scale) / Knm_train.shape[0])\n", + "\n", + "Knm_train /= K_scale\n", + "Knm_test /= K_scale" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In computing the RKHS features, it might be wise to discard some of the smaller eigenvalues. For instance, if it has been centered, $\\mathbf{K}_{MM}$ has one _exactly_ zero eigenvalue, and we should take it out of the projection. [(Honeine 2014)](https://arxiv.org/pdf/1407.2904.pdf)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "vmm, Umm = np.linalg.eigh(Kmm)\n", + "\n", + "# Umm/vmm are already sorted, but in *increasing* order, so reverse them\n", + "Umm = np.flip(Umm, axis=1)\n", + "vmm = np.flip(vmm, axis=0)\n", + "\n", + "Umm = Umm[:, vmm > 0]\n", + "vmm = vmm[vmm > 0]\n", + "\n", + "Phi = (\n", + " Knm_train\n", + " @ Umm[:, : n_active - 1]\n", + " @ np.diagflat(1.0 / np.sqrt(vmm[0 : n_active - 1]))\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Re-center and scale the X data\n", + "X_train = (X_train - X_center) / X_scale\n", + "X_test = (X_test - X_center) / X_scale" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Sparse KPCA" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sparse kernel principal component analysis (sKPCA) is formulated in the same way as standard KPCA, with the exception that an approximate kernel matrix is used. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\mathbf{\\tilde{\\Phi}}$ is the feature matrix for the train points in the RKHS defined by the $M$ active set. Sparse KPCA can be understood (and derived) as PCA in the active set RKHS, by computing and diagonalising the covariance matrix built from $\\mathbf{\\tilde{\\Phi}}$. The covariance should be computed using *centered* kernel features, as discussed above\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{C} = \\mathbf{\\tilde{\\Phi}}^T \\mathbf{\\tilde{\\Phi}} = \\mathbf{U}_C \\mathbf{\\Lambda}_C \\mathbf{U}_C^T.\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "C = np.dot(Phi.T, Phi)\n", + "\n", + "v_C, U_C = np.linalg.eigh(C)\n", + "\n", + "# U_C/v_C are already sorted, but in *increasing* order, so reverse them\n", + "U_C = np.flip(U_C, axis=1)\n", + "v_C = np.flip(v_C, axis=0)\n", + "\n", + "U_C = U_C[:, v_C > 0]\n", + "v_C = v_C[v_C > 0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Projecting the Sparse KPCA\n", + "Projecting into latent space, we get\n", + "\n", + "\\begin{align}\n", + " \\mathbf{T} &= \\mathbf{\\tilde{\\Phi}} \\hat{\\mathbf{U}}_C \\\\\n", + " &= \\left(\\mathbf{K}_{NM}- \\bar{\\mathbf{K}}_M\\right)\\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{-1/2} \\hat{\\mathbf{U}}_C \\\\\n", + " &= \\mathbf{K}_{NM}\\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{-1/2} \\hat{\\mathbf{U}}_C -\\bar{\\mathbf{\\Phi}}\\hat{\\mathbf{U}}_C\\\\\n", + " &= \\mathbf{K}_{NM} \\mathbf{P}_{KT} - \\mathbf{\\bar{T}}\n", + "\\end{align}\n", + "\n", + "where our sKPCA projector from kernel space $\\mathbf{P}_{KT} = \\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{-1/2}\\mathbf{\\hat{U}}_C$, where $\\mathbf{\\hat{U}}_C$ contains the first $n_{PCA}$ eigenvectors of $\\mathbf{C}$. $\\mathbf{\\bar{T}} = \\bar{\\mathbf{\\Phi}}\\hat{\\mathbf{U}}_C$ centers in the latent space, and is computed and stored for future use." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PKT = (\n", + " Umm[:, : n_active - 1]\n", + " @ np.diagflat(1.0 / np.sqrt(vmm[0 : n_active - 1]))\n", + " @ U_C[:, :n_PC]\n", + ")\n", + "\n", + "T_train = Knm_train @ PKT\n", + "T_test = Knm_test @ PKT" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "ref_kpca = KernelPCA(\n", + " n_components=n_PC, kernel=\"rbf\", gamma=1.0, fit_inverse_transform=True\n", + ")\n", + "ref_kpca.fit(X_train)\n", + "T_kpca = ref_kpca.transform(X_test)\n", + "\n", + "plot_projection(\n", + " Y_test,\n", + " check_mirrors(T_test, T_kpca),\n", + " fig=fig,\n", + " ax=axes[0],\n", + " title=\"Sparse KPCA on {} Environments\".format(Kmm.shape[0]),\n", + " **cmaps\n", + ")\n", + "plot_projection(\n", + " Y_test,\n", + " T_kpca,\n", + " fig=fig,\n", + " ax=axes[1],\n", + " title=\"KPCA on {} Environments\".format(X_train.shape[0]),\n", + " **cmaps\n", + ")\n", + "\n", + "fig.subplots_adjust(wspace=0.4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also reconstruct $\\mathbf{X}$ using $\\mathbf{P}_{TX} = \\mathbf{\\Lambda}^{-1}\\mathbf{T}^T\\mathbf{X}$, as in KPCA." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PTX = np.diagflat(1.0 / (v_C[:n_PC])) @ T_train.T @ X_train\n", + "\n", + "Xr_test = T_test @ PTX" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Error and Loss\n", + "\n", + "The same loss functions are used as in KPCA, so we can compare the loss with that of KPCA" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K_approx_train = T_train @ T_train.T\n", + "\n", + "K_test_test = kernel_func(X_test, X_test)\n", + "K_approx_test = T_test @ T_test.T\n", + "\n", + "table_from_dict(\n", + " [\n", + " get_stats(\n", + " x=X_test,\n", + " xr=ref_kpca.inverse_transform(T_kpca),\n", + " y=Y_test,\n", + " t=T_kpca,\n", + " k=K_test,\n", + " kapprox=T_kpca @ T_kpca.T,\n", + " ),\n", + " get_stats(\n", + " x=X_test,\n", + " xr=Xr_test,\n", + " y=Y_test,\n", + " t=T_test,\n", + " k=K_test_test,\n", + " kapprox=K_approx_test,\n", + " ),\n", + " ],\n", + " headers=[\"KPCA\", \"sKPCA\"],\n", + " title=\"sKPCA\",\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Sparse KRR\n", + "\n", + "## Sparse KRR Weights\n", + "Let's see how sparsity works out in the case of regression. \n", + "\n", + "If we now build a (regularized) linear regression in the RKHS we get the loss\n", + "\n", + "\\begin{equation}\n", + "\\ell = \\lVert \\mathbf{Y} - \\mathbf{\\tilde{\\Phi}}\\mathbf{P}_{\\mathbf{\\tilde{\\Phi}} Y} \\rVert^2 + \n", + "\\lambda \\lVert\\mathbf{P}_{\\mathbf{\\tilde{\\Phi}} Y} \\rVert^2\n", + "\\end{equation}\n", + "\n", + "This is solved by \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{\\mathbf{\\tilde{\\Phi}} Y} = \\left(\\mathbf{\\tilde{\\Phi}}^T \\mathbf{\\tilde{\\Phi}}+ \\lambda \\mathbf{I}\\right)^{-1} \\mathbf{\\tilde{\\Phi}}^T \\mathbf{Y}\n", + "\\end{equation}\n", + "\n", + "or, by writing the last $\\mathbf{\\tilde{\\Phi}}^T$ in terms of the kernel:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{\\mathbf{\\tilde{\\Phi}} Y} = \\left(\\mathbf{\\tilde{\\Phi}}^T \\mathbf{\\tilde{\\Phi}}+ \\lambda \\mathbf{I}\\right)^{-1} \\mathbf{\\Lambda}_{MM}^{-1/2} \\mathbf{U}_{MM}^T \\mathbf{K}_{NM}^T \\mathbf{Y}\n", + "\\end{equation}\n", + "\n", + "**Note**: For (kernel) ridge regression, we can use either the centered feature matrix $\\mathbf{\\tilde{\\Phi}}$ or the uncentered feature matrix $\\mathbf{\\Phi}$. If we use $\\mathbf{\\tilde{\\Phi}}$, the property matrix $\\mathbf{Y}$ must also be centered for consistency." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "regularization = 1e-6" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's start from after we've computed our sparse kernels and recompute $\\mathbf{\\tilde{\\Phi}}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%time\n", + "\n", + "vmm, Umm = np.linalg.eigh(Kmm)\n", + "\n", + "# Umm/vmm are already sorted, but in *increasing* order, so reverse them\n", + "Umm = np.flip(Umm, axis=1)\n", + "vmm = np.flip(vmm, axis=0)\n", + "\n", + "Umm = Umm[:, vmm > 0]\n", + "vmm = vmm[vmm > 0]\n", + "\n", + "Phi = (\n", + " Knm_train\n", + " @ Umm[:, : n_active - 1]\n", + " @ np.diagflat(1.0 / np.sqrt(vmm[0 : n_active - 1]))\n", + ")\n", + "\n", + "PPY = Phi.T @ Phi\n", + "PPY = PPY + regularization * np.eye(Phi.shape[1])\n", + "PPY = np.linalg.pinv(PPY) @ Phi.T @ Y_train" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## An Often Cheaper, More Elegant Route\n", + "\n", + "We cast this expression into the more commonly used form by a series of simple manipulations that remove the need for diagonalizing $K_{MM}$ and computing $\\mathbf{\\tilde{\\Phi}}$. First, we redefine the weights so that \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\tilde{\\Phi}}\\mathbf{P}_{\\mathbf{\\tilde{\\Phi}} Y} = \n", + "\\mathbf{K}_{NM} \\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{-1/2} \\mathbf{P}_{\\mathbf{\\tilde{\\Phi}}Y} = \n", + "\\mathbf{K}_{NM} \\tilde{\\mathbf{P}_{K Y}}.\n", + "\\end{equation}\n", + "\n", + "Then,\n", + "\n", + "\\begin{align}\n", + "\\tilde{\\mathbf{P}_{K Y}} &= \n", + "\\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{-1/2}\n", + "\\mathbf{P}_{\\mathbf{\\tilde{\\Phi}} Y} \\\\\n", + "& = \\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{-1/2}\n", + "\\left(\\mathbf{\\tilde{\\Phi}}^T \\mathbf{\\tilde{\\Phi}}+ \\lambda \\mathbf{I}_M\\right)^{-1} \n", + "\\mathbf{\\Lambda}_{MM}^{-1/2} \\mathbf{U}_{MM}^T \n", + "\\mathbf{K}_{NM}^T \\mathbf{Y}\\\\\n", + "& = \n", + "\\left(\\mathbf{U}_{MM}\\mathbf{\\Lambda}_{MM}^{1/2}\\mathbf{\\tilde{\\Phi}}^T \\mathbf{\\tilde{\\Phi}}\\mathbf{\\Lambda}_{MM}^{1/2}\\mathbf{U}_{MM}^T+ \\lambda \\mathbf{U}_{MM}\\mathbf{\\Lambda}_{MM}\\mathbf{U}_{MM}^T\\right)^{-1} \n", + "\\mathbf{K}_{NM}^T \\mathbf{Y}.\n", + "\\end{align}\n", + "\n", + "Now, by noting that \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{U}_{MM} \\mathbf{\\Lambda}_{MM}^{1/2} \n", + "\\mathbf{\\tilde{\\Phi}}^T \\mathbf{\\tilde{\\Phi}}\n", + "\\mathbf{\\Lambda}_{MM}^{1/2} \\mathbf{U}_{MM}^T = \n", + "\\mathbf{K}_{NM}^T \\mathbf{K}_{NM},\n", + "\\end{equation}\n", + "\n", + "we see that the sparse KRR model weights is computed by\n", + "\n", + "\\begin{equation}\n", + "\\tilde{\\mathbf{P}_{K Y}} = \n", + "\\left(\\mathbf{K}_{NM}^T \\mathbf{K}_{NM}+ \\lambda \\mathbf{K}_{MM}\\right)^{-1} \n", + "\\mathbf{K}_{NM}^T \\mathbf{Y}.\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%time\n", + "\n", + "PKY = Knm_train.T @ Knm_train + regularization * Kmm\n", + "PKY = np.linalg.pinv(PKY)\n", + "PKY = PKY @ Knm_train.T @ Y_train" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you see, this trick provides a (in some cases considerable) speed-up." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Y_skrr_train = Knm_train @ PKY\n", + "Y_skrr_test = Knm_test @ PKY" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We compare our results with those from KRR." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "ref_krr = KernelRidge(alpha=regularization, **kernel_params)\n", + "ref_krr.fit(X=K_train, y=Y_train)\n", + "Y_krr = ref_krr.predict(X=K_test)\n", + "\n", + "plot_regression(Y_test[:, 0], Y_krr[:, 0], title=\"KRR\", fig=fig, ax=axes[0], **cmaps)\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " Y_skrr_test[:, 0],\n", + " title=\"Sparse KRR on {} Environments\".format(n_active),\n", + " fig=fig,\n", + " ax=axes[1],\n", + " **cmaps\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Error and Loss\n", + "\n", + "Here our loss function is:\n", + "\n", + "\\begin{equation}\n", + "\\ell_{regr} = \\left\\lVert \\mathbf{Y} - \\mathbf{K}_{NM}\\tilde{\\mathbf{P}_{K Y}}\\right\\rVert^2\n", + "\\end{equation}\n", + "\n", + "which we compare with KRR." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "table_from_dict(\n", + " [\n", + " get_stats(\n", + " x=X_test,\n", + " y=Y_test,\n", + " yp=Y_krr,\n", + " ),\n", + " get_stats(\n", + " x=X_test,\n", + " y=Y_test,\n", + " yp=Y_skrr_test,\n", + " ),\n", + " ],\n", + " headers=[\"KRR\", \"sKRR\"],\n", + " title=\"Ridge Regression\",\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Sparse KPCovR" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For Sparse KPCovR, instead of using the Nyström approximation as in previous sparse methods, we formulate sparse KPCovR from KPCovR in a similar manner to how we derived feature space PCovR from sample space PCovR in the [PCovR Notebook](2_PrincipalCovariatesRegression.ipynb).\n", + "\n", + "## A (Very) Quick Recap of Sample and Feature Space PCovR\n", + "In PCovR, we maximize the similarity\n", + "\n", + "\\begin{equation}\n", + "\\rho = \\operatorname{Tr}\\left(\\tilde{\\mathbf{T}}^T\\mathbf{\\tilde{K}}\\tilde{\\mathbf{T}}\\right),\n", + "\\end{equation}\n", + "\n", + "by taking as our whitened projection $\\tilde{\\mathbf{T}} = \\mathbf{XP}_{X\\tilde{T}}$ the eigenvectors corresponding to the $n_{PCA}$ largest eigenvalues of\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{\\tilde{K}} = \\alpha {\\mathbf{X} \\mathbf{X}^T}\n", + " + (1 - \\alpha) {\\hat{\\mathbf{Y}} \\hat{\\mathbf{Y}}^T},\n", + "\\end{equation}\n", + "\n", + "which combines correlations between the samples in feature and property space. \n", + "\n", + "If the number of features is less than the number of samples, we can equivalently rewrite our similarity function as\n", + "\n", + "\\begin{align}\n", + "\\rho &= \\operatorname{Tr}\\left(\\mathbf{P}_{X\\tilde{T}}^T\\mathbf{C}^{1/2}\\mathbf{C}^{-1/2}\\mathbf{X}^T\\mathbf{\\tilde{K}}\\mathbf{X}\\mathbf{C}^{-1/2}\\mathbf{C}^{1/2}\\mathbf{P}_{X\\tilde{T}}\\right)\n", + "\\end{align}\n", + "\n", + "and diagonalize a modified covariance\n", + "\n", + "\\begin{equation}\n", + "\\tilde{\\mathbf{C}} = \\mathbf{C}^{-1/2}\\mathbf{X}^T\\mathbf{\\tilde{K}}\\mathbf{X}\\mathbf{C}^{-1/2}\n", + "\\end{equation}\n", + "\n", + "where $\\mathbf{C} = \\mathbf{X}^T\\mathbf{X}$ to avoid diagonalizing the $n_{samples} \\times n_{samples}$ matrix $\\tilde{\\mathbf{K}}$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Now we just do feature-space PCovR in the RKHS\n", + "\n", + "In KPCovR, we maximize the similarity\n", + "\n", + "\\begin{equation}\n", + "\\rho = \\operatorname{Tr}\\left(\\tilde{\\mathbf{T}}^T\\mathbf{\\tilde{K}}\\tilde{\\mathbf{T}}\\right),\n", + "\\end{equation}\n", + "\n", + "however here $\\tilde{\\mathbf{T}} = \\mathbf{KP}_{KT}$.\n", + "We compute the projection in feature space by maximizing:\n", + "\n", + "\\begin{align}\n", + "\\rho = \\operatorname{Tr}\\left(\\mathbf{P}_{K\\tilde{T}}^T\\mathbf{\\tilde{\\Phi}}\\mathbf{\\tilde{\\Phi}}^T\\mathbf{\\tilde{K}}\\mathbf{\\tilde{\\Phi}}\\mathbf{\\tilde{\\Phi}}^T\\mathbf{P}_{K\\tilde{T}}\\right)\n", + "\\end{align}\n", + "\n", + "where $\\mathbf{K} = \\mathbf{\\tilde{\\Phi}}\\mathbf{\\tilde{\\Phi}}^T$.\n", + "It would make sense to use $\\mathbf{\\tilde{\\Phi}}^T\\mathbf{\\tilde{K}}\\mathbf{\\tilde{\\Phi}}$ as our sparse \"kernel\", but we must insert an identity to ensure that its eigenvectors are orthonormal. We use the covariance, defined as $\\mathbf{C} = \\mathbf{\\tilde{\\Phi}}^T\\mathbf{\\tilde{\\Phi}}$, giving:\n", + "\n", + "\\begin{align}\n", + "\\rho=\\operatorname{Tr}\\left(\\mathbf{P}_{K\\tilde{T}}^T\\mathbf{\\tilde{\\Phi}}\\mathbf{C}^{1/2}\n", + "\\mathbf{C}^{-1/2}\n", + "\\mathbf{\\tilde{\\Phi}}^T\\mathbf{\\tilde{K}}\\mathbf{\\tilde{\\Phi}}\\mathbf{C}^{-1/2}\n", + "\\mathbf{C}^{1/2}\n", + "\\mathbf{\\tilde{\\Phi}}^T\\mathbf{P}_{K\\tilde{T}}\\right)\n", + "\\end{align}\n", + "\n", + "which ensures orthonormality, as \n", + "\n", + "\\begin{align}\n", + "\\left(\\mathbf{P}_{K\\tilde{T}}^T\\mathbf{\\tilde{\\Phi}}\\mathbf{C}^{1/2}\n", + "\\mathbf{C}^{1/2}\n", + "\\mathbf{\\tilde{\\Phi}}^T\\mathbf{P}_{K\\tilde{T}}\\right)\n", + "&=\\left(\\mathbf{P}_{K\\tilde{T}}^T\\mathbf{\\tilde{\\Phi}}\\mathbf{\\tilde{\\Phi}}^T\\mathbf{\\tilde{\\Phi}}\\mathbf{\\tilde{\\Phi}}^T\\mathbf{P}_{K\\tilde{T}}\\right)\\\\\n", + "&=\\left(\\mathbf{P}_{K\\tilde{T}}^T\\mathbf{K}^T\\mathbf{K}\\mathbf{P}_{K\\tilde{T}}\\right)\\\\\n", + "&=\\left(\\tilde{\\mathbf{T}}^T\\tilde{\\mathbf{T}}\\right)\\\\\n", + "&=\\mathbf{I}\n", + "\\end{align}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "C = np.dot(Phi.T, Phi)\n", + "\n", + "v_C, U_C = np.linalg.eigh(C)\n", + "\n", + "# U_C/v_C are already sorted, but in *increasing* order, so reverse them\n", + "U_C = np.flip(U_C, axis=1)\n", + "v_C = np.flip(v_C, axis=0)\n", + "\n", + "U_C = U_C[:, v_C > 0]\n", + "v_C = v_C[v_C > 0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "In analogy with to feature-space PCovR, we define\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\tilde{C}} = \\mathbf{C}^{-1/2}\n", + "\\mathbf{\\tilde{\\Phi}}^T\\mathbf{\\tilde{K}}\\mathbf{\\tilde{\\Phi}}\\mathbf{C}^{-1/2}\n", + "\\end{equation}\n", + "\n", + "which evaluates to\n", + "\\begin{equation}\n", + "\\mathbf{\\tilde{C}} = \\alpha \\frac{\\mathbf{C}} {\\operatorname{Tr}(\\mathbf{C})/N} + (1 - \\alpha) \\mathbf{C}^{-1/2}\\mathbf{\\tilde{\\Phi}}^T\\mathbf{\\hat{Y}}\n", + "\\mathbf{\\hat{Y}}^T\\mathbf{\\tilde{\\Phi}}\\mathbf{C}^{-1/2},\n", + "\\end{equation}\n", + "\n", + "Here we normalize our covariance matrix by the factor $\\operatorname{Tr}(\\mathbf{C})/N$ to achieve a balance between the KRR and KPCA parts.\n", + "\n", + "**Note**: Since we use centered $\\mathbf{\\tilde{\\Phi}}$ for the KPCA part, we have to use $\\mathbf{\\tilde{\\Phi}}$ for the KRR part to keep it consistent. We can substitute $\\mathbf{\\hat{Y}}$ with the linear regression solution computed directly in active points RKHS: $\\mathbf{Y}_{sKRR} = \\mathbf{\\tilde{\\Phi}}\\left(\\mathbf{C}+ \\lambda \\mathbf{I}\\right)^{-1}\\mathbf{\\tilde{\\Phi}}^T \\mathbf{Y}$.\n", + "\n", + "" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "alpha = 0.5\n", + "regularization = 1e-6\n", + "\n", + "Csqrt = U_C @ np.diagflat(np.sqrt(v_C)) @ U_C.T\n", + "iCsqrt = U_C @ np.diagflat(1.0 / np.sqrt(v_C)) @ U_C.T\n", + "\n", + "C_pca = C / (np.trace(C) / C.shape[0])\n", + "\n", + "C_lr = np.linalg.pinv(C + regularization * np.eye(C.shape[0]))\n", + "C_lr = iCsqrt @ Phi.T @ Phi @ C_lr @ Phi.T @ Y_train.reshape(-1, Y_train.shape[-1])\n", + "C_lr = C_lr @ C_lr.T\n", + "\n", + "Ct = alpha * C_pca + (1 - alpha) * C_lr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can then find the eigendecomposition of \n", + "$\\mathbf{\\tilde{C}}=\n", + "\\mathbf{U}_\\mathbf{\\tilde{C}}\\mathbf{\\Lambda}_\\mathbf{\\tilde{C}}\\mathbf{U}_\\mathbf{\\tilde{C}}^T$ and \n", + "solve for $\\mathbf{P}_{\\tilde{\\Phi} T}$ (again analogous to feature-space PCovR, swapping $\\mathbf{\\tilde{\\Phi}}$ for $\\mathbf{X}$): \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{\\tilde{\\Phi} T}=\\mathbf{C}^{-1/2}\\mathbf{\\hat{U}}_\\mathbf{\\tilde{C}}\\mathbf{\\hat{\\Lambda}}_\\mathbf{\\tilde{C}}^{1/2} \n", + "\\end{equation}\n", + "\n", + "where the $\\hat{\\cdot}$ decoration denotes a truncation to $n_{PCA}$ components, as usual." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v_Ct, U_Ct = np.linalg.eigh(Ct)\n", + "\n", + "# U_Ct/v_Ct are already sorted, but in *increasing* order, so reverse them\n", + "U_Ct = np.flip(U_Ct, axis=1)\n", + "v_Ct = np.flip(v_Ct, axis=0)\n", + "\n", + "U_Ct = U_Ct[:, v_Ct > 0]\n", + "v_Ct = v_Ct[v_Ct > 0]\n", + "\n", + "PPT = iCsqrt @ U_Ct[:, :n_PC] @ np.diag(np.sqrt(v_Ct[:n_PC]))\n", + "v_Ct.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Projecting into Latent Space" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our projection in feature space takes the form:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{T} = \\mathbf{\\tilde{\\Phi}}_{NM}\\mathbf{P}_{\\tilde{\\Phi} T}\n", + "\\end{equation}\n", + "\n", + "If we want to project using a kernel rather than a feature space vector, this becomes:\n", + "\n", + "\\begin{align}\n", + "\\mathbf{T} &= \\left(\\mathbf{K}_{NM}-\\mathbf{\\bar{K}}_M\\right)\\mathbf{U}_{MM}\\mathbf{\\Lambda}_{MM}^{-1/2}\\mathbf{P}_{\\tilde{\\Phi} T} \\\\\n", + "&=\\mathbf{K}_{NM}\\mathbf{U}_{MM}\\mathbf{\\Lambda}_{MM}^{-1/2}\\mathbf{C}^{-1/2}\\mathbf{\\hat{U}}_\\mathbf{\\tilde{C}}\\mathbf{\\hat{\\Lambda}}_\\mathbf{\\tilde{C}}^{1/2} - \\mathbf{\\bar{\\Phi}}\\mathbf{P}_{\\tilde{\\Phi} T} \\\\\n", + "&= \\mathbf{K}_{NM}\\mathbf{P}_{KT} - \\mathbf{\\bar{T}}\n", + "\\end{align}\n", + "\n", + "where $\\mathbf{P}_{K T} = \\mathbf{P}_{K\\Phi} \\mathbf{P}_{\\Phi T} = \n", + "\\mathbf{U}_{MM}\\mathbf{\\Lambda}_{MM}^{-1/2}\\mathbf{C}^{-1/2}\\mathbf{\\hat{U}}_\\mathbf{\\tilde{C}}\\mathbf{\\hat{\\Lambda}}_\\mathbf{\\tilde{C}}^{1/2} $." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PKT = Umm[:, :n_active-1] @ np.diagflat(1/np.sqrt(vmm[:n_active-1])) @ PPT" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T = Knm_train @ PKT" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "T_skpcovr_test = Knm_test @ PKT" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We again compare to the non-sparse kernel version, giving" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "ref = KPCovR(mixing=alpha, n_components=2, center=True, **kernel_params)\n", + "ref.fit(X_train, Y_train)\n", + "t = ref.transform(X_test)\n", + "y = ref.predict(X_test)\n", + "\n", + "plot_projection(\n", + " Y_test,\n", + " check_mirrors(T_skpcovr_test, t),\n", + " fig=fig,\n", + " ax=axes[0],\n", + " title=\"Sparse KPCovR\",\n", + " **cmaps\n", + ")\n", + "plot_projection(Y_test, t, fig=fig, ax=axes[1], title=\"KPCovR\", **cmaps)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Predicting the Properties\n", + "\n", + "Property prediction takes the exact same form as in KPCovR, except with $\\mathbf{T}$ supplied by our sparse construction." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "PTY = T.T @ T\n", + "PTY = np.linalg.pinv(PTY) @ T.T @ Y_train" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Ypred = Knm_test @ PKT @ PTY\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=dbl_fig)\n", + "\n", + "plot_regression(\n", + " Y_test[:, 0],\n", + " Ypred[:, 0],\n", + " fig=fig,\n", + " ax=axes[0],\n", + " title=f\"Sparse KPCovR with {n_active} Environments\",\n", + " **cmaps,\n", + ")\n", + "plot_regression(Y_test[:, 0], y[:, 0], fig=fig, ax=axes[1], title=\"KPCovR\", **cmaps)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Next: CUR Decomposition and Feature Selection\n", + "\n", + "Continue on to the [next notebook](5_CUR.ipynb)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Implementation in `skcosmo`\n", + "\n", + "Here we have directly implemented sparse methods, many of which do not require the explicit determination of the feature vectors $\\mathbf{\\Phi}$. Instead, it is possible to determine the feature vectors and use simple, linear models for the regression and dimensionality reduction.\n", + "\n", + "Currently, `scikit-learn` gives a feature generator under kernel_approximation.Nystroem. This determines a sparse kernel with a random active set, and in `scikit-cosmo` we are actively developing a version where the active set can be predetermined." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.kernel_approximation import Nystroem" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.11" + }, + "toc": { + "base_numbering": 1, + "nav_menu": { + "height": "210px", + "width": "289px" + }, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "186.917px" + }, + "toc_section_display": true, + "toc_window_display": true + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/notebooks/5_CUR.ipynb b/notebooks/5_CUR.ipynb new file mode 100644 index 0000000..a3138c1 --- /dev/null +++ b/notebooks/5_CUR.ipynb @@ -0,0 +1,1341 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction and Background\n", + "\n", + "In this notebook, we demonstrate how to use CUR matrix decomposition to provide a low-rank approximation for a matrix. [(Mahoney 2009)](https://doi.org/10.1073/pnas.0803205106), [(Wikipedia)](https://en.wikipedia.org/wiki/CUR_matrix_approximation)\n", + "\n", + "As should not be surprising at this point, for each model, we first go step-by-step through the derivation, with equations, embedded links, and citations supplied where useful. Lastly, we employ a \"Utility Class\" for the model, which is found in the utilities folder and contains all necessary functions." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python3\n", + "import sys\n", + "import time\n", + "\n", + "# Maths things\n", + "import numpy as np\n", + "import scipy.sparse as sps\n", + "\n", + "# Plotting\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import rcParams, cm\n", + "\n", + "# Progress Bar\n", + "from tqdm.auto import tqdm\n", + "\n", + "# Local Utilities for Notebook\n", + "sys.path.append(\"../\")\n", + "from utilities.general import load_variables\n", + "from utilities.plotting import (\n", + " plot_simple,\n", + " plot_projection,\n", + " plot_regression,\n", + " check_mirrors,\n", + " get_cmaps,\n", + " table_from_dict,\n", + ")\n", + "from sklearn.decomposition import PCA\n", + "from sklearn.linear_model import Ridge as LR\n", + "from skcosmo.selection import FeatureCUR, FeatureFPS\n", + "from skcosmo.pcovr import pcovr_covariance\n", + "\n", + "cmaps = get_cmaps()\n", + "plt.style.use(\"../utilities/kernel_pcovr.mplstyle\")\n", + "dbl_fig = (2 * plt.rcParams[\"figure.figsize\"][0], plt.rcParams[\"figure.figsize\"][1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we must load the data. For a step-by-step explanation of this, please see [Importing Data](X_ImportingData.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var_dict = load_variables(n_FPS=None)\n", + "locals().update(var_dict)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Fundamentals of CUR\n", + "\n", + "PCA makes it possible to identify the directions of the maximal variance of a dataset. Finding a projection of a new point along those coordinates, however, requires computing all the features in the initial description of the problem.\n", + "\n", + "\n", + "CUR decomposition, instead, attempts to find a low-[rank](https://en.wikipedia.org/wiki/Rank_(linear_algebra)) approximation of the feature matrix that is computed without having to evaluate every feature, or without using every point in the data set. Usually, the matrices that enter the decomposition are labelled $\\mathbf{C}$, $\\mathbf{U}$, and $\\mathbf{R}$, with reference to columns and rows of the initial matrix. To avoid naming conflicts with other matrices used in the rest of the tutorial, for a given matrix $\\mathbf{A}$, we use the subscripts $c$ and $r$ to denote the matrices constructed out of the _columns_ and _rows_ of $\\mathbf{A}$, and $\\mathbf{S}$ for the rectangular matrix determined by $\\mathbf{A}_c$ and $\\mathbf{A}_r$. In other words, $\\mathbf{C}\\to\\mathbf{A}_c$, $\\mathbf{R}\\to\\mathbf{A}_r$, and $\\mathbf{U}\\to\\mathbf{S}$ and\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{A} \\approx \\tilde{\\mathbf{A}} \\equiv \\mathbf{A}_c \\mathbf{S} \\mathbf{A}_r,\n", + "\\end{equation}\n", + "\n", + "Many strategies have been proposed to choose the best columns and rows. We summarize a variation on the theme that was introduced in [(Imbalzano 2018)](https://doi.org/10.1063/1.5024611), that is comparatively time consuming, but deterministic and efficient in reducing the number of features needed to approximate $\\mathbf{A}$. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this exercise, we compute the CUR decomposition of our training set $\\mathbf{X}$. \n", + "Because we later use CUR to choose features, we omitted the step of furthest point sampling in loading our data." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X_train.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Choosing the Columns\n", + "\n", + "The CUR algorithm we implement modifies in-place the feature matrix. For this reason, we use a copy to perform the column selection" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "nCUR = 50\n", + "X_copy = X_train.copy()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The $c$ columns and $r$ rows are chosen based upon their \"influence\" on the overall matrix. We compute this \"influence\" using a **normalized statistical leverage score** $\\pi$ computed from the [**singular value decomposition**](https://en.wikipedia.org/wiki/Singular_value_decomposition): $\\mathbf{X} = \\mathbf{U}_K\\mathbf{\\Sigma U}_C^T$, where $\\mathbf{U_K}$ and $\\mathbf{U_C}$ are the right and left principal components, respectively, and coincide with the eigenvectors of the Gram matrix $\\mathbf{K} = \\mathbf{XX}^T$ and the covariance $\\mathbf{C} = \\mathbf{X}^T\\mathbf{X}$, also respectively. $\\mathbf{\\Sigma}$ is a rectangular-diagonal matrix with the singular values, which equal the square roots of the non-zero eigenvalues of both $\\mathbf{C}$ or $\\mathbf{K}$. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%time\n", + "(U_K, sig, U_C) = np.linalg.svd(X_copy)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "it helps (depending on the size of the matrix!) to use the sparse SVD from scipy.sparse to compute only $k$ components of the SVD, where $k$ is the target rank." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "k=1\n", + "\n", + "%time\n", + "(U_K, sig, U_C) = sps.linalg.svds(X_copy,k)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the $j^{th}$ column, the importance score is given by\n", + "\n", + "\\begin{equation}\n", + "\\pi_j = \\sum_i^k (U_C)_{ji}^2,\n", + "\\end{equation}\n", + "\n", + "where $k$ is again the target rank of the new matrix and $(U_C)_{ji}$ is the value in the $j^{th}$ row and $i^{th}$ column of $\\mathbf{U}_C$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pi = (U_C[:k] ** 2.0).sum(axis=0)\n", + "j = pi.argmax()\n", + "\n", + "plt.plot(pi)\n", + "plt.scatter(j, max(pi))\n", + "plt.xlabel(\"j\")\n", + "plt.ylabel(r\"$\\pi_j$\")\n", + "plt.title(f\"Column {j} is most influential.\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Orthogonalizing the Rest of the Columns\n", + "\n", + "Most CUR algorithms select elements in a stochastic manner based on the statistical leverage score. Here we select in a deterministic manner the most influential feature. \n", + "After choosing the $j^{th}$ column, we must orthogonalize the remaining $j'$ columns with respect to the $j^{th}$ column that has just been selected and removed. This way we make sure that redundant entries won't be chosen over and over.\n", + "\n", + "\\begin{equation}\n", + "X_{j'} = X_{j'} - X_{j}\\left(\\frac{\\mathbf{X}_j\\cdot \\mathbf{X}_{j'}}{\\mathbf{X}_j\\cdot \\mathbf{X}_{j}}\\right).\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v = X_copy[:, j] / np.sqrt(X_copy[:, j] @ X_copy[:, j])\n", + "\n", + "for i in range(X_copy.shape[1]):\n", + " X_copy[:, i] -= v * np.dot(v, X_copy[:, i])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "we can repeat the procedure several times, until we've collected enough entries" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "idxs = [j]\n", + "\n", + "for n in tqdm(range(nCUR - 1)):\n", + " (U_K, sig, U_C) = sps.linalg.svds(X_copy, k)\n", + " pi = (U_C[:k] ** 2.0).sum(axis=0)\n", + " idxs.append(pi.argmax())\n", + "\n", + " v = X_copy[:, idxs[-1]] / np.sqrt(X_copy[:, idxs[-1]] @ X_copy[:, idxs[-1]])\n", + "\n", + " for i in range(X_copy.shape[1]):\n", + " X_copy[:, i] -= v * np.dot(v, X_copy[:, i])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have our column indices and construct $\\mathbf{X}_C$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "idxs = np.asarray(idxs)\n", + "\n", + "X_c = X_train[:, idxs]\n", + "X_c.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Choosing the Rows\n", + "If the matrix we are decomposing is symmetric, we can use the same indices for the columns and rows. If it is non-symmetric (such as $\\mathbf{X}$ is here), the $r$ most influential rows are found by computing the $r$ most influential columns of the transpose of the matrix" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "idxs_r = []\n", + "X_T = X_train.copy().T\n", + "\n", + "for n in tqdm(range(nCUR)):\n", + " (U_K, sig, U_C) = sps.linalg.svds(X_T, k)\n", + " pi = (U_C[:k] ** 2.0).sum(axis=0)\n", + " idxs_r.append(pi.argmax())\n", + "\n", + " v = X_T[:, idxs_r[-1]] / np.sqrt(X_T[:, idxs_r[-1]] @ X_T[:, idxs_r[-1]])\n", + "\n", + " for i in range(X_T.shape[1]):\n", + " X_T[:, i] -= v * np.dot(v, X_T[:, i])\n", + "\n", + "X_r = X_train[idxs_r]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constructing the Approximation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One determines $\\mathbf{S}$ by computing the [pseudoinverse](https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse) of $\\mathbf{X}_c$ and $\\mathbf{X}_r$,\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{S} = \\mathbf{X}_c^- \\mathbf{X} \\mathbf{X}_r^- = (\\mathbf{X}_c^T \\mathbf{X}_c)^{-1} \\mathbf{X}_c^T \\mathbf{X}(\\mathbf{X}_r^T\\mathbf{X}_r)^{-1} \\mathbf{X}_r^T .\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S_c = np.linalg.pinv(X_c)\n", + "S_r = np.linalg.pinv(X_r)\n", + "\n", + "S = S_c @ X_train @ S_r" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The approximate $\\mathbf{\\tilde{X}}$ is the same shape as $\\mathbf{X}$, but is low-rank. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Xt = X_c @ S @ X_r\n", + "\n", + "print(np.linalg.matrix_rank(Xt), np.linalg.matrix_rank(X_train))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "... and approximates $\\mathbf{X}$, in a way that can be improved by increasing the number of rows and columns" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "np.linalg.norm(Xt - X_train) / np.linalg.norm(X_train)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def approx_X(A, col_idx, row_idx=None):\n", + " \"\"\" Approximates the full matrix with selected features \"\"\"\n", + "\n", + " A_c = A[:, col_idx]\n", + " S_c = np.linalg.pinv(A_c)\n", + "\n", + " A_r = A[row_idx]\n", + "\n", + " if row_idx is not None:\n", + " S_r = np.linalg.pinv(A_r)\n", + " S = S_c @ A @ S_r\n", + " else:\n", + " S = S_c\n", + "\n", + " return A_c @ S @ A_r" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CUR for Feature Selection\n", + "\n", + "If one chooses to use CUR to select columns/features (analogous to how we have used FPS), the row matrix $\\mathbf{X}_r$ is just the full $\\mathbf{X}$, and so one determines $\\mathbf{S}$ by computing the pseudoinverse of $\\mathbf{X}_c$ and $\\mathbf{X}$,\n", + "\\begin{equation}\n", + "\\mathbf{S} = \\mathbf{X}_c^- \\mathbf{X} \\mathbf{X}^-\n", + "=(\\mathbf{X}_c^T \\mathbf{X}_c)^{-1} \\mathbf{X}_c^T \\mathbf{X} (\\mathbf{X}^T\\mathbf{X})^{-1} \\mathbf{X}^T.\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S_c = np.linalg.pinv(X_c)\n", + "S_X = np.linalg.pinv(X_train)\n", + "\n", + "S = S_c @ X_train @ S_X\n", + "\n", + "Xt_raw = X_c @ S @ X_train" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For feature selection $\\tilde{\\mathbf{X}}$ reduces to:\n", + "\n", + "\\begin{align}\n", + "\\tilde{\\mathbf{X}} &= \\mathbf{X}_c(\\mathbf{X}_c^T \\mathbf{X}_c)^{-1} \\mathbf{X}_c^T \\mathbf{X} (\\mathbf{X}^T\\mathbf{X})^{-1} \\mathbf{X}^T\\mathbf{X}\\\\\n", + "\\tilde{\\mathbf{X}} &= \\mathbf{X}_c(\\mathbf{X}_c^T \\mathbf{X}_c)^{-1} \\mathbf{X}_c^T \\mathbf{X}\n", + "\\end{align}\n", + "\n", + "so $\\mathbf{S}$ is instead computed as\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{S} = (\\mathbf{X}_c^T \\mathbf{X}_c)^{-1} \\mathbf{X}_c^T\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S = np.linalg.pinv(X_c)\n", + "Xt = X_c @ S @ X_train" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "np.linalg.norm(Xt_raw - Xt)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We use the utility `approx_A(X_train, idx)` in `utilities/CUR.py` to do this process from now on. \n", + "\n", + "With this dataset (but not all datasets), CUR minimizes the loss compared to FPS, especially for small numbers of columns." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ns = np.array([int(10 ** x) for x in np.linspace(1, np.log10(nCUR), 20)])\n", + "ifps = FeatureFPS(X=X_train).select(n)\n", + "\n", + "X_CUR = [approx_X(X_train, idxs[:n]) for n in ns]\n", + "X_FPS = [approx_X(X_train, ifps[:n]) for n in ns]\n", + "\n", + "err_CUR = np.array(\n", + " [np.linalg.norm(X_train - Xt) / np.linalg.norm(X_train) for Xt in X_CUR]\n", + ")\n", + "err_FPS = np.array(\n", + " [np.linalg.norm(X_train - Xt) / np.linalg.norm(X_train) for Xt in X_FPS]\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(1, figsize=dbl_fig)\n", + "\n", + "plt.loglog(ns, err_CUR, marker=\"o\", label=\"CUR\", c=\"r\")\n", + "plt.loglog(ns, err_FPS, marker=\"o\", label=\"FPS\", c=\"b\")\n", + "\n", + "ax.set_xlabel(\"# Columns\")\n", + "ax.set_ylabel(r\"$\\frac{|X-\\tilde{X}|}{|X|}$\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Using the Approximation in ML Models\n", + "\n", + "## Projecting into Latent Space" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Whenever the features are used to approximate distances or scalar products, it is possible to obtain a $n_{samples}\\times n_{CUR}$ reduced feature matrix $\\mathbf{T} = \\mathbf{X}_c \\mathbf{P}_{X_c T}$ that yields the exact same values as when using the approximate $\\tilde{\\mathbf{X}}$. For the sake of brevity, we abbreviate $\\mathbf{P}_{X_c T}$ to $\\mathbf{P}_c$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The idea is to compute $\\mathbf{T}$ such that $\\mathbf{TT}^T$ is identical to $\\mathbf{\\tilde{X}\\tilde{X}}^T$. Given the definition of $\\mathbf{\\tilde{X}}$, we get \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\tilde{X}\\tilde{X}}^T = \\mathbf{X}_c\\mathbf{SX}_r\\mathbf{X}_r^T\\mathbf{S}^T\\mathbf{X}_c^T=\n", + "\\mathbf{X}_c \\mathbf{P}_c\\mathbf{P}_c^T \\mathbf{X}_c^T = \\mathbf{TT}^T\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Which yields the symmytric solution\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{P}_{c} = \\left[ \\mathbf{SX}_r\\mathbf{X}_r^T\\mathbf{S} \\right]^{1/2}. \\label{eq:cur-t}\n", + "\\end{equation}\n", + "\n", + "The $n_{CUR} \\times n_{CUR}$ matrix $\\mathbf{P}_{c}$ is computed once and re-used every time one needs to compute $\\mathbf{T}$ for new samples. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S_c = np.linalg.pinv(X_c)\n", + "S_r = np.linalg.pinv(X_r)\n", + "\n", + "S = S_c @ X_train @ S_r\n", + "\n", + "SX = S @ X_r\n", + "SXXS = SX @ SX.T\n", + "\n", + "v_SX, U_SX = np.linalg.eigh(SXXS)\n", + "v_SX[v_SX < 1e-12] = 0\n", + "\n", + "P_c = U_SX @ np.diagflat(np.sqrt(v_SX))\n", + "\n", + "T = X_c @ P_c\n", + "T_test = X_test[:, idxs] @ P_c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From now on, we use the utility function `compute_P(X_c, S, X_r)` in `utilities/CUR.py` to do this. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def compute_P(A_c, S, A_r, thresh=1e-12):\n", + " \"\"\" Computes the latent-space projector for the feature matrix \"\"\"\n", + " SA = S @ A_r\n", + " SA = SA @ SA.T\n", + "\n", + " v_SA, U_SA = np.linalg.eigh(SA)\n", + " v_SA[v_SA < thresh] = 0\n", + "\n", + " return U_SA @ np.diagflat(np.sqrt(v_SA))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Representation error" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The CUR latent space approximates very well the principal components of the feature space. The eigenvalues of the latent-space covariance match those of the full covariance. Note also how the scaling by $\\mathbf{P}_c$ of $\\mathbf{X}_c$ improves dramatically the match." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(2, sharex=True, figsize=(10, 12))\n", + "\n", + "eigTTT = np.array(list(reversed(np.linalg.eigvalsh(T.T @ T))))\n", + "eigXcTXc = np.array(list(reversed(np.linalg.eigvalsh(X_c.T @ X_c)[-T.shape[1] :])))\n", + "eigXTX = np.array(\n", + " list(reversed(np.linalg.eigvalsh(X_train.T @ X_train)[-T.shape[1] :]))\n", + ")\n", + "\n", + "ax[0].semilogy(eigTTT, \"r\", label=r\"$\\lambda_{T^T T}$\")\n", + "ax[0].semilogy(eigXcTXc, \"r--\", label=r\"$\\lambda_{X_c^T X_c}$\")\n", + "ax[0].semilogy(eigXTX, \"b\", label=r\"$\\lambda_{X^T X}$\")\n", + "\n", + "ax[0].legend()\n", + "ax[0].set_ylabel(r\"$\\lambda_n$\", fontsize=20)\n", + "\n", + "error = [abs(t - a) / a for t, a in zip(eigTTT, eigXTX)]\n", + "ax[1].semilogy(error, marker=\"o\")\n", + "ax[1].set_ylabel(\n", + " r\"$\\frac{|\\lambda_{X^T X}-\\lambda_{T^T T}|}{|\\lambda_{X^T X}|}$\", fontsize=20\n", + ")\n", + "ax[1].set_xlabel(\"n\", fontsize=20)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A measure of error is given by the accuracy in representing the Gram matrix (the Torgenson loss)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(\"Torgenson loss with raw column selection\", \n", + " np.linalg.norm(X_train @ X_train.T - X_c @ X_c.T))\n", + "print(\"Torgenson loss with scaled, CUR latent space\", \n", + " np.linalg.norm(X_train @ X_train.T - T @ T.T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## PCA Performance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's compare the projections and errors with the original $\\mathbf{X}$ and the CUR feature-selected $\\mathbf{\\tilde{X}}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pca_high_rank = PCA(n_components=2)\n", + "pca_high_rank.fit(X_train)\n", + "T_high_rank = pca_high_rank.transform(X_test)\n", + "\n", + "S = np.linalg.pinv(X_c)\n", + "P = compute_P(X_train[:, idxs], S, X_train)\n", + "\n", + "# we find the CUR latent space for train and test\n", + "T_train = X_train[:, idxs] @ P\n", + "T_test = X_test[:, idxs] @ P\n", + "\n", + "pca_low_rank = PCA(n_components=2)\n", + "pca_low_rank.fit(T_train)\n", + "T_low_rank = pca_low_rank.transform(T_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The projections based on the CUR selected features reproduce well those based on the full dataset." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plotting\n", + "fig, ax = plt.subplots(1,2, figsize=(12,5))\n", + "\n", + "plot_projection(Y=Y_test, T=T_high_rank, fig=fig, ax=ax[0], \n", + " title=\"Projection using Original Data\", \n", + " **cmaps)\n", + "plot_projection(Y=Y_test, T=check_mirrors(T_low_rank,T_high_rank), \n", + " fig=fig, ax=ax[1], \n", + " title=\"Projection using Low-Rank Approximation\", \n", + " **cmaps)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "PCA statistics are not particularly meaningful, because they report on the performance of PCA in representing the full or CUR-reduced feature space." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## LR Performance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is more meaningful to compare the performance of a regression model built on the full $\\mathbf{X}$ or on the latent CUR space" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "lr_high_rank = LR(alpha=1e-6)\n", + "lr_high_rank.fit(X_train, Y_train)\n", + "Ylr_high_rank = lr_high_rank.predict(X_test)\n", + "\n", + "lr_low_rank = LR(alpha=1e-6)\n", + "lr_low_rank.fit(T_train, Y_train)\n", + "Ylr_low_rank = lr_low_rank.predict(T_test)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plotting\n", + "\n", + "fig, ax = plt.subplots(1,2, figsize=(12,5))\n", + "\n", + "Yerr = np.abs(Y_test-Ylr_high_rank)\n", + "plot_regression(Y=Y_test[:,0], Yp=Ylr_high_rank[:,0], \n", + " fig=fig, ax=ax[0], \n", + " title=\"Regression using Original Data\", \n", + " vmin=Yerr.min(), vmax=Yerr.max(),\n", + " **cmaps)\n", + "plot_regression(Y=Y_test[:,0], Yp=Ylr_low_rank[:,0],\n", + " fig=fig, ax=ax[1], \n", + " vmin=Yerr.min(), vmax=Yerr.max(),\n", + " title=\"Regression using Low-Rank Approximation\", \n", + " **cmaps)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Need for Orthogonalizing\n", + "\n", + "Now that we know how to compute the error of each approximation, we look at the importance of the orthogonalization procedure discussed in Sec. 2.2. \n", + "\n", + "Imagine we were to choose all of our columns at once, corresponding to the top $n_{CUR}$ features based on their leverage score." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "(U_K, sig, U_C) = np.linalg.svd(X_train)\n", + "pi = (U_C[:k]**2.0).sum(axis=0)\n", + "\n", + "idxs_oneoff = np.flip(np.argsort(pi))[:nCUR]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Or, as is typically done with CUR, we iteratively choose our columns, but without the step of orthogonalizing." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X_copy = X_train.copy()\n", + "\n", + "idxs_no_orth=[]\n", + "for n in tqdm(range(nCUR)):\n", + " (U_K, sig, U_C) = sps.linalg.svds(X_copy,k)\n", + " pi = (U_C[:k]**2.0).sum(axis=0)\n", + "\n", + " idxs_no_orth.append(pi.argmax())\n", + " X_copy[:,idxs_no_orth]=0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we compare the Gram matrix approximation performance" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S_oneoff = np.linalg.pinv(X_train[:, idxs_oneoff]) @ X_train @ np.linalg.pinv(X_train)\n", + "P_oneoff = compute_P(X_train[:, idxs_oneoff], S_oneoff, X_train)\n", + "T_train_oneoff = X_train[:, idxs_oneoff] @ P_oneoff\n", + "T_test_oneoff = X_test[:, idxs_oneoff] @ P_oneoff\n", + "\n", + "S_no_orth = np.linalg.pinv(X_train[:, idxs_no_orth]) @ X_train @ np.linalg.pinv(X_train)\n", + "P_no_orth = compute_P(X_train[:, idxs_no_orth], S_no_orth, X_train)\n", + "T_train_no_orth = X_train[:, idxs_no_orth] @ P_no_orth\n", + "T_test_no_orth = X_test[:, idxs_no_orth] @ P_no_orth\n", + "\n", + "print(\"Torgenson loss with one-off leverage score selection\", \n", + " np.linalg.norm(X_train @ X_train.T-T_train_oneoff@T_train_oneoff.T))\n", + "\n", + "print(\"Torgenson loss with iterative selection, no orthogonalisation\", \n", + " np.linalg.norm(X_train@X_train.T-T_train_no_orth@T_train_no_orth.T))\n", + "\n", + "print(\"Torgenson loss with iterative orthogonalisation\", \n", + " np.linalg.norm(X_train@X_train.T-T_train@T_train.T))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PCov-CUR" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The New Leverage Scores\n", + "\n", + "The PCovR formulation is particularly appealing to select a small number of ML features to be used for machine learning, because it allows incorporating information on the ability of different features to predict the target properties.\n", + "We propose to proceed as in Section 3, but to compute the leverage scores by computing the eigenvectors of the PCovR covariance matrix $\\mathbf{\\tilde{C}}$ in place of the singular value decomposition, given by \n", + "\n", + "\\begin{equation}\n", + "\\tilde{\\mathbf{C}} = \\alpha \\mathbf{C}\n", + " + (1 - \\alpha) \\mathbf{C}^{1/2}\\left(\\mathbf{C}+\\lambda \\mathbf{I}\\right)^{-1}\\mathbf{X}^T{\\mathbf{Y} \\mathbf{Y}^T}\\mathbf{X}\\left(\\mathbf{C}+\\lambda \\mathbf{I}\\right)^{-1}\\mathbf{C}^{1/2}\n", + "\\end{equation}\n", + "\n", + "where $\\mathbf{C} = \\mathbf{X}^T\\mathbf{X}$. The best results are obtained by computing leverage scores using a number of eigenvectors that is smaller or equal than the number of properties in $\\mathbf{Y}$. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because we have to calculate $\\mathbf{\\tilde{C}}$ iteratively, we use a utility function `get_Ct(X, Y, alpha)`" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X_copy = X_train.copy()\n", + "Y_copy = Y_train.copy()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "k = 1\n", + "alpha = 0.5\n", + "nCUR = 10\n", + "Ct = pcovr_covariance(X=X_copy, Y=Y_copy, mixing=alpha, rcond=1e-7)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v_Ct, U_Ct = sps.linalg.eigs(Ct, k=1)\n", + "U_Ct = U_Ct[:, np.argsort(-v_Ct)]\n", + "v_Ct = v_Ct[np.argsort(-v_Ct)]\n", + "\n", + "pi = (U_Ct[:,:k]**2.0).sum(axis=1)\n", + "j = pi.argmax()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.plot(pi)\n", + "plt.scatter(j, max(pi))\n", + "plt.xlabel(\"j\")\n", + "plt.ylabel(r\"$\\pi_j$\")\n", + "plt.title(f\"Column {j} is most influential.\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X_c = X_copy[:, [j]]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Adjusting the Remaining Columns\n", + "\n", + "The only additional change that needs to be incorporated in the procedure described in Sec. 2.2 involves eliminating at each step the components of the property matrix $\\mathbf{Y}$ that is described by the features that have already been selected and removed. Computing at each step the reduced vector $\\mathbf{T} = \\mathbf{X}_c\\mathbf{P}_{c}$, one should perform the update \n", + "\n", + "\\begin{equation}\n", + " \\mathbf{Y} = \\mathbf{Y} - \\mathbf{T} \\left(\\mathbf{T}^T \\mathbf{T}\\right)^{-1}\\mathbf{T}^T \\mathbf{Y}.\n", + "\\end{equation}\n", + "\n", + "Note that when the linear regression is performed without regularisation, the transformation from $\\mathbf{X}_c$ to $\\mathbf{T}$ is inconsequential (as it can be seen just by cancelling out instances of $\\mathbf{P}_{c}$, which one can do when $\\mathbf{P}_{c}$ is invertible and symmetric). We can then avoid the calculation of the projection matrix and simply do\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{Y} = \\mathbf{Y} - \\mathbf{X}_c \\left(\\mathbf{X}_c^T \\mathbf{X}_c\\right)^{-1}\\mathbf{X}_c^T \\mathbf{Y}.\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S = np.linalg.pinv(X_c)\n", + "\n", + "SX = S @ X_copy\n", + "SX = SX @ SX.T \n", + "\n", + "v_SX, U_SX = np.linalg.eigh(SX) \n", + "v_SX[v_SX<1e-12] = 0\n", + "\n", + "P_c = U_SX @ np.diagflat(np.sqrt(v_SX))\n", + "\n", + "T = X_c @ P_c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "See how the two vectors are the same" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v1 = np.linalg.pinv(T.T @ T)\n", + "v1 = T @ v1\n", + "v1 = v1 @ T.T\n", + "\n", + "v2 = np.linalg.pinv(X_c.T @ X_c)\n", + "v2 = X_c @ v2\n", + "v2 = v2 @ X_c.T\n", + "print(np.linalg.norm(v1-v2))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Y_copy -= v2 @ Y_copy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just like in Sec. 2.2, we must orthogonalize the remaining $j'$ columns in $\\mathbf{X}$ with respect to the $j^{th}$ column that has just been removed.\n", + "\n", + "\\begin{equation}\n", + "X_{kj'} = X_{kj'} - X_{kj}\\left(\\frac{\\mathbf{X}_j\\cdot \\mathbf{X}_{j'}}{\\mathbf{X}_j\\cdot \\mathbf{X}_{j}}\\right).\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "v = X_copy[:,j]/np.sqrt(X_copy[:, j] @ X_copy[:, j])\n", + "\n", + "for i in range(X_copy.shape[1]):\n", + " X_copy[:,i] -= v * np.dot(v,X_copy[:,i])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Choosing the Remaining Columns\n", + "\n", + "We then iterate until we've chosen the right number of columns (beware: this can be slow!)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "idxs = [j]\n", + "\n", + "for n in tqdm(range(nCUR-1)):\n", + " \n", + " try:\n", + " Ct = pcovr_covariance(X=X_copy, Y=Y_copy, mixing=alpha, rcond=1e-7)\n", + " except:\n", + " print(f\"Only {n} features possible\")\n", + " break\n", + " \n", + " v_Ct, U_Ct = sps.linalg.eigs(Ct, k=1)\n", + " U_Ct = U_Ct[:, np.argsort(-v_Ct)]\n", + " v_Ct = v_Ct[np.argsort(-v_Ct)]\n", + " \n", + " pi = (U_Ct[:,:k]**2.0).sum(axis=1)\n", + " \n", + " j=pi.argmax()\n", + " idxs.append(j)\n", + " \n", + " X_c = X_copy[:, idxs]\n", + " v = np.linalg.pinv(X_c.T @ X_c)\n", + " v = X_c @ v\n", + " v = v @ X_c.T\n", + "\n", + " Y_copy -= v @ Y_copy\n", + " \n", + " v = X_copy[:,j]/np.sqrt(X_copy[:, j] @ X_copy[:, j])\n", + "\n", + " for i in range(X_copy.shape[1]):\n", + " X_copy[:,i] -= v * np.dot(v,X_copy[:,i])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "idxs = np.asarray(idxs)\n", + "idxs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## LR Performance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We do the usual gig to find the CUR latent space" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S = np.linalg.pinv(X_train[:,idxs])\n", + "P = compute_P(X_train[:, idxs], S, X_train)\n", + "\n", + "# we find the CUR latent space for train and test\n", + "T_pcov = X_train[:, idxs] @ P\n", + "T_pcov_test = X_test[:, idxs] @ P\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "... and show how choosing columns with a PCovR-based leverage score improve substantially the regression performance (note that you must have run the previous cells in the notebook to see the stats from the vanilla CUR)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "lr_pcov = LR(alpha=1e-6)\n", + "lr_pcov.fit(T_pcov, Y_train)\n", + "Ylr_pcov = lr_pcov.predict(T_pcov_test)\n", + "\n", + "plot_regression(Y_test, Ylr_pcov)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Utility Classes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## CUR Framework" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "cur = FeatureCUR(X=X_train, progress_bar=True)\n", + "idx_cur = cur.select(max(ns))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "errors = [np.linalg.norm(X_test - approx_X(X_test, idx_cur[:n]))**2.0 / np.linalg.norm(X_test)**2 for n in tqdm(ns)]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot_simple(np.array([ns, errors]).T, **cmaps)\n", + "plt.xlabel(r\"$n_{CUR}$\", fontsize=20)\n", + "plt.ylabel(r\"$\\frac{\\left| X - \\tilde{X} \\right|}{| X |}$\", fontsize=20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## PCov-CUR\n", + "\n", + "If you want to compute your importance scores using $\\mathbf{U}_{\\tilde{C}}$, you can provide the class `\\mixing < 1` and a set of properties" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "cur = FeatureCUR(X=X_train, Y=Y_train, mixing=0.5, progress_bar=True)\n", + "idx_pcov = cur.select(max(ns))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "error_pcovs = [\n", + " np.linalg.norm(X_test - approx_X(X_test, idx_pcov[:n])) ** 2.0\n", + " / np.linalg.norm(X_test) ** 2\n", + " for n in tqdm(ns)\n", + "]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot_simple(np.array([ns, error_pcovs]).T, **cmaps)\n", + "plt.xlabel(r\"$n_{CUR}$\", fontsize=20)\n", + "plt.ylabel(r\"$\\frac{\\left| X - \\tilde{X} \\right|}{| X |}$\", fontsize=20)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.linear_model import RidgeCV\n", + "def regression_error(idx):\n", + " ridge = RidgeCV(fit_intercept=False, alphas = np.logspace(-8,-4,10), cv=2)\n", + " ridge.fit(X_train[:, idx], Y_train)\n", + " return np.linalg.norm(Y_test - ridge.predict(X_test[:, idx]))**2.0 / np.linalg.norm(Y_test)**2.0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "error_regr_pcovs = [\n", + " regression_error(idx_pcov[:n])\n", + " for n in tqdm(ns)\n", + "]\n", + "error_regr_cur = [\n", + " regression_error(idx_cur[:n])\n", + " for n in tqdm(ns)\n", + "]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plt.loglog(ns, error_regr_pcovs, c='b', label='PCov-CUR')\n", + "plt.loglog(ns, error_regr_cur, c='r', label='Classic CUR')\n", + "plt.xlabel(r\"$n_{CUR}$\", fontsize=20)\n", + "plt.ylabel(r\"$\\frac{\\left| Y - \\hat{Y} \\right|}{| Y |}$\", fontsize=20)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.11" + }, + "toc": { + "base_numbering": 1, + "nav_menu": { + "height": "210px", + "width": "289px" + }, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "186.917px" + }, + "toc_section_display": true, + "toc_window_display": true + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/notebooks/6_Putting_it_All_Together.ipynb b/notebooks/6_Putting_it_All_Together.ipynb new file mode 100644 index 0000000..0451f8b --- /dev/null +++ b/notebooks/6_Putting_it_All_Together.ipynb @@ -0,0 +1,992 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this notebook, we will tie in many of the pieces covered in this tutorial.\n", + "\n", + "First, we will take a materials dataset, in the form of cartesian coordinates, and translate it into SOAP descriptors using `librascal`, as was covered briefly in [**X_ImportingData.ipynb**](X_ImportingData.ipynb).\n", + "\n", + "Next, we'll reduce the feature space of these SOAP vectors using PCov-CUR, which is covered in [**5_CUR.ipynb**](5_CUR.ipynb). \n", + "\n", + "From here, we'll select an _active_ set of samples using PCov-CUR and use them to build a set of sparse kernels, as was introduced [**4_SparseKernelMethods.ipynb**](4_SparseKernelMethodsipynb), and use this sparse kernel to build a `SparseKPCovR` map.\n", + "\n", + "Finally, we will port this `SparseKPCovR` into a `chemiscope` visualization (covered in [**1_LinearMethods.ipynb**](1_LinearMethods.ipynb)), which can be loaded on [chemiscope.org](chemiscope.org).\n", + "\n", + "With each of the sections, we'll provide a \"fast-forward\" cell, where you can skip the section by un-commenting and executing the cell. For example, if you have pre-computed your SOAP vectors and would like to simply import them, skip section 1 and execute the cell under `1.1 Skip Computing SOAPS`.\n", + "\n", + "To run all cells of this notebook, you will need to have the following packages installed:\n", + "- numpy (https://numpy.org/)\n", + "- scikit-learn (https://www.scikit-learn.org)\n", + "- scipy (https://www.scipy.org)\n", + "- matplotlib (https://www.https://matplotlib.org/)\n", + "- ase (https://wiki.fysik.dtu.dk/ase/)\n", + "- librascal (https://github.com/cosmo-epfl/librascal)\n", + "- scikit-cosmo (https://github.com/cosmo-epfl/scikit-cosmo)\n", + "- chemiscope ((https://github.com/cosmo-epfl/chemiscope)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python3\n", + "import sys\n", + "import numpy as np\n", + "from sklearn.linear_model import RidgeCV\n", + "\n", + "\n", + "def calc_rmse(y1, y2, y_scaler, rounding=4):\n", + " \"\"\"quick function to compute the root-mean-squared-error in real units\n", + "\n", + " Parameters\n", + " ==========\n", + " y1, y2: ndarray (n_samples x n_properties)\n", + " predicted and true property values in reduced units.\n", + " order is not important.\n", + " y_scaler: trained scaler which can return y1 and y2 to real units by calling y_scaler.inverse_transform\n", + " rounding: int\n", + " number of decimals to round to, defaults to 4\n", + " \"\"\"\n", + "\n", + " rmse = round(\n", + " np.mean(\n", + " (y_scaler.inverse_transform(y1) - y_scaler.inverse_transform(y2)) ** 2.0\n", + " )\n", + " ** 0.5,\n", + " 4,\n", + " )\n", + " return rmse" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Load data and Compute SOAP Vectors" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Atomistic structure manipulation\n", + "from ase import io\n", + "\n", + "# Librascal\n", + "from rascal.representations import SphericalInvariants as SOAP" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Because we are using environment-centred properties in this demonstration, we pull the properties from the frame.arrays object.**" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Within the 20 frames we have 2538 environments.\n" + ] + } + ], + "source": [ + "N = 20\n", + "input_file = \"../datasets/CSD-1000R.xyz\"\n", + "properties = [\"CS_local\", \"CS_total\"]\n", + "target = \"atom\"\n", + "\n", + "# Read the first N frames of the input file\n", + "frames = np.asarray(io.read(input_file, index=\":{}\".format(N)), dtype=object)\n", + "\n", + "# Wrap the frames\n", + "for frame in frames:\n", + " frame.wrap()\n", + "\n", + "Y_raw = np.vstack(\n", + " [np.concatenate([frame.arrays[prop] for frame in frames]) for prop in properties]\n", + ").T\n", + "print(\"Within the {} frames we have {} environments.\".format(N, len(Y_raw)))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "There are 2520 features\n" + ] + } + ], + "source": [ + "# Compute SOAPs (from librascal tutorial in X_ImportingData.ipynb)\n", + "hypers = dict(\n", + " soap_type=\"PowerSpectrum\",\n", + " interaction_cutoff=3.5,\n", + " max_radial=6,\n", + " max_angular=6,\n", + " gaussian_sigma_type=\"Constant\",\n", + " gaussian_sigma_constant=0.4,\n", + " cutoff_smooth_width=0.5,\n", + ")\n", + "soap = SOAP(**hypers)\n", + "\n", + "soap_rep = soap.transform(frames)\n", + "X_raw = soap_rep.get_features(soap)\n", + "\n", + "num_features = X_raw.shape[1]\n", + "print(f\"There are {num_features} features\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# np.savez('soap_file.npz', X=X_raw, Y=Y_raw, property_names=properties, target=target)\n", + "# np.savez('soap_hypers.npz', **hypers)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Skip Computing SOAPs" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# # Atomistic structure manipulation\n", + "# from ase import io\n", + "\n", + "# # Read/load SOAP vectors from numpy file\n", + "# soap_file = 'soap_file.npz'\n", + "# data = np.load(soap_file)\n", + "# X_raw = data['X'] # soap vectors (n_samples x n_features)\n", + "# Y_raw = data['Y'] # property vectors (n_samples x n_properties)\n", + "# target = data['target']\n", + "# properties = data['property_names'] # names of your properties\n", + "\n", + "# hyper_file = 'soap_hypers.npz'\n", + "# hypers = np.load(hyper_file)\n", + "\n", + "# num_features = X_raw.shape[1]\n", + "\n", + "# # If you end up wanting a chemiscope, you'll need to load your frames as well\n", + "# ase_file = \"../datasets/CSD-1000R.xyz\"\n", + "# frames = np.asarray(io.read(ase_file, ':'), dtype=object)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Split into training, validation, and testing subset and standardize" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Do a random, test-train split" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.model_selection import train_test_split\n", + "\n", + "f_train = 0.7\n", + "f_test = 0.3\n", + "\n", + "i_train, i_test = train_test_split(np.arange(X_raw.shape[0]), test_size=f_test)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "# np.savez('split_file.npz', i_train=i_train, i_test=i_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Skip test-train split" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# # Import testing and training indices from numpy file\n", + "\n", + "# index_file = 'split_file.npz'\n", + "\n", + "# data = np.load(index_file)\n", + "# i_train = data['i_train']\n", + "# i_test = data['i_test']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Scale and Center data" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "from skcosmo.preprocessing import StandardFlexibleScaler\n", + "\n", + "X_raw_train, X_raw_test = X_raw[i_train], X_raw[i_test]\n", + "Y_train, Y_test = Y_raw[i_train], Y_raw[i_test]\n", + "\n", + "x_scaler = StandardFlexibleScaler(column_wise=False)\n", + "y_scaler = StandardFlexibleScaler(column_wise=True)\n", + "\n", + "Y_train = y_scaler.fit_transform(Y_train)\n", + "Y_test = y_scaler.transform(Y_test)\n", + "Y = y_scaler.transform(Y_raw)\n", + "\n", + "X_raw_train = x_scaler.fit_transform(X_raw_train)\n", + "X_raw_test = x_scaler.transform(X_raw_test)\n", + "X = x_scaler.transform(X_raw)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Sub-select the SOAP Features" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The best results from PCov-CUR comes from using regression properties, so we can do a quick cross-validated ridge regression." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "This regression has an RMSE of 12.6616ppm on the testing set.\n" + ] + } + ], + "source": [ + "r = RidgeCV(cv=4, fit_intercept=False, alphas=np.logspace(-8, 2, 10))\n", + "r.fit(X_raw_train, Y_train)\n", + "\n", + "Yp_train = r.predict(X_raw_train)\n", + "Yp_test = r.predict(X_raw_test)\n", + "rmse = calc_rmse(Y_test, Yp_test, y_scaler)\n", + "\n", + "print(f\"This regression has an RMSE of {rmse}ppm on the testing set.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reducing the number of features\n", + "Because (for now) using CUR is more costly than FPS, let's reduce the number of features first with FPS.\n", + "\n", + "We have set `mixing` to 0.5 for all the following methods." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use FPS on the features to remove redundancies" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Selecting 630 features\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "4558eb8b73334c2abed5341bbd851dd1", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=629.0), HTML(value='')))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "from skcosmo.selection import FeatureFPS\n", + "\n", + "num_FPS = int(num_features / 4)\n", + "fps_mixing = 0.5\n", + "\n", + "print(f\"Selecting {num_FPS} features\")\n", + "ffps = FeatureFPS(X=X_raw_train, Y=Yp_train, mixing=fps_mixing, progress_bar=True)\n", + "fps_idx = np.array(ffps.select(num_FPS))\n", + "\n", + "X_fps_train = X_raw_train[:, fps_idx]\n", + "X_fps_test = X_raw_test[:, fps_idx]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# # Skip using FPS\n", + "\n", + "# fps_idx = np.arange(X_raw_train.shape[1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Demonstrate the superiority of the FPS indices to a set of random selections" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# r = RidgeCV(cv=4, fit_intercept=False, alphas=np.logspace(-8, 2, 10))\n", + "# r.fit(X_fps_train, Y_train)\n", + "\n", + "# Yp_test = r.predict(X_fps_test)\n", + "# rmse = calc_rmse(Yp_test, Y_test, y_scaler)\n", + "\n", + "# print(\n", + "# f\"The regression now has an RMSE of {rmse}ppm on the testing set, using only {num_FPS} / {num_features} features.\"\n", + "# )\n", + "\n", + "# n_random = 10\n", + "# rmses = []\n", + "\n", + "# for i in range(n_random):\n", + "# random_feat = np.random.choice(num_features, size=num_FPS)\n", + "# r.fit(X_raw_train[:, random_feat], Y_train)\n", + "# Yp_random_test = r.predict(X_raw_test[:, random_feat])\n", + "\n", + "# rmses.append(calc_rmse(Yp_random_test, Y_test, y_scaler))\n", + "\n", + "# rmse = round(np.mean(rmses), 4)\n", + "# rmse_dev = round(np.std(rmses), 2)\n", + "\n", + "# print(f\"By comparison, a regression on {num_FPS} random features gives an RMSE of {rmse}±{rmse_dev} ppm.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use CUR selection to find the most information-rich feature vectors\n", + "\n", + "Note: This process can take some time, especially with larger matrices." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Selecting 252 features\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "8dff63eeb8bc460d968fa8d866634eef", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=252.0), HTML(value='')))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "from skcosmo.selection import FeatureCUR\n", + "\n", + "num_CUR = int(num_features / 10)\n", + "cur_mixing = 0.5\n", + "\n", + "print(f\"Selecting {num_CUR} features\")\n", + "fcur = FeatureCUR(X=X_fps_train, Y=Yp_train, mixing=cur_mixing, progress_bar=True)\n", + "cur_idx = fps_idx[fcur.select(num_CUR)]" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "X_train = X_raw_train[:, cur_idx]\n", + "X_test = X_raw_test[:, cur_idx]" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "# np.savez('cur_file.npz', idx=cur_idx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Demonstrate the superiority of the CUR indices to a set of random selections" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "# r = RidgeCV(cv=4, fit_intercept=False, alphas=np.logspace(-8, 2, 10))\n", + "# r.fit(X_raw_train[:, cur_idx], Y_train)\n", + "\n", + "# Yp_test = r.predict(X_raw_test[:, cur_idx])\n", + "# rmse = calc_rmse(Yp_test, Y_test, y_scaler)\n", + "\n", + "# print(f\"The regression now has an RMSE of {rmse}ppm on the testing set, using only {num_CUR} / {num_features} features.\")\n", + "\n", + "# r.fit(X_raw_train[:, fps_idx[:num_CUR]], Y_train)\n", + "\n", + "# Yp_test = r.predict(X_raw_test[:, fps_idx[:num_CUR]])\n", + "# rmse = calc_rmse(Yp_test, Y_test, y_scaler)\n", + "\n", + "# print(f\"A regression with {num_CUR} FPS features has an RMSE of {rmse}ppm on the testing set.\")\n", + "\n", + "# n_random = 10\n", + "# rmses = []\n", + "\n", + "# for i in range(n_random):\n", + "# random_feat = np.random.choice(num_features, size=num_FPS)\n", + "# r.fit(X_raw_train[:, random_feat], Y_train)\n", + "# Yp_random_test = r.predict(X_raw_test[:, random_feat])\n", + "\n", + "# rmses.append(calc_rmse(Yp_random_test, Y_test, y_scaler))\n", + "\n", + "# rmse = round(np.mean(rmses), 4)\n", + "# rmse_dev = round(np.std(rmses), 2)\n", + "\n", + "# print(f\"By comparison, a regression on {num_CUR} random features gives an RMSE of {rmse}±{rmse_dev} ppm.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Skip CUR Feature Selection" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "# # Import feature indices from numpy file\n", + "\n", + "# index_file = 'cur_file.npz'\n", + "# data = np.load(index_file)\n", + "# idx = data['idx']\n", + "\n", + "# X_train = X_raw_train[:, idx]\n", + "# X_test = X_raw_test[:, idx]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Choosing the active set of environments" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Selecting 177 samples\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "d150bd5e42254d01b507cd106b6dd60d", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=177.0), HTML(value='')))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "from skcosmo.selection import SampleCUR\n", + "\n", + "num_active = int(len(i_train) / 10)\n", + "sample_mixing = 0.5\n", + "\n", + "print(f\"Selecting {num_active} samples\")\n", + "scur = SampleCUR(X=X_train, Y=Yp_train, mixing=sample_mixing, progress_bar=True)\n", + "sample_idx = scur.select(num_active)\n", + "\n", + "X_active = X_train[sample_idx]" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "# np.savez('active_set_file.npz', idx=sample_idx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Skip Choosing Active Set" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "# # Import active set indices from numpy file\n", + "\n", + "# index_file = 'active_set_file.npz'\n", + "# data = np.load(index_file)\n", + "# sample_idx = data['idx']\n", + "\n", + "# X_active = X_train[sample_idx]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Constructing a Sparse KPCovR" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.metrics.pairwise import pairwise_kernels\n", + "from scipy.linalg import svd\n", + "\n", + "from skcosmo.pcovr import KPCovR\n", + "from matplotlib import pyplot as plt\n", + "\n", + "kernel = \"rbf\"\n", + "kernel_params = {\"gamma\": 0.2}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Determine the active kernel\n", + "**Keep in mind that this example is originally written with an environment-centred property, and therefore we can use an environment kernel.**\n", + "\n", + "We'll construct a sparse nystroem approximation in a similar manner to sklearn.kernel_approximation.nystroem, deviating in the specification of the active set (the sklearn-counterpart randomly determines an active set)." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "active_kernel = pairwise_kernels(\n", + " X_active, metric=kernel, filter_params=True, **kernel_params\n", + ")\n", + "\n", + "# By including the right singular vectors into the RKHS features, we normalize and center the RKHS.\n", + "# This is equivalent to the scaled kernels discussed in 4_SparseKernelMethods.ipynb,\n", + "# where K_train = Phi_train @ Phi_train.T and K_test = Phi_train @ Phi_test.T.\n", + "\n", + "U, S, V = svd(active_kernel)\n", + "S = np.maximum(S, 1e-12)\n", + "normalization = np.dot(U / np.sqrt(S), V)\n", + "components = X_active.copy()\n", + "\n", + "Phi_train = np.dot(\n", + " pairwise_kernels(\n", + " X_train, components, metric=kernel, filter_params=True, **kernel_params\n", + " ),\n", + " normalization.T,\n", + ")\n", + "\n", + "Phi_test = np.dot(\n", + " pairwise_kernels(\n", + " X_test, components, metric=kernel, filter_params=True, **kernel_params\n", + " ),\n", + " normalization.T,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Train the KPCovR" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because we've explicitly determined our RKHS features, we can train a _linear_ KPCovR on the RKHS features and obtain the same result as SparseKPCovR." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "kpcovr_hypers = dict(mixing=0.5, n_components=5)\n", + "\n", + "kpcovr = KPCovR(kernel=\"linear\", center=True, **kpcovr_hypers)\n", + "kpcovr.fit(\n", + " Phi_train, Y_train, \n", + " Yhat=Yp_train # This will throw an error if the RidgeCV in Section 3 has been skipped. \n", + ") \n", + "\n", + "T_train = kpcovr.transform(Phi_train)\n", + "T_test = kpcovr.transform(Phi_test)\n", + "plt.scatter(T_train[:, 0], T_train[:, 1], c=Yp_train[:, 0])" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "# np.savez('kpcovr_file.npz', T_train=T_train, T_test=T_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Skip Computing KPCovR" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "# # Import kpcovr projection from numpy file\n", + "\n", + "# kpcovr_file = 'kpcovr_file.npz'\n", + "# data = np.load(kpcovr_file)\n", + "# T_train = data['T_train']\n", + "# T_test = data['T_test']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Compare the predictive power of KPCovR and KPCA components" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "# r = RidgeCV(cv=4, fit_intercept=False, alphas=np.logspace(-8, 2, 10))\n", + "# r.fit(T_train, Y_train)\n", + "\n", + "# Yp_test = r.predict(T_test)\n", + "# rmse = calc_rmse(Yp_test, Y_test, y_scaler)\n", + "\n", + "# print(\n", + "# f\"The regression on {kpcovr.n_components} KPCovR principal components has an RMSE of {rmse}ppm on the testing set.\"\n", + "# )\n", + "\n", + "# from sklearn.decomposition import KernelPCA\n", + "\n", + "# kpca = KernelPCA(n_components=kpcovr.n_components, kernel=\"linear\")\n", + "# kpca.fit(Phi_train)\n", + "# T_train_kpca = kpca.transform(Phi_train)\n", + "# T_test_kpca = kpca.transform(Phi_test)\n", + "\n", + "# r.fit(T_train_kpca, Y_train)\n", + "# Yp_kpca_test = r.predict(T_test_kpca)\n", + "# rmse = calc_rmse(Yp_kpca_test, Y_test, y_scaler)\n", + "\n", + "# print(\n", + "# f\"By comparison, a regression on {kpcovr.n_components} KPCA components gives an RMSE of {rmse}ppm.\"\n", + "# )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exporting to chemiscope" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "import chemiscope\n", + "\n", + "output_name = \"kpcovr-chemiscope.json\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Chemiscope is an online interactive visualizer that allows you to look at the projection in relation with the structures. Here, we'll create a chemiscope input file combining the training set and the testing set." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "T = np.zeros((X_raw.shape[0], kpcovr.n_components))\n", + "T[i_test] = T_test\n", + "T[i_train] = T_train\n", + "\n", + "train_test = np.zeros(X_raw.shape[0])\n", + "train_test[i_train] = 1\n", + "\n", + "is_active = np.zeros(X_raw.shape[0])\n", + "is_active[i_train[sample_idx]] = 1\n", + "\n", + "n_cur = 10\n", + "cur_features = np.zeros((X_raw.shape[0], n_cur))\n", + "cur_features[i_test] = X_raw_test[:, cur_idx[:n_cur]]\n", + "cur_features[i_train] = X_raw_train[:, cur_idx[:n_cur]]\n", + "\n", + "chemiscope_properties = chemiscope_properties = {\n", + " \"kpcovr\": {\n", + " \"target\": \"atom\", \n", + " \"values\": T[:, :kpcovr.n_components]\n", + " },\n", + " \"cur_feature\": {\n", + " \"target\": \"atom\", \n", + " \"values\": cur_features[:, :n_cur]\n", + " },\n", + " **{\n", + " prop_name: {\"target\": target, \"values\": Y[:, i]}\n", + " for i, prop_name in enumerate(properties)\n", + " },\n", + " \"is_training_point\": {\"target\": target, \"values\": train_test},\n", + " \"is_active_point\": {\"target\": target, \"values\": is_active},\n", + "}\n", + "\n", + "meta = {\n", + " \"name\": \"...\", # str, dataset name\n", + " \"description\": \"...\", # str, dataset description\n", + " \"authors\": [ # list of str, dataset authors, OPTIONAL\n", + " \"...\",\n", + " ],\n", + " \"references\": [ # list of str, references for this dataset,\n", + " \"...\", # OPTIONAL\n", + " ],\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "chemiscope.write_input(\n", + " output_name,\n", + " frames=frames,\n", + " properties=chemiscope_properties,\n", + " meta=meta,\n", + " cutoff=hypers[\"interaction_cutoff\"],\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.11" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": {}, + "toc_section_display": true, + "toc_window_display": true + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/X_ImportingData.ipynb b/notebooks/X_ImportingData.ipynb new file mode 100644 index 0000000..acf8d2a --- /dev/null +++ b/notebooks/X_ImportingData.ipynb @@ -0,0 +1,306 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction and Background\n", + "\n", + "In this notebook we step through the importing and partitioning of the dataset. For other notebooks, this is done using a utility function found in `../utilities/general.py`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#!/usr/bin/env python3\n", + "import sys\n", + "\n", + "# Maths things\n", + "import numpy as np\n", + "\n", + "# Atomistic structure manipulation\n", + "from ase.io import read, write\n", + "\n", + "sys.path.append('../')\n", + "\n", + "# Librascal\n", + "from rascal.representations import SphericalInvariants as SOAP\n", + "\n", + "# Local Utilities for Notebook\n", + "from utilities.general import FPS, center_matrix, normalize_matrix, load_variables\n", + "from utilities.kernels import linear_kernel, gaussian_kernel, center_kernel" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Import data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Structures are read using the ASE I/O library from an extended XYZ file, that contains also information on the properties of the structures or the atoms. In this case, we read a property that contains the local chemical shieldings as computed by GIPAW-DFT." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "N=10\n", + "input_file=\"../datasets/CSD-1000R.xyz\"\n", + "properties = [\"CS_local\", \"CS_total\"]\n", + " \n", + "# Read the first N frames of CSD-500\n", + "frames = read(input_file, index=':{}'.format(N))\n", + "\n", + "# Extract chemical shifts\n", + "for frame in frames:\n", + " frame.wrap()\n", + "\n", + "Y = np.vstack([np.concatenate([frame.arrays[property] for frame in frames]) for property in properties]).T\n", + "\n", + "print(\"Within the {} frames we have {} environments.\".format(N, len(Y)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Compute SOAP Vectors\n", + "We use the SOAP power spectrum vectors as atomic descriptors for the structures [(Bartók, 2013)](https://doi.org/10.1103/PhysRevB.87.184115).\n", + "Understanding SOAP vectors is not necessary for this tutorial, although they are crucial for correlating chemical environments and materials properties. For now, consider the power spectrum SOAP vectors as a three-body correlation function which includes information on each atom, its relationships with neighboring atoms, and the relationships between pairs of neighbors. The correlation function is expanded on a dense basis, and the feature vector contains more information than it is necessary for these tutorials, so we use [farthest point sampling](https://en.wikipedia.org/wiki/Farthest-first_traversal) to only include 200 components of the SOAP vectors while still retaining much of their diversity.\n", + "\n", + "SOAP vectors are computed with the librascal package [(librascal GitHub)](https://github.com/cosmo-epfl/librascal). If you don't want (or cannot) install librascal, you can download a precomputed version datafile `precomputed.npz`, that you should store in the `datasets/` folder, as discussed in the [foreword](0_Foreword.ipynb) to this tutorial. You should then be able to run all tutorials without having to install librascal. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "n_FPS = 200\n", + "\n", + "# Compute SOAPs (from librascal tutorial)\n", + "soap = SOAP(soap_type='PowerSpectrum',\n", + " interaction_cutoff=3.5,\n", + " max_radial=6,\n", + " max_angular=6,\n", + " gaussian_sigma_type='Constant',\n", + " gaussian_sigma_constant=0.4,\n", + " cutoff_smooth_width=0.5)\n", + "\n", + "soap_rep = soap.transform(frames)\n", + "X_raw = soap_rep.get_features(soap)\n", + "\n", + "num_features = X_raw.shape[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "here we prepare a file that can be used to initialize all local variables without having to read the raw data file or using `librascal` to compute the features" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "np.savez(\"../datasets/precomputed.npz\", n_atoms=[], indices=[], X=X_raw, Y=Y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(f\"Each SOAP vector contains {num_features} components.\\\n", + " \\nWe use furthest point sampling to generate a subsample of our SOAP vectors.\")\n", + "\n", + "# FPS the components\n", + "col_idxs, col_dist = FPS(X_raw.T, n_FPS)\n", + "X = X_raw[:, col_idxs]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Prepare data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Splitting into Testing and Training\n", + "Data is split into a training and testing set, and normalized based on the train set. \n", + "This makes it easier to compare performance of PCA and linear regression based on the intrinsic\n", + "variability, and makes the whole analysis dimensionless." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Splits in train and test sets\n", + "n_train = int(len(Y)/2)\n", + "n_test = len(Y)-n_train\n", + "r_train = np.asarray(range(len(Y)))\n", + "np.random.shuffle(r_train)\n", + "i_test = list(sorted(r_train[n_train:]))\n", + "i_train = list(sorted(r_train[:n_train]))\n", + "\n", + "X_train = X[i_train]\n", + "Y_train = Y[i_train]\n", + "X_test = X[i_test]\n", + "Y_test = Y[i_test]\n", + "\n", + "print(f'Shape of testing data is: {X_train.shape}, ||X|| = {np.linalg.norm(X_train)}.') " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Centering and Normalizing Data\n", + "In order to simplify the algebra in what follows, and to treat features and properties on the same grounds, we center and normalize the data. In other words, we calculate the means and standard deviation for the two training arrays (X_train and Y_train) and normalize the other matrices based upon these values." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Calculate the center of the training data\n", + "X_center = X_train.mean(axis=0)\n", + "Y_center = Y_train.mean(axis=0)\n", + "\n", + "# Center total dataset\n", + "X = center_matrix(X, center=X_center)\n", + "Y = center_matrix(Y, center=Y_center)\n", + "\n", + "# Center training data\n", + "X_train = center_matrix(X_train, center=X_center)\n", + "Y_train = center_matrix(Y_train, center=Y_center)\n", + "\n", + "# Center testing data\n", + "X_test = center_matrix(X_test, center=X_center)\n", + "Y_test = center_matrix(Y_test, center=Y_center)\n", + "\n", + "# Calculate the scale of the training data\n", + "X_scale = np.linalg.norm(X_train) / np.sqrt(n_train)\n", + "Y_scale = np.linalg.norm(Y_train) / np.sqrt(n_train)\n", + "\n", + "# Scale the total dataset\n", + "X = normalize_matrix(X, scale=X_scale)\n", + "Y = normalize_matrix(Y, scale=Y_scale)\n", + "\n", + "# Scale the training data\n", + "X_train = normalize_matrix(X_train, scale=X_scale)\n", + "Y_train = normalize_matrix(Y_train, scale=Y_scale)\n", + "\n", + "# Scale the testing data\n", + "X_test = normalize_matrix(X_test, scale=X_scale)\n", + "Y_test = normalize_matrix(Y_test, scale=Y_scale)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Generating Kernels\n", + "In later notebooks ([Kernel Methods](3_KernelMethods.ipynb) and [Sparse Kernel Methods](4_SparseKernelMethods.ipynb)) we use kernels rather than the raw features. They can be computed as follows using the utility functions and default parameters" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K_train = gaussian_kernel(X_train, X_train)\n", + "K_train = center_kernel(K_train)\n", + "\n", + "K_test = gaussian_kernel(X_test, X_train)\n", + "K_test = center_kernel(K_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Loading data with the Utility Class\n", + "\n", + "The data preparation protocol that is explained in this notebook can be automated using a utility class found in `utilities/general_utils.py`. This call is used in all the example notebooks, and sets all of the variables locally." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "var_dict = load_variables()\n", + "locals().update(var_dict)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.11" + }, + "toc": { + "base_numbering": 1, + "nav_menu": { + "height": "210px", + "width": "289px" + }, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "186.933px" + }, + "toc_section_display": true, + "toc_window_display": true + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/notebooks/X_NotationGlossary.ipynb b/notebooks/X_NotationGlossary.ipynb new file mode 100644 index 0000000..0b0ad0e --- /dev/null +++ b/notebooks/X_NotationGlossary.ipynb @@ -0,0 +1,195 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Notation Glossary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Abbreviations:\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
CUR Surprisingly not an acronym.
Name comes from original CUR notation, where $\\mathbf{A} = \\mathbf{CUR}$.
KPCA Kernel Principal Components Analysis
KPCovR Kernel Principal Covariates Regression
KRR Kernel Ridge Regression
LR Linear Regression
PCA Principcal Components Analysis
PCovR Principal Covariates Regression
RKHS Reproducing Kernel Hilbert Space
SKPCA Sparse Kernel Principal Components Analysis
SKPCovR Sparse Kernel Principal Covariates Regression
SKRR Sparse Kernel Ridge Regression
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Matrix Notations, where $\\mathbf{A}$ is a matrix $\\in \\mathbb{R}$ \n", + "\n", + "\n", + "
$\\mathbf{A}_{NM}$ Sparse matrix $\\mathbf{A}$ with $N$ rows and $M$ columns
\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
Operations
$\\mathbf{A}^T$ Transpose of matrix $\\mathbf{A}$
$\\mathbf{A}^{ -1}$ Inverse of invertible matrix $\\mathbf{A}$
$\\lVert\\mathbf{A}\\rVert = \\sqrt{\\operatorname{Tr}(\\mathbf{AA}^T)}$ Frobenius Norm
$\\operatorname{Tr}(\\mathbf{A})$ Trace of $\\mathbf{A}$
$\\operatorname{diag}(\\mathbf{A})$ Diagonal matrix with $\\mathbf{A}$ as entries
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Variable Names\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "
General Variables
$\\mathbf{I_N}$ $N \\times N$ identity matrix
$\\mathbf{1_N}$ $N \\times N$ matrix where each entry is $1/N$.
N Size of the Data Set, typically $N = n_{samples}$
M Size of the Active Set, typically $M\\leq N$
\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "
Data Variables
$\\mathbf{X}$ Input dataset of size $n_{samples} \\times n_{features}$
$\\mathbf{Y}$ Properties of the input data, matrix of size $n_{samples} \\times n_{properties}$
\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "
Eigendecompositions
$\\mathbf{U_A}$ Set of eigenvectors of a matrix $\\mathbf{A}$ represented as columns.
Sorted according to their corresponding eigenvalues in decreasing order.
$\\mathbf{\\Lambda_A}$ Diagonal matrix of eigenvalues of matrix $\\mathbf{A}$.
Sorted in decreasing order from top left to bottom right.
Corresponding matrix denoted in a subscript.
$\\mathbf{\\hat{U}}$ A truncated set of eigenvectors, typically those corresponding to the largest $n_{PCA}$ eigenvalues in PCA.
$\\mathbf{\\hat{\\Lambda}}$ Diagonal matrix of the largest eigenvalues, typically truncated to the $n_{PCA}$ largest in PCA.
\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "
Kernels and Covariance
$k(x,x')$ Kernel of $x$ and $x'$
$\\mathbf{K}$ Kernel matrix between all data points
$\\mathbf{C}$ Covariance matrix
$\\mathbf{\\Phi}$ Input dataset in feature space
$\\mathbf{\\tilde{\\Phi}}$ Centered input dataset in feature space
\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "
Projections and Regressions
$\\ell$ Loss measure
$\\rho$ Similarity measure
$\\lambda$ Regularization parameter.
$\\mathbf{T}$ Latent-space projection
$\\tilde{\\mathbf{T}}$ Whitened latent-space projection such that $\\tilde{\\mathbf{T}}\\tilde{\\mathbf{T}}^T = \\mathbf{I}$
$\\mathbf{P}_{AB}$ Projectors from the space of $\\mathbf{A}$ to the space of $\\mathbf{B}$.
$PC_i$ $i^{th}$ Principal Component
$\\mathbf{W}$ Regression weights
$\\mathbf{\\hat{Y}}$ Values predicted from regression
\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "
Principal Covariates Regression
$\\alpha$ Projection/regression tuning parameter
$\\mathbf{\\tilde{K}}$ Structure space \"mixture matrix\" between projection and regression.
Often involves a factor of $\\mathbf{AA}^T$, similar to the kernel.
$\\mathbf{\\tilde{C}}$ Feature space \"mixture matrix\" between projection and regression.
Often involves a factor of $\\mathbf{A}^T\\mathbf{A}$, similar to the covariance.
\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "\n", + "\t\n", + "
CUR Decomposition
$(\\mathbf{U}_K, \\mathbf{\\Sigma}, \\mathbf{U}_C)$ SVD decomposition of a matrix
$\\mathbf{A}\\approx\\mathbf{A}_c \\mathbf{SA}_r$ Approximation of a matrix using $c$ columns and $r$ rows
$\\pi_{j}$ Normalized statistical leverage score.
Represents the importance of a given column.
$\\mathbf{P}_c$ Adjustment of CUR approximation for projecting into latent space.
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{"structure": 19, "center": 68, "cutoff": 3.5}, {"structure": 19, "center": 69, "cutoff": 3.5}, {"structure": 19, "center": 70, "cutoff": 3.5}, {"structure": 19, "center": 71, "cutoff": 3.5}, {"structure": 19, "center": 72, "cutoff": 3.5}, {"structure": 19, "center": 73, "cutoff": 3.5}, {"structure": 19, "center": 74, "cutoff": 3.5}, {"structure": 19, "center": 75, "cutoff": 3.5}]} \ No newline at end of file diff --git a/tests/CSD-test.npz b/tests/CSD-test.npz new file mode 100644 index 0000000..48ee9fa Binary files /dev/null and b/tests/CSD-test.npz differ diff --git a/tests/pcovr.py b/tests/pcovr.py new file mode 100644 index 0000000..1fd2731 --- /dev/null +++ b/tests/pcovr.py @@ -0,0 +1,53 @@ +import numpy as np +from sklearn import exceptions +from sklearn.utils.validation import check_X_y + +from utilities.sklearn_covr.pcovr import PCovR + +def run_tests(): + data = np.load('./tests/CSD-test.npz') + X = data["X"] + Y = data["Y"] + + # Basic Test of PCovR Errors + lr_errors = np.nan * np.zeros(21) + pca_errors = np.nan * np.zeros(21) + for i, alpha in enumerate(np.linspace(0,1,21)): + pcovr = PCovR(alpha = alpha, + n_components=2, + regularization=1e-6, + tol=1e-12) + pcovr.fit(X, Y) + + T = pcovr.transform(X) + Xr = pcovr.inverse_transform(T) + Yp = pcovr.predict(X) + lr_errors[i] = np.linalg.norm(Y-Yp)**2.0 / np.linalg.norm(Y)**2.0 + pca_errors[i] = np.linalg.norm(X-Xr)**2.0 / np.linalg.norm(X)**2.0 + + assert not np.isnan(lr_errors[i]) and not np.isnan(pca_errors[i]) + + assert all(lr_errors[i] <= lr_errors[i+1] and pca_errors[i] >= pca_errors[i+1]for i in range(len(lr_errors)-1)) + + # Test of PCovR Fitting + pcovr = PCovR(alpha = 0.5, + n_components=2, + regularization=1e-6, + tol=1e-12) + + try: + T = pcovr.transform(X) + except exceptions.NotFittedError: + print("Premature transformation failed in expected manner") + + # Test of T shape + pcovr.fit(X, Y) + T = pcovr.transform(X) + + assert check_X_y(X, T, multi_output=True) + + + +if __name__ == "__main__": + run_tests() + print("Everything passed") diff --git a/utilities/__init__.py b/utilities/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/utilities/chemiscope.py b/utilities/chemiscope.py new file mode 100644 index 0000000..a97ac59 --- /dev/null +++ b/utilities/chemiscope.py @@ -0,0 +1,152 @@ +# -*- coding: utf-8 -*- +''' +Generate JSON input files for the default chemiscope visualizer. +''' +import numpy as np + + +def _typetransform(data): + if isinstance(data[0], str): + return list(map(str, data)) + elif isinstance(data[0], bytes): + return list(map(lambda u: u.decode('utf8'), data)) + else: + try: + return [float(value) for value in data] + except ValueError: + raise Exception('unsupported type in property') + + +def _linearize(name, values): + ''' + Transform 2D arrays in multiple 1D arrays, converting types to fit json as + needed. + ''' + assert isinstance(values, np.ndarray) + data = {} + + if len(values.shape) == 1: + data[name] = _typetransform(values) + elif len(values.shape) == 2: + for i in range(values.shape[1]): + data[f'{name}[{i + 1}]'] = _typetransform(values[:, i]) + else: + raise Exception('unsupported ndarray property') + + return data + + +def _frame_to_json(frame): + data = {} + data['size'] = len(frame) + data['names'] = list(frame.symbols) + data['x'] = [float(value) for value in frame.positions[:, 0]] + data['y'] = [float(value) for value in frame.positions[:, 1]] + data['z'] = [float(value) for value in frame.positions[:, 2]] + + if (frame.cell.lengths() != [0.0, 0.0, 0.0]).all(): + data['cell'] = list(np.concatenate(frame.cell)) + + return data + + +def _generate_environments(frames, cutoff): + environments = [] + for frame_id, frame in enumerate(frames): + for center in range(len(frame)): + environments.append({ + 'structure': frame_id, + 'center': center, + 'cutoff': cutoff, + }) + return environments + + +def chemiscope_input(meta, frames, projection, prediction, + properties, property_names=None, + untrained_properties=None, untrained_property_names=None, + cutoff=None, + ): + ''' + Get a dictionary which can be saved as JSON and used as input data for the + chemiscope visualizer (https://chemiscope.org). + + :param dict meta: metadata of the dataset, see the documentation at + https://chemiscope.org/docs/tutorial.html#input-file-format-for-chemiscope + for more information + :param list frames: list of `ase.Atoms`_ objects containing all the + structures + :param array projection: projection of the structural descriptor in latent + space + :param array prediction: predicted values for the properties for all + environments in the frames + :param array properties: actual value for properties for all environments in + the frames + :param list property_names: name of the properties being considered + :param array untrained_properties: actual value for properties for all environments in + the frames that are not included in the regression + :param list untrained_property_names: name of the untrained properties being considered + :param float cutoff: optional. If present, will be used to generate + atom-centered environments + + .. _`ase.Atoms`: https://wiki.fysik.dtu.dk/ase/ase/atoms.html + ''' + AUTHORIZED_KEYS = ["name", "description", "authors", "references"] + data = { + 'meta': { + key: value for key, value in meta.items() if key in AUTHORIZED_KEYS + } + } + + projection = np.asarray(projection) + prediction = np.asarray(prediction) + property = np.asarray(properties) + + if not property_names: + property_names = [f'property_{i}' for i in range(properties.shape[1])] + + assert projection.shape[0] == prediction.shape[0] + assert projection.shape[0] == property.shape[0] + assert len(property_names) == property.shape[1] + n_atoms = sum(len(f) for f in frames) + + if projection.shape[0] == len(frames): + target = 'structure' + elif projection.shape[0] == n_atoms: + target = 'atom' + else: + raise Exception( + "the number of features do not match the number of environments" + ) + + error = np.abs(properties - prediction) + result = {} + for name, values in _linearize("projection", projection).items(): + result[name] = {"target": target, "values": values} + + for i, property_name in enumerate(property_names): + for name, values in _linearize( + property_name, properties[:, i]).items(): + result[name] = {"target": target, "values": values} + + for name, values in _linearize("predicted {}".format( + property_name), prediction[:, i]).items(): + result[name] = {"target": target, "values": values} + + for name, values in _linearize( + "{} error".format(property_name), error[:, i]).items(): + result[name] = {"target": target, "values": values} + + if(untrained_property_names is not None): + for i, property_name in enumerate(untrained_property_names): + for name, values in _linearize( + property_name, untrained_properties[:, i]).items(): + result[name] = {"target": target, "values": values} + + data['properties'] = result + data['structures'] = [_frame_to_json(frame) for frame in frames] + + if cutoff is not None: + data['environments'] = _generate_environments(frames, cutoff) + + return data diff --git a/utilities/cmap2d_rb.npz b/utilities/cmap2d_rb.npz new file mode 100644 index 0000000..9367eba Binary files /dev/null and b/utilities/cmap2d_rb.npz differ diff --git a/utilities/colorbars.py b/utilities/colorbars.py new file mode 100644 index 0000000..fea3831 --- /dev/null +++ b/utilities/colorbars.py @@ -0,0 +1,234 @@ +#!/usr/bin/python + +import matplotlib as mpl +import matplotlib.pyplot as plt +from matplotlib.colors import LinearSegmentedColormap +import numpy as np + + +class cbar(object): + """ + Base class for color bars + """ + + def __init__(self): + self.cbar = None + + def make_cbar(self, name, RGB_list): + self.cbar = LinearSegmentedColormap.from_list(name, RGB_list) + plt.register_cmap(cmap=self.cbar) + + def __call__(self, val): + return self.cbar(val) + + +class cring(object): + """ + Base class for periodic color bars + """ + + def __init__(self): + self.cbar = None + + def make_cbar(self, name, RGB_list): + self.cbar = LinearSegmentedColormap.from_list(name, RGB_list) + plt.register_cmap(cmap=self.cbar) + + def __call__(self, val): + return self.cbar(val) + + +class cbarHot(cbar): + """ + Class to make the custom 'cbarHot' COSMO colorbar + """ + + def __init__(self, mn=0.0, mx=1.0): + + # 5th degree polynomial fit to the individual RGB values of the + # Mathematica COSMO colorbar at 1000 sample points + x = np.linspace(mn, mx, 100) + + # R, G, B value polynomial coefficients in decreasing order + r = np.array([28.384, -66.085, 54.494, -16.557, -0.232, 0.991]) + g = np.array([4.196, -8.275, 9.143, -5.479, -0.086, 0.995]) + b = np.array([-2.312, 4.468, -3.085, -0.128, 0.052, 0.997]) + + # Build polynomial + pr = np.polyval(r, x) + pg = np.polyval(g, x) + pb = np.polyval(b, x) + + # Wrap back RGB values into the [0, 1] allowed range + # (endpoints may fall outside [0, 1] due to error in the fit) + for i in [pr, pg, pb]: + i[np.where(i > 1.0)] = 1.0 + i[np.where(i < 0.0)] = 0.0 + + # Build colormap and register it with Matplotlib + cbar_name = 'cbarHot' + if(mn!=0 or mx!=1.0): + cbar_name +='_{}_{}'.format(mn, mx) + self.make_cbar(cbar_name, np.column_stack((pr, pg, pb))) + + +class cbarHot_alt(cbar): + """ + Class to make the custom 'cbarHot' COSMO colorbar in an alternate + construction, based on blending with an existing Python colorbar. + Appearance is not quite the same as the Mathematica colorbar, + but is similar. + """ + + def __init__(self, mn=0.0, mx=1.0): + + # Build color bar on 1000 sample points + x = np.linspace(mn, mx, 1000) + + # Extract 1000 sample points from existing color bar + # Only use partial segment of the colorbar (0.0 to 0.8) + y = np.linspace(0.0, 0.8, 1000) + + # RGB values + rgbWhite = np.array([1.0, 1.0, 1.0])*np.ones((1000, 3)) + rgb1 = np.array([1.0, 0.5, 0.0])*np.ones((1000, 3)) + rgbPurple = np.array([0.5, 0.0, 0.5])*np.ones((1000, 3)) + + # Blend with the 'ocean' colorbar + cm = plt.get_cmap('ocean') + + # Blend ratios + dsc = cm(1.0-y)**1.1 + c1 = (1.0-x)**4 + c2 = x**10 + c3 = (x-0.1)**2 + + # Blend colors + blend1 = np.einsum('ij,i->ij', dsc[:, 0:3], 1.0-c1) \ + + np.einsum('ij,i->ij', rgbWhite, c1) + blend2 = np.einsum('ij,i->ij', blend1, 1.0-c3) \ + + np.einsum('ij,i->ij', rgbPurple, c3) + blend3 = np.einsum('ij,i->ij', blend2, 1.0-c2) \ + + np.einsum('ij,i->ij', rgb1, c2) + + # Build the colormap and register it with Matplotlib + cbar_name = 'cbarHot' + if(mn!=0 or mx!=1.0): + cbar_name +='_{}_{}'.format(mn, mx) + self.make_cbar(cbar_name, blend3) + + +class cbarBWR(cbar): + """ + Class to make the custom 'cbarBWR' COSMO colorbar. + A similar colorbar exists already in Matplotlib, and + (in my opinion) looks a little nicer: 'RdBu' + """ + + def __init__(self, mn=0.0, mx=1.0): + + # Build colorbar using 1000 sample points + x = np.linspace(mn, mx, 1000) + + # RGB values + rgbBlack = np.array([0.0, 0.0, 0.0])*np.ones((1000, 3)) + rgbWhite = np.array([1.0, 1.0, 1.0])*np.ones((1000, 3)) + rgb1 = np.array([0.0, 0.4, 1.0])*np.ones((1000, 3)) + rgb2 = np.array([1.0, 0.3, 0.0])*np.ones((1000, 3)) + + # Blend ratios + c1 = np.sin(x*np.pi/2) + c2 = np.cos(x*np.pi/2) + c3 = 2*np.sin(x*np.pi)**4 + 4*np.sin(x*np.pi)**16 \ + + 8*np.sin(x*np.pi)**64 + 32*np.sin(x*np.pi)**256 + c3 /= np.amax(c3) + c4 = np.cos(x*np.pi)**16 + + # Normalize ratios to add to 1 + norm = np.amax(c1+c2+c3+c4) + c1 /= norm + c2 /= norm + c3 /= norm + c4 /= norm + + # Blend colors + blend = np.einsum('ij,i->ij', rgb2, c1) \ + + np.einsum('ij,i->ij', rgb1, c2) \ + + np.einsum('ij,i->ij', rgbWhite, c3) \ + + np.einsum('ij,i->ij', rgbBlack, c4) + + # Build the colormap and register it with Matplotlib + cbar_name = 'cbarBWR' + if(mn!=0 or mx!=1.0): + cbar_name +='_{}_{}'.format(mn, mx) + + self.make_cbar(cbar_name, blend) + + +class cbarPhi(cring): + """ + Class to make custom COSMO periodic colorbar + """ + + def __init__(self, mn=0.0, mx=1.0): + + # Build colorbar using 1000 sample points + x = np.linspace(mn, mx, 1000) + + # RGB values + rgbBlack = np.array([0.0, 0.0, 0.0])*np.ones((1000, 3)) + rgbWhite = np.array([1.0, 1.0, 1.0])*np.ones((1000, 3)) + rgb1 = np.array([0.0, 0.4, 0.9])*np.ones((1000, 3)) + rgb2 = np.array([1.0, 0.3, 0.0])*np.ones((1000, 3)) + + # Blend ratios + c1 = 0.5*np.cos(x*np.pi+np.pi/4+np.pi/4)**4 + c2 = 1.0*np.sin(x*np.pi+np.pi/4+np.pi/4)**8 + c3 = np.cos(x*np.pi+np.pi/4)**4 + c4 = np.cos(x*np.pi+np.pi/2+np.pi/4)**4 + + # Normalize ratios to sum to 1 + norm = np.amax(c1+c2+c3+c4) + c1 /= norm + c2 /= norm + c3 /= norm + c4 /= norm + + # Blend colors + blend = np.einsum('ij,i->ij', rgbBlack, c1) \ + + np.einsum('ij,i->ij', rgbWhite, c2) \ + + np.einsum('ij,i->ij', rgb1, c3) + \ + np.einsum('ij,i->ij', rgb2, c4) + + # Build the colormap and register it with Matplotlib + cbar_name = 'cbarPhi' + if(mn!=0 or mx!=1.0): + cbar_name +='_{}_{}'.format(mn, mx) + + self.make_cbar(cbar_name, blend) + + +class cbarMPLtrunc(cbar): + + def __init__(self, mpl_cmap='jet', mn=0.0, mx=1.0): + + # Build colorbar using 1000 sample points + x = np.linspace(mn, mx, 1000) + cmap = mpl.cm.get_cmap(mpl_cmap) + + blend = np.array([cmap(xx) for xx in x]) + + # Build the colormap and register it with Matplotlib + cbar_name = mpl_cmap + if(mn!=0 or mx!=1.0): + cbar_name +='_{}_{}'.format(mn, mx) + + self.make_cbar(cbar_name, blend) + +def load(): + for cb in [cbarHot, cbarBWR, cbarPhi]: + cb(mn=0.0, mx=1.0) + cbarHot(mn=0.3, mx=1.05) + cbarMPLtrunc('bone_r',0.2, 1.0) + cbarMPLtrunc('Reds',0.3, 1.0) + cbarMPLtrunc('Blues',0.3, 1.0) diff --git a/utilities/deprecated/CUR.py b/utilities/deprecated/CUR.py new file mode 100644 index 0000000..ac506b2 --- /dev/null +++ b/utilities/deprecated/CUR.py @@ -0,0 +1,298 @@ +import numpy as np +import time +from scipy.sparse.linalg import svds as svd +from scipy.sparse.linalg import eigs as speig +import scipy + +from tqdm import tqdm as tqdm + + +def sorted_eig(mat, thresh=0.0, n=None, sps=True): + """ + Returns n eigenvalues and vectors sorted + from largest to smallest eigenvalue + """ + if(sps): + from scipy.sparse.linalg import eigs as speig + if(n is None): + n = mat.shape[0] - 1 + val, vec = speig(mat, k=n, tol=thresh) + val = np.real(val) + vec = np.real(vec) + + idx = sorted(range(len(val)), key=lambda i: -val[i]) + val = val[idx] + vec = vec[:, idx] + + else: + val, vec = np.linalg.eigh(mat) + val = np.flip(val, axis=0) + vec = np.flip(vec, axis=1) + + vec[:, val < thresh] = 0 + val[val < thresh] = 0 + + return val[:n], vec[:, :n] + + +def approx_A(A, col_idx, row_idx=None): + """ Approximates the full matrix with selected features """ + + A_c = A[:, col_idx] + S_c = np.linalg.pinv(A_c) + + A_r = A[row_idx] + + if(row_idx is not None): + S_r = np.linalg.pinv(A_r) + S = np.matmul(S_c, np.matmul(A, S_r)) + else: + S = S_c + + return np.matmul(A_c, np.matmul(S, A_r)) + + +def compute_P(A_c, S, A_r, thresh=1e-12): + """ Computes the latent-space projector for the feature matrix """ + SA = np.matmul(S, A_r) + SA = np.matmul(SA, SA.T) + + v_SA, U_SA = np.linalg.eigh(SA) + v_SA[v_SA < thresh] = 0 + + return np.matmul(U_SA, np.diagflat(np.sqrt(v_SA))) + + +def get_Ct(X, Y, alpha=0.5, regularization=1e-6): + """ + Creates the PCovR modified covariance + ~C = (alpha) * X^T X + + (1-alpha) * (X^T X)^(-1/2) ~Y ~Y^T (X^T X)^(-1/2) + + where ~Y is the properties obtained by linear regression. + """ + + cov = X.T @ X + + if(alpha < 1.0): + # changing these next two lines can cause a LARGE error + Cinv = np.linalg.pinv(cov, hermitian=True) + try: + Csqrt = scipy.linalg.sqrtm(cov) + except: + v, U = sorted_eig(cov) + Csqrt = U @ np.diagflat(np.sqrt(v)) @ U.T + + # parentheses speed up calculation greatly + Y_hat = Csqrt @ Cinv @ (X.T @ Y) + + if(len(Y_hat.shape) < 2): + Y_hat = Y_hat.reshape((-1, 1)) + + C_lr = Y_hat @ Y_hat.T + + else: + C_lr = np.zeros(cov.shape) + + C_pca = cov + C = alpha*C_pca + (1.0-alpha)*C_lr + + return C + + +def svd_select(A, n, k=1, idxs=None, sps=False, **kwargs): + """ + Selection function which computes the CUR + indices using the SVD Decomposition + """ + + if(idxs is None): + idxs = [] # indexA is initially empty. + else: + idxs = list(idxs) + Acopy = A.copy() + + for nn in range(n): + if(len(idxs) <= n): + if(not sps): + (S, v, D) = np.linalg.svd(Acopy) + else: + (S, v, D) = svd(Acopy, k) + D = D[np.flip(np.argsort(v))] + pi = (D[:k]**2.0).sum(axis=0) + pi[idxs] = 0 # eliminate possibility of selecting same column twice + i = pi.argmax() + idxs.append(i) + + v = Acopy[:, idxs[nn]] / \ + np.sqrt(np.matmul(Acopy[:, idxs[nn]], Acopy[:, idxs[nn]])) + + for i in range(Acopy.shape[1]): + Acopy[:, i] -= v * np.dot(v, Acopy[:, i]) + + return list(idxs) + + +def pcovr_select(A, n, Y, alpha, k=1, idxs=None, sps=False, **kwargs): + """ + Selection function which computes the CUR + indices using the PCovR `Covariance` matrix + """ + + Acopy = A.copy() + Ycopy = Y.copy() + + if(idxs is None): + idxs = [] # indexA is initially empty. + else: + idxs = list(idxs) + + try: + for nn in tqdm(range(n)): + if(len(idxs) <= nn): + + Ct = get_Ct(Acopy, Ycopy, alpha=alpha) + + if(not sps): + v_Ct, U_Ct = sorted_eig(Ct, n=k) + else: + v_Ct, U_Ct = speig(Ct, k) + U_Ct = U_Ct[:, np.flip(np.argsort(v_Ct))] + + pi = (np.real(U_Ct)[:, :k]**2.0).sum(axis=1) + pi[idxs] = 0 # eliminate possibility of selecting same column twice + j = pi.argmax() + idxs.append(j) + + v = np.linalg.pinv( + np.matmul(Acopy[:, idxs[:nn+1]].T, Acopy[:, idxs[:nn+1]])) + v = np.matmul(Acopy[:, idxs[:nn+1]], v) + v = np.matmul(v, Acopy[:, idxs[:nn+1]].T) + + Ycopy -= np.matmul(v, Ycopy) + + v = Acopy[:, idxs[nn]] / \ + np.sqrt(np.matmul(Acopy[:, idxs[nn]], Acopy[:, idxs[nn]])) + + + for i in range(Acopy.shape[1]): + Acopy[:, i] -= v * np.dot(v, Acopy[:, i]) + except: + print("INCOMPLETE AT {}/{}".format(len(idxs), n)) + + return list(idxs) + + +selections = dict(svd=svd_select, pcovr=pcovr_select) + + +class CUR: + """ + Performs CUR Decomposition on a Supplied Matrix + + ---Arguments--- + matrix: matrix to be decomposed + precompute: (int, tuple, Nonetype) number of columns, rows to be computed + upon instantiation. Defaults to None. + feature_select: (bool) whether to compute only column indices + pi_function: () Importance metric and selection for the matrix + symmetry_tolerance: (float) Tolerance by which a matrix is symmetric + params: (dict) Dictionary of additional parameters to be passed to the + pi function + + ---References--- + 1. G. Imbalzano, A. Anelli, D. Giofre, S. Klees, J. Behler, + and M. Ceriotti, J. Chem. Phys.148, 241730 (2018) + """ + + def __init__(self, matrix, + precompute=None, + feature_select=False, + pi_function='svd', + symmetry_tolerance=1e-4, + params={} + ): + self.A = matrix + self.symmetric = self.A.shape == self.A.T.shape and \ + np.all(np.abs(self.A-self.A.T)) < symmetry_tolerance + self.fs = feature_select + if(isinstance(pi_function, str)): + self.select = selections.get(pi_function, None) + else: + self.select = pi_function + self.params = params + + if(pi_function == 'pcovr'): + try: + assert all([x in params for x in ['Y', 'alpha']]) + except: + print( + "For column selection with PCovR, `Y` and `alpha` must be entries in `params`") + + self.idx_c, self.idx_r = None, None + if(precompute is not None): + if(isinstance(precompute, int)): + self.idx_c, self.idx_r = self.compute_idx( + precompute, precompute) + else: + self.idx_c, self.idx_r = self.compute_idx(*precompute) + + def compute_idx(self, n_c, n_r): + idx_c = self.select(self.A, n_c, idxs=self.idx_c, **self.params) + if(self.fs): + idx_r = np.asarray(range(self.A.shape[1])) + elif(not self.symmetric): + idx_r = self.select(self.A.T, n_r, idxs=self.idx_r, **self.params) + else: + idx_r = idx_c + return idx_c, idx_r + + def compute(self, n_c, n_r=None): + """ + Compute the n_c selected columns and n_r selected rows + """ + if(self.fs): + n_r = self.A.shape[1] + elif(self.symmetric and n_r == None): + n_r = n_c + elif(n_r == None): + print("You must specify a n_r for non-symmetric matrices.") + + if(self.idx_c is None or (not self.fs and self.idx_r is None)): + idx_c, idx_r = self.compute_idx(n_c, n_r) + self.idx_c, self.idx_r = idx_c, idx_r + elif(len(self.idx_c) < n_c or len(self.idx_r) < n_r): + idx_c, idx_r = self.compute_idx(n_c, n_r) + self.idx_c, self.idx_r = idx_c, idx_r + else: + idx_c = self.idx_c[:n_c] + idx_r = self.idx_r[:n_r] + + # The CUR Algorithm + A_c = self.A[:, idx_c] + if(self.symmetric and not self.fs): + A_r = A_c.T + elif(self.fs): + A_r = self.A.copy() + else: + A_r = self.A[idx_r, :] + + # Compute S. + S = np.matmul(np.matmul(np.linalg.pinv(A_c), self.A), + np.linalg.pinv(A_r)) + return A_c, S, A_r + + def compute_P(self, n_c): + """ + Computes the projector into latent-space for ML models + """ + + A_c, S, A_r = self.compute(n_c) + self.P = compute_P(A_c, S, A_r) + + def loss(self, n_c, n_r=None): + """ + Error between approximated matrix and target + """ + A_c, S, A_r = self.compute(n_c, n_r) + return np.linalg.norm(self.A - np.matmul(A_c, np.matmul(S, A_r)))/np.linalg.norm(self.A) diff --git a/utilities/deprecated/classes.py b/utilities/deprecated/classes.py new file mode 100644 index 0000000..138e426 --- /dev/null +++ b/utilities/deprecated/classes.py @@ -0,0 +1,1436 @@ +import numpy as np +from .general import FPS, get_stats, sorted_eig, eig_inv, center_matrix, normalize_matrix +from .kernels import linear_kernel, center_kernel, gaussian_kernel + +kernels = { + "gaussian": gaussian_kernel, + "linear": linear_kernel +} + + +class Model: + """ + Super-class defined for all models + + ----Attributes---- + center: (boolean) whether to shift all inputs to zero mean + regularization: (float) parameter to offset all small eigenvalues + for regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Methods---- + postprocess: un-centers and un-scales outputs according to scale and center + attributes + preprocess: centers and scales provided inputs according to scale and center + attributes + """ + + def __init__(self, regularization=1e-12, scale=False, center=False, *args, **kwargs): + self.regularization = regularization + + self.center = center + self.scale = scale + self.X_center = None + self.X_scale = None + + # self.X_center = 0 + # self.Y_center = 0 + # self.X_scale = 1 + # self.Y_scale = 1 + # self.K_ref = None + + def preprocess(self, X=None, Y=None, K=None, + X_ref=None, Y_ref=None, K_ref=None, rcond=1.0E-12, + *args, **kwargs): + """ + Scale and center the input data as designated by the model parameters + `scale` and `center`. These parameters are set on the model level to + enforce the same centering and scaling for all data supplied to the + model. i.e. if a model is trained on centered input X, it must be + supplied a similarly centered input X' for transformation. + """ + + if(X_ref is None and X is not None): + X_ref = X.copy() + + if(Y_ref is None and Y is not None): + Y_ref = Y.copy() + + if self.center: + if X_ref is not None and self.X_center is None: + self.X_center = X_ref.mean(axis=0) + + if isinstance(self, Regression): + if Y_ref is not None and self.Y_center is None: + self.Y_center = Y_ref.mean(axis=0) + + if isinstance(self, Kernelized): + if K_ref is None and K is not None: + K_ref = K + + if K_ref is not None and self.K_ref is None: + self.K_ref = K_ref + + if self.scale: + if X_ref is not None and self.X_scale is None: + self.X_scale = np.linalg.norm(X_ref - self.X_center) / np.sqrt(X_ref.shape[0]) + + if isinstance(self, Regression): + if Y_ref is not None and self.Y_scale is None: + self.Y_scale = np.linalg.norm(Y_ref - self.Y_center, axis=0) / np.sqrt(Y_ref.shape[0] / Y_ref.shape[1]) + + if X is not None: + Xcopy = X.copy() + if self.center: + Xcopy = center_matrix(Xcopy, self.X_center) + if self.scale: + Xcopy = normalize_matrix(Xcopy, scale=self.X_scale) + else: + Xcopy = None + + if Y is not None: + Ycopy = Y.copy() + if self.center: + Ycopy = center_matrix(Ycopy, self.Y_center) + if self.scale: + Ycopy = normalize_matrix(Ycopy, scale=self.Y_scale) + else: + Ycopy = None + + if K is not None: + Kcopy = K.copy() + if self.center and isinstance(self, Sparsified): + K_center = np.mean(self.K_ref, axis=0) + Kcopy = center_matrix(Kcopy, K_center) + elif self.center: + Kcopy = center_kernel(Kcopy, reference=self.K_ref) + if self.scale and isinstance(self, Sparsified): + try: + K_ref_centered = self.K_ref - np.mean(self.K_ref, axis=0) + self.K_scale = K_ref_centered @ np.linalg.pinv(self.Kmm, rcond=rcond) @ K_ref_centered.T + self.K_scale = np.sqrt(np.trace(self.K_scale) / self.K_ref.shape[0]) + Kcopy = normalize_matrix(Kcopy, scale=self.K_scale) + except AttributeError: + print("Error: Kmm is required for the scaling but it has not been set") + elif self.scale: + self.K_scale = np.trace(center_kernel(self.K_ref)) / self.K_ref.shape[0] + Kcopy = normalize_matrix(Kcopy, scale=self.K_scale) + else: + Kcopy = None + + return Xcopy, Ycopy, Kcopy + + def postprocess(self, X=None, Y=None, *args, **kwargs): + """ + Undoes any scaling and center on the output data for comparison + """ + + if X is not None: + Xcopy = X.copy() + if self.scale: + Xcopy = normalize_matrix(Xcopy, scale=(1.0 / self.X_scale)) + if self.center: + Xcopy = center_matrix(Xcopy, -self.X_center) + else: + Xcopy = None + + if Y is not None: + Ycopy = Y.copy() + if self.scale: + Ycopy = normalize_matrix(Ycopy, scale=(1.0 / self.Y_scale)) + if self.center: + Ycopy = center_matrix(Ycopy, -self.Y_center) + else: + Ycopy = None + + return Xcopy, Ycopy + + +class Decomposition(Model): + """ + Super-class defined for any decompositions ala PCA + + ----Attributes---- + PTX: projector from latent space to input space + PXT: projector from input space to latent space + n_PC (int) number of principal components to store + + ----Inherited Attributes---- + center: (boolean) whether to shift all inputs to zero mean + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and center + attributes + preprocess: centers and scales provided inputs according to scale and center + attributes + """ + + def __init__(self, n_PC=2, *args, **kwargs): + super().__init__(*args, **kwargs) + self.n_PC = n_PC + self.PXT = None + self.PTX = None + + +class Regression(Model): + """ + Super-class defined for any regressions + + ----Attributes---- + PXY: projector from input space to property space + + ----Inherited Attributes---- + center: (boolean) whether to shift all inputs to zero mean + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and center + attributes + preprocess: centers and scales provided inputs according to scale and center + attributes + + """ + def __init__(self, *args, **kwargs): + super().__init__(*args, **kwargs) + self.PXY = None + self.Y_center = None + self.Y_scale = None + + +class Kernelized(Model): + """ + Super-class defined for any kernelized methods + + ----Attributes---- + PKT: projector from kernel space to latent space + PKY: projector from kernel space to property space + PTK: projector from latent space to kernel space + X: input used to train the model, if further kernels need be constructed + kernel: function to construct the kernel of the input data + + ----Inherited Attributes---- + center: (boolean) whether to shift all inputs to zero mean + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and center + attributes + preprocess: centers and scales provided inputs according to scale and center + attributes + + """ + + def __init__(self, kernel_type='linear', *args, **kwargs): + super().__init__(*args, **kwargs) + + self.kernel = None + if isinstance(kernel_type, str): + if kernel_type in kernels: + self.kernel = kernels[kernel_type] + elif callable(kernel_type): + self.kernel = kernel_type + + if self.kernel is None: + raise Exception( + 'Kernel Error: Please specify either {} or pass a suitable \ + kernel function.'.format(kernels.keys()) + ) + + self.PKT = None + self.PTK = None + self.PKY = None + self.X = None + self.K_ref = None + self.K_scale = None + + +class Sparsified(Kernelized): + """ + Super-class defined for any kernelized methods + + ----Attributes---- + n_active: (int) size of the active set + X_sparse: active set used to train the model, if further kernels need + be constructed + + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PTK: projector from latent space to kernel space + PTX: projector from latent space to input space + X: input used to train the model, if further kernels need be constructed + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and center + attributes + preprocess: centers and scales provided inputs according to scale and center + attributes + """ + + def __init__(self, n_active, *args, **kwargs): + super().__init__(*args, **kwargs) + + self.n_active = n_active + self.X_sparse = None + + +class PCovRBase(Decomposition, Regression): + """ + Super-class defined for PCovR style methods + + ----Attributes---- + PTY: projector from latent space to property space + Yhat: regressed properties + alpha: (float) mixing parameter between decomposition and regression + + ----Inherited Attributes---- + PTX: projector from latent space to input space + PXT: projector from input space to latent space + n_PC (int) number of principal components to store + PXY: projector from input space to property space + center: (boolean) whether to shift all inputs to zero mean + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and center + attributes + preprocess: centers and scales provided inputs according to scale and center + attributes + """ + + def __init__(self, alpha, *args, **kwargs): + super(PCovRBase, self).__init__(*args, **kwargs) + self.alpha = alpha + self.PTY = None + self.Yhat = None + + # # band-aid to inheritance error + # if('center' in kwargs): + # self.center=kwargs['center'] + # if('scale' in kwargs): + # self.scale=kwargs['scale'] + + +class PCA(Decomposition): + """ + Performs principal component analysis + + ----Inherited Attributes---- + PTX: projector from latent space to input space + PXT: projector from input space to latent space + center: (boolean) whether to shift all inputs to zero mean + n_PC: (int) number of principal components to store + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Methods---- + fit: fit the PCA + statistics: provide available statistics for the decomposition + transform: transform data based on the PCA fit + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and center + attributes + preprocess: centers and scales provided inputs according to scale and center + attributes + + ----References---- + 1. https://en.wikipedia.org/wiki/Principal_component_analysis + 2. M. E. Tipping 'Sparse Kernel Principal Component Analysis', + Advances in Neural Information Processing Systems 13, 633 - 639, 2001 + """ + + def __init__(self, n_PC=None, *args, **kwargs): + super().__init__(n_PC=n_PC, *args, **kwargs) + + def fit(self, X): + """ + Fits the PCA + + ----Arguments---- + X: centered data on which to build the PCA + """ + + X, _, _ = self.preprocess(X=X, X_ref=X) + + # Compute covariance + C = (X.T @ X) / (X.shape[0] - 1) + + # Compute eigendecomposition of covariance matrix + v, U = sorted_eig(C, thresh=self.regularization, n=self.n_PC) + + self.PXT = U[:, :self.n_PC] + self.PTX = self.PXT.T + + def transform(self, X): + """ + Transforms the PCA + + ----Arguments---- + X: centered data to transform based on the PCA + """ + + X, _, _ = self.preprocess(X=X) + + if self.PXT is None: + raise Exception("Error: must fit the PCA before transforming") + else: + # Compute PCA scores + T = X @ self.PXT + return T + + def statistics(self, X): + T = self.transform(X) + + X_PCA = T @ self.PTX + X_PCA, _ = self.postprocess(X=X_PCA) + + return get_stats(x=X, t=T, xr=X_PCA) + + +class LR(Regression): + """ + Performs linear regression + + ----Inherited Attributes---- + PXY: projector from input space to property space + center: (boolean) whether to shift all inputs to zero mean + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Methods---- + fit: fit the linear regression model by computing regression weights + statistics: provide available statistics for the regression + transform: compute predicted Y values + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and center + attributes + preprocess: centers and scales provided inputs according to scale and center + attributes + + ----References---- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligents + Laboratory Systems 14(1): 155-164, 1992 + 2. https://en.wikipedia.org/wiki/Linear_regression + """ + + def __init__(self, *args, **kwargs): + super().__init__(*args, **kwargs) + + def fit(self, X, Y): + """ + Fits the linear regression model + + ----Arguments---- + X: centered, independent (predictor) variable + Y: centered, dependent (response) variable + """ + + X, Y, _ = self.preprocess(X=X, Y=Y, X_ref=X, Y_ref=Y) + + # Compute inverse of covariance + XTX = (X.T @ X) + XTX = XTX + self.regularization * np.eye(X.shape[1]) + XTX = np.linalg.pinv(XTX) + + # Compute LR solution + self.PXY = XTX @ X.T @ Y + + def transform(self, X): + """ + Computes predicted Y values + + ----Arguments---- + X: centered, independent (predictor) variable + """ + + X, _, _ = self.preprocess(X=X) + + # Compute predicted Y + Yp = X @ self.PXY + _, Yp = self.postprocess(Y=Yp) + + return Yp + + def statistics(self, X, Y): + Yp = self.transform(X) + return get_stats(x=X, y=Y, yp=Yp) + + +class KPCA(Kernelized, Decomposition): + """ + Performs kernel principal component analysis on a dataset + based on a kernel between all of the constituent data points + + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PKY: projector from kernel space to property space (null) + PTK: projector from latent space to kernel space + PXT: projector from input space to latent space + X: input used to train the model, if further kernels need be constructed + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + n_PC (int) number of principal components to store + regularization: (float) parameter to offset all small eigenvalues for regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Methods---- + fit: fit the KPCA + statistics: provide available statistics for the decomposition + transform: transform data based on the KPCA fit + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and + center attributes + preprocess: centers and scales provided inputs according to scale and + center attributes + + ----References---- + 1. https://en.wikipedia.org/wiki/Kernel_principal_component_analysis + 2. M. E. Tipping, 'Sparse Kernel Principal Component Analysis', + Advances in Neural Information Processing Systems 13, 633 - 639, 2001 + """ + + def __init__(self, n_PC, *args, **kwargs): + super(KPCA, self).__init__(n_PC=n_PC, *args, **kwargs) + + def fit(self, X=None, K=None): + X, _, K = self.preprocess(X=X, K=K, X_ref=X, K_ref=K) + + if K is None: + K = self.kernel(X, X) + K = center_kernel(K) + + if X is not None: + self.X = X + else: + print( + "No input data supplied during fitting. \n" + "Transformations/statistics only available for kernel inputs." + ) + + # Compute eigendecomposition of kernel + v, U = sorted_eig(K, + thresh=self.regularization, n=self.n_PC) + + v_inv = eig_inv(v[:self.n_PC]) + + self.PKT = U[:, :self.n_PC] @ np.diagflat(np.sqrt(v_inv)) + + T = K @ self.PKT + self.PTK = np.diagflat(v_inv) @ T.T @ K + + if X is not None: + self.PTX = np.diagflat(v_inv) @ T.T @ X + + def transform(self, X=None, K=None): + X, _, K = self.preprocess(X=X, K=K) + + if self.PKT is None: + raise Exception("Error: must fit the KPCA before transforming") + elif X is None and K is None: + raise Exception("Either the kernel or input data must be specified.") + else: + # Compute KPCA transformation + if K is None: + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.kernel(self.X, self.X)) + + T = K @ self.PKT + + return T + + def statistics(self, X=None, Y=None, K=None): + if X is None and K is None: + raise Exception( + "Either the kernel or input data must be specified." + ) + else: + # Compute KPCA transformation + if K is None: + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.kernel(self.X, self.X)) + + T = K @ self.PKT + + Kapprox = T @ self.PTK + + if self.PTX is not None: + Xr = T @ self.PTX + Xr, _ = self.postprocess(X=Xr) + else: + Xr = None + + return get_stats(k=K, kapprox=Kapprox, x=X, xr=Xr, t=T) + + +class KRR(Kernelized, Regression): + """ + Performs kernel ridge regression + + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PKY: projector from kernel space to property space + PTK: projector from latent space to kernel space + X: input used to train the model, if further kernels need be constructed + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + regularization: (float) parameter to offset all small eigenvalues for regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Methods---- + fit: fit the kernel ridge regression model by computing regression weights + statistics: provide available statistics for the regression + transform: compute predicted Y values + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and center attributes + preprocess: centers and scales provided inputs according to scale and center attributes + + ----References---- + 1. M. Ceriotti, M. J. Willatt, G. Csanyi, + 'Machine Learning of Atomic - Scale Properties + Based on Physical Principles', Handbook of Materials Modeling, + Springer, 2018 + """ + + def __init__(self, *args, **kwargs): + super(KRR, self).__init__(*args, **kwargs) + + def fit(self, X=None, Y=None, K=None): + X, Y, K = self.preprocess(X=X, K=K, Y=Y, X_ref=X, K_ref=K, Y_ref=Y) + + if K is None: + K = self.kernel(X, X) + self.K = K.copy() + K = center_kernel(K, self.K) + + if X is not None: + self.X = X + else: + print( + "No input data supplied during fitting. \n" + "Transformations/statistics only available for kernel inputs." + ) + + # Regularize the model + Kreg = K + np.eye(K.shape[0]) * self.regularization + + # Solve the model + self.PKY = np.linalg.solve(Kreg, Y) + + def transform(self, X=None, K=None): + X, _, K = self.preprocess(X=X, K=K) + + if self.PKY is None: + raise Exception("Error: must fit the KPCA before transforming") + elif X is None and K is None: + raise Exception("Either the kernel or input data must be specified.") + else: + # Compute KPCA transformation + if K is None: + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.K) + + Yp = K @ self.PKY + _, Yp = self.postprocess(Y=Yp) + + return Yp + + def statistics(self, X=None, Y=None, K=None): + Yp = self.transform(X=X, K=K) + return get_stats(x=X, y=Y, yp=Yp, k=K) + + +class SparseKPCA(Sparsified, Decomposition): + """ + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PKY: projector from kernel space to property space + PKY: projector from kernel space to property space (null) + PTK: projector from latent space to kernel space + PXT: projector from input space to latent space + X: input used to train the model, if further kernels need be constructed + X_sparse: active set used to train the model, if further kernels need be + constructed + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + n_PC (int) number of principal components to store + n_active: (int) size of the active set + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Methods---- + fit: fit the KPCA + statistics: provide available statistics for the decomposition + transform: transform data based on the KPCA fit + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and + center attributes + preprocess: centers and scales provided inputs according to scale and + center attributes + + ----References---- + 1. https://en.wikipedia.org/wiki/Kernel_principal_component_analysis + 2. M. E. Tipping, 'Sparse Kernel Principal Component Analysis', + Advances in Neural Information Processing Systems 13, 633 - 639, 2001 + """ + + def __init__(self, n_PC, *args, **kwargs): + super(SparseKPCA, self).__init__(n_PC=n_PC, *args, **kwargs) + + def fit(self, X=None, Kmm=None, Knm=None, *args, **kwargs): + # *args left in for backwards compatibility + + if X is None: + assert (Knm is not None and Kmm is not None) + X, _, _ = self.preprocess(X=X, X_ref=X) + + if Kmm is None or Knm is None: + i_sparse, _ = FPS(X, self.n_active) + + self.X_sparse = X[i_sparse, :] + + Kmm = self.kernel(self.X_sparse, self.X_sparse) + + Knm = self.kernel(X, self.X_sparse) + + if self.center: + Kmm = center_kernel(Kmm) + self.Kmm = Kmm + _, _, Knm = self.preprocess(K=Knm, K_ref=Knm) + + # Compute eigendecomposition of kernel + vmm, Umm = sorted_eig( + Kmm, thresh=self.regularization, n=self.n_active) + + U_active = Umm[:, :self.n_active - 1] + v_invsqrt = np.diagflat(np.sqrt(eig_inv(vmm[0:self.n_active - 1]))) + U_active = U_active @ v_invsqrt + + phi_active = Knm @ U_active + + C = phi_active.T @ phi_active + + v_C, U_C = sorted_eig( + C, thresh=self.regularization, n=self.n_active) + + self.PKT = U_active @ U_C[:, :self.n_PC] + T = Knm @ self.PKT + + if X is not None: + self.PTX = np.diagflat(eig_inv(v_C[:self.n_PC])) @ T.T @ X + + def transform(self, X=None, Knm=None): + X, _, Knm = self.preprocess(X=X, K=Knm) + + if self.PKT is None: + raise Exception("Error: must fit the KPCA before transforming") + else: + if Knm is None and self.X_sparse is not None: + Knm = self.kernel(X, self.X_sparse) + _, _, Knm = self.preprocess(K=Knm) + + # Compute KPCA transformation + T = Knm @ self.PKT + + return T + + def statistics(self, X, Knm=None, K_test=None): + T = self.transform(X, Knm=Knm) + Kapprox = T @ T.T + + if K_test is None: + K_test = self.kernel(X, X) + # TODO: need to change this for the new centering? + K_test = center_kernel(K_test) + + + if self.PTX is not None: + Xr = T @ self.PTX + Xr, _ = self.postprocess(X=Xr) + else: + Xr = None + + return get_stats(k=K_test, kapprox=Kapprox, x=X, xr=Xr, t=T) + + +class SparseKRR(Sparsified, Regression): + """ + Performs sparsified kernel ridge regression + + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PTK: projector from latent space to kernel space + PTX: projector from latent space to input space + PXY: projector from input space to property space + X: input used to train the model, if further kernels need be constructed + X_sparse: active set used to train the model, if further kernels need be + constructed + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + n_active: (int) size of the active set + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and + center attributes + preprocess: centers and scales provided inputs according to scale and + center attributes + + ----Methods---- + fit: fit the kernel ridge regression model by computing regression weights + statistics: provide available statistics for the regression + transform: compute predicted Y values + + ----References---- + 1. M. Ceriotti, M. J. Willatt, G. Csanyi, + 'Machine Learning of Atomic - Scale Properties + Based on Physical Principles', Handbook of Materials Modeling, + Springer, 2018 + 2. A. J. Smola, B. Scholkopf, 'Sparse Greedy Matrix Approximation + for Machine Learning', Proceedings of the 17th International + Conference on Machine Learning, 911 - 918, 2000 + """ + + def __init__(self, *args, **kwargs): + super(SparseKRR, self).__init__(*args, **kwargs) + + def fit(self, X, Y, Kmm=None, Knm=None): + X, Y, _ = self.preprocess(X=X, X_ref=X, Y=Y, Y_ref=Y) + + if Kmm is None or Knm is None: + i_sparse, _ = FPS(X, self.n_active) + + self.X_sparse = X[i_sparse, :] + + if Kmm is None: + Kmm = self.kernel(self.X_sparse, self.X_sparse) + + if Knm is None: + Knm = self.kernel(X, self.X_sparse) + + if self.center: + Kmm = center_kernel(Kmm) + self.Kmm = Kmm + _, _, Knm = self.preprocess(K=Knm, K_ref=Knm) + + # Compute max eigenvalue of regularized model + PKY = np.linalg.pinv(Knm.T @ Knm + (self.regularization * Kmm)) + self.PKY = PKY @ Knm.T @ Y + + def transform(self, X, Knm=None): + X, _, Knm = self.preprocess(X=X, K=Knm) + + if self.PKY is None: + raise Exception("Error: must fit the KRR model before transforming") + else: + if Knm is None: + Knm = self.kernel(X, self.X_sparse) + _, _, Knm = self.preprocess(K=Knm) + + Yp = Knm @ self.PKY + _, Yp = self.postprocess(Y=Yp) + + return Yp + + def statistics(self, X, Y, Knm=None): + Yp = self.transform(X, Knm=Knm) + + return get_stats(x=X, y=Y, yp=Yp) + + +class MDS(Decomposition): + """ + Performs multidimensional scaling + + ----Attributes---- + n_MDS: (int) number of principal components to store + + ----Inherited Attributes---- + PTX: projector from latent space to input space + PXT: projector from input space to latent space + center: (boolean) whether to shift all inputs to zero mean + regularization: (float) parameter to offset all small eigenvalues for regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Methods---- + fit: fit the PCA + statistics: provide available statistics for the decomposition + transform: transform data based on the PCA fit + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and center attributes + preprocess: centers and scales provided inputs according to scale and center attributes + + ----References---- + 1. https://en.wikipedia.org/wiki/Multidimensional_scaling + 2. Torgerson, W.S. 'Multidimensional scaling: I. Theory and method', + Psychometrika 17, 401 - 419, 1952 + https://doi.org/10.1007/BF02288916 + """ + + def __init__(self, n_MDS=None, *args, **kwargs): + super().__init__(n_PC=n_MDS, *args, **kwargs) + + def fit(self, X): + """ + Fits the PCA + + ----Arguments---- + X: centered and normalized data on which to build the MDS + """ + + X, _, _ = self.preprocess(X=X, X_ref=X) + + # Compute covariance + K = X @ X.T + + # Compute eigendecomposition of covariance matrix + v, U = sorted_eig(K, thresh=self.regularization, n=self.n_PC) + + T = U[:, :self.n_PC] @ np.diagflat(np.sqrt(v[:self.n_PC])) + + self.PXT = np.linalg.lstsq(X, T, rcond=None)[0] + self.PTX = np.linalg.lstsq(T, X, rcond=None)[0] + + def transform(self, X): + """ + Transforms using MDS + + ----Arguments---- + X: centered data to transform based on MDS + """ + + X, _, _ = self.preprocess(X=X) + + if self.PXT is None: + raise Exception("Error: must fit the MDS before transforming") + else: + # Compute PCA scores + T = X @ self.PXT + return T + + def statistics(self, X): + T = self.transform(X) + Xr = T @ self.PTX + Xr, _ = self.postprocess(X=Xr) + + stats = get_stats(x=X, t=T, xr=Xr) + kernel_error = np.linalg.norm((X @ X.T) - (T @ T.T)) ** 2.0 + stats['Strain'] = kernel_error / np.linalg.norm((X @ X.T)) + + return stats + + +class PCovR(PCovRBase): + """ + Performs PCovR, detecting whether the data set is in Sample or Feature Space + + ----Attributes---- + space: whether to compute in feature or sample space + + ----Inherited Attributes---- + PTX: projector from latent space to input space + PTY: projector from latent space to property space + PXT: projector from input space to latent space + PXY: projector from input space to property space + Yhat: regressed properties + alpha: (float) mixing parameter between decomposition and regression + center: (boolean) whether to shift all inputs to zero mean + n_PC (int) number of principal components to store + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and + center attributes + preprocess: centers and scales provided inputs according to scale and + center attributes + + + ----References---- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligent + Laboratory Systems 14(1): 155-164, 1992 + 2. M. Vervolet, H. A. L. Kiers, W. Noortgate, E. Ceulemans, + 'PCovR: An R Package for Principal Covariates Regression', + Journal of Statistical Software 65(1):1-14, 2015 + """ + + def __init__(self, alpha=0.0, n_PC=None, space='auto', *args, **kwargs): + super().__init__(alpha=alpha, n_PC=n_PC, *args, **kwargs) + self.space = space + + def fit_feature_space(self, X, Y): + # Compute the inverse square root of the covariance of X + C = (X.T @ X) + v_C, U_C = sorted_eig(C, thresh=self.regularization) + U_C = U_C[:, v_C > self.regularization] + v_C = v_C[v_C > self.regularization] + + Csqrt = (U_C @ np.diagflat(np.sqrt(v_C)) @ U_C.T) + iCsqrt = (U_C @ np.diagflat(np.sqrt(eig_inv(v_C))) @ U_C.T) + + C_pca = X.T @ X + C_lr = iCsqrt @ X.T @ self.Yhat + C_lr = C_lr @ C_lr.T + + Ct = self.alpha * C_pca + (1.0 - self.alpha) * C_lr + + v_Ct, U_Ct = sorted_eig(Ct, thresh=self.regularization, n=self.n_PC) + + v_inv = eig_inv(v_Ct[:self.n_PC]) + + PXV = iCsqrt @ U_Ct[:, :self.n_PC] + + self.PXT = PXV @ np.diagflat(np.sqrt(v_Ct[:self.n_PC])) + self.PTX = np.diagflat(np.sqrt(v_inv)) @ U_Ct[:, :self.n_PC].T @ Csqrt + PTY = np.diagflat(np.sqrt(v_inv)) @ U_Ct[:, :self.n_PC].T @ iCsqrt + self.PTY = PTY @ X.T @ Y + + def fit_structure_space(self, X, Y): + K_pca = (X @ X.T) + K_lr = (self.Yhat @ self.Yhat.T) + + Kt = (self.alpha * K_pca) + (1.0 - self.alpha) * K_lr + + v, U = sorted_eig(Kt, thresh=self.regularization, n=self.n_PC) + + v_inv = eig_inv(v[:self.n_PC]) + T = U[:, :self.n_PC] @ np.diagflat(np.sqrt(v[:self.n_PC])) + + P_lr = (X.T @ X) + np.eye(X.shape[1]) * self.regularization + P_lr = np.linalg.pinv(P_lr) + P_lr = P_lr @ X.T @ Y + + if len(Y.shape) == 1: + P_lr = P_lr.reshape((-1, 1)) + + P_lr = P_lr @ self.Yhat.T + + P_pca = X.T + + P = (self.alpha * P_pca) + (1.0 - self.alpha) * P_lr + self.PXT = P @ U[:, :self.n_PC] @ np.diag(np.sqrt(v_inv)) + self.PTY = np.diagflat(v_inv) @ T.T @ Y + + self.PTX = np.diagflat(v_inv) @ T.T @ X + + def fit(self, X, Y, Yhat=None): + X, Y, _ = self.preprocess(X=X, Y=Y) + + if Yhat is None: + # lr = + # lr.fit(X, Y) + + self.Yhat = X @ np.linalg.pinv(X.T @ X + self.regularization*np.eye(X.shape[1])) @ X.T @ Y + + else: + self.Yhat = Yhat + + if len(Y.shape) == 1: + self.Yhat = self.Yhat.reshape(-1, 1) + + sample_heavy = X.shape[0] > X.shape[1] + if (self.space == 'feature' or sample_heavy) and self.space != 'structure': + if X.shape[0] > X.shape[1] and self.space != 'feature': + print("# samples > # features, computing in feature space") + self.fit_feature_space(X, Y) + elif self.space == 'structure' or not sample_heavy: + if sample_heavy and self.space != 'structure': + print("# samples < # features, computing in structure space") + self.fit_structure_space(X, Y) + else: + raise Exception( + 'Space Error: Please specify either space = "structure", ' + '"feature", or "auto" to designate the space to use.' + ) + + def transform(self, X): + if self.PXT is None or self.PTY is None: + raise Exception("Error: must fit the PCovR model before transforming") + else: + X, _, _ = self.preprocess(X=X) + T = X @ self.PXT + Yp = X @ self.PXT @ self.PTY + Xr = T @ self.PTX + Xr, Yp = self.postprocess(X=Xr, Y=Yp) + return T, Yp, Xr + + def loss(self, X, Y): + T, Yp, Xr = self.transform(X) + + Lpca = np.linalg.norm(X - Xr) ** 2 / np.linalg.norm(X) ** 2 + Llr = np.linalg.norm(Y - Yp) ** 2 / np.linalg.norm(Y) ** 2 + + return Lpca, Llr + + def statistics(self, X, Y): + T, Yp, Xr = self.transform(X) + + return get_stats(x=X, y=Y, yp=Yp, t=T, xr=Xr) + + +class KPCovR(PCovRBase, Kernelized): + """ + Performs KPCovR, as described in Helfrecht (2020), which combines Kernel + Principal Components Analysis (KPCA) and Kernel Ridge Regression (KRR) + + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PKY: projector from kernel space to property space + PTK: projector from latent space to kernel space + PTX: projector from latent space to input space + PTY: projector from latent space to property space + PXT: projector from input space to latent space + PXY: projector from input space to property space + X: input used to train the model, if further kernels need be constructed + Yhat: regressed properties + alpha: (float) mixing parameter between decomposition and regression + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + n_PC (int) number of principal components to store + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and + center attributes + preprocess: centers and scales provided inputs according to scale and + center attributes + + ---References--- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligent + Laboratory Systems 14(1): 155-164, 1992 + 2. M. Vervolet, H. A. L. Kiers, W. Noortgate, E. Ceulemans, + 'PCovR: An R Package for Principal Covariates Regression', + Journal of Statistical Software 65(1):1-14, 2015 + """ + + def __init__(self, n_PC=None, *args, **kwargs): + super(KPCovR, self).__init__(n_PC=n_PC, *args, **kwargs) + + def fit(self, X, Y, K=None, Yhat=None): + X, Y, K = self.preprocess(X=X, X_ref=X, Y=Y, Y_ref=Y, K=K, K_ref=K) + + if K is None: + K = self.kernel(X, X) + self.K = K + K = center_kernel(K) + else: + self.K = K + + if X is not None: + self.X = X + else: + print( + "No input data supplied during fitting. \n" + "Transformations/statistics only available for kernel inputs." + ) + + # Compute maximum eigenvalue of kernel matrix + if Yhat is None: + Yhat = K @ np.linalg.pinv(K, rcond=self.regularization) @ Y + + if len(Y.shape) == 1: + Yhat = Yhat.reshape(-1, 1) + + K_pca = K + K_lr = Yhat @ Yhat.T + + Kt = (self.alpha * K_pca) + (1.0 - self.alpha) * K_lr + + self.v, self.U = sorted_eig(Kt, thresh=self.regularization, n=self.n_PC) + + P_krr = np.linalg.solve(K + np.eye(len(K)) * self.regularization, Yhat) + P_krr = P_krr @ Yhat.T + + P_kpca = np.eye(K.shape[0]) + + P = (self.alpha * P_kpca) + (1.0 - self.alpha) * P_krr + + v_inv = eig_inv(self.v[:self.n_PC]) + + self.PKT = P @ self.U[:, :self.n_PC] @ np.diagflat(np.sqrt(v_inv)) + T = K @ self.PKT + + PT = np.linalg.pinv(T.T @ T) @ T.T + + self.PTK = PT @ K + self.PTY = PT @ Y + self.PTX = PT @ X + + def transform(self, X=None, K=None): + if self.PKT is None: + raise Exception("Error: must fit the PCovR model before transforming") + elif X is None and K is None: + raise Exception("Either the kernel or input data must be specified.") + else: + X, _, K = self.preprocess(X=X, K=K) + + if K is None and self.X is not None: + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.K) + elif K is None: + raise Exception("This functionality is not available.") + return + + T = K @ self.PKT + Yp = T @ self.PTY + Xr = T @ self.PTX + + Xr, Yp = self.postprocess(X=Xr, Y=Yp) + + if T.shape[1] == 1: + T = np.array((T.reshape(-1), np.zeros(T.shape[0]))).T + + return T, Yp, Xr + + def lkpcovr(self, X=None, Y=None, K_test=None, K_testtest=None): + + if K_test is None and self.X is not None: + K_test = self.kernel(X, self.X) + K_test = center_kernel(K_test, reference=self.K) + elif K_test is None: + raise ValueError( + "Must provide a kernel or a feature vector, in which case the " + "train features should be available in the class" + ) + + if(K_testtest is None and X is not None): + K_testtest = self.kernel(X, X) + K_testtest = (K_testtest - np.mean(K_test.T, axis=0) + - np.mean(K_test, axis=1).reshape(-1, 1) + + np.mean(self.K)) + else: + raise ValueError( + "Must provide a kernel between test features or a feature vector." + ) + + T_train = self.K @ self.PKT + T_test = K_test @ self.PKT + TTT = np.linalg.pinv(T_train.T @ T_train) + + return ((np.trace(K_testtest) - + 2 * np.trace(K_test @ T_train @ TTT @ T_test.T) + + np.trace(T_train @ TTT @ (T_test.T @ T_test) @ self.PTK)) / + np.trace(K_testtest)) + + def loss(self, X=None, Y=None, K=None, K_testtest=None): + if K is None and self.X is not None: + K = self.kernel(X, self.X) + + K = center_kernel(K, reference=self.K) + elif K is None: + raise ValueError( + "Must provide a kernel or a feature vector, in which case the " + "train features should be available in the class" + ) + + T, Yp, Xr = self.transform(X=X, K=K) + + Lregr = np.linalg.norm(Y - Yp)**2 / np.linalg.norm(Y)**2 + Lproj = self.lkpcovr(X=X, Y=Y, K_test=K, K_testtest=K_testtest) + return Lproj, Lregr + + def statistics(self, X, Y, K=None, K_testtest=None): + """ + Computes the loss values and reconstruction errors for + KPCovR for the given predictor and response variables + + ---Arguments--- + X: independent (predictor) variable + Y: dependent (response) variable + + ---Returns--- + dictionary of available statistics + """ + + if K is None and self.X is not None: + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.K) + + T, Yp, Xr = self.transform(X=X, K=K) + + Kapprox = T @ self.PTK + + stats = {r"$\ell_{proj}$": self.lkpcovr(X=X, Y=Y, K_test=K, K_testtest=K_testtest)} + + return get_stats(x=X, y=Y, yp=Yp, t=T, xr=Xr, + k=K, kapprox=Kapprox, **stats) + + +class SparseKPCovR(PCovRBase, Sparsified): + """ + Performs KPCovR, as described in Helfrecht (2020) + which combines Kernel Principal Components Analysis (KPCA) + and Kernel Ridge Regression (KRR), on a sparse active set + of variables + + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PKY: projector from kernel space to property space + PTK: projector from latent space to kernel space + PTX: projector from latent space to input space + PTY: projector from latent space to property space + PXT: projector from input space to latent space + PXY: projector from input space to property space + X: input used to train the model, if further kernels need be constructed + X_sparse: active set used to train the model, if further kernels need be + constructed + Yhat: regressed properties + alpha: (float) mixing parameter between decomposition and regression + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + n_PC (int) number of principal components to store + n_active: (int) size of the active set + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and + center attributes + preprocess: centers and scales provided inputs according to scale and + center attributes + + ---References--- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligent + Laboratory Systems 14(1): 155-164, 1992 + 2. M. Vervolet, H. A. L. Kiers, W. Noortgate, E. Ceulemans, + 'PCovR: An R Package for Principal Covariates Regression', + Journal of Statistical Software 65(1):1-14, 2015 + """ + + def __init__(self, n_PC=None, *args, **kwargs): + super(SparseKPCovR, self).__init__(n_PC=n_PC, *args, **kwargs) + + def fit(self, X, Y, X_sparse=None, Kmm=None, Knm=None): + X, Y, _ = self.preprocess(X=X, X_ref=X, Y=Y, Y_ref=Y) + + if X_sparse is None: + fps_idxs, _ = FPS(X, self.n_active) + self.X_sparse = X[fps_idxs, :] + else: + self.X_sparse = X_sparse + + if Kmm is None: + Kmm = self.kernel(self.X_sparse, self.X_sparse) + + if self.center: + Kmm = center_kernel(Kmm) + self.Kmm = Kmm + + if Knm is None: + Knm = self.kernel(X, self.X_sparse) + + _, _, self.Knm = self.preprocess(K=Knm, K_ref=Knm) + + vmm, Umm = sorted_eig( + Kmm, thresh=self.regularization, n=self.n_active) + vmm_inv = eig_inv(vmm[:self.n_active - 1]) + + phi_active = self.Knm @ Umm[:, :self.n_active - 1] @ np.diagflat(np.sqrt(vmm_inv)) + + C = phi_active.T @ phi_active + + v_C, U_C = sorted_eig(C, thresh=0) + U_C = U_C[:, v_C > 0] + v_C = v_C[v_C > 0] + v_C_inv = eig_inv(v_C) + + Csqrt = U_C @ np.diagflat(np.sqrt(v_C)) @ U_C.T + iCsqrt = U_C @ np.diagflat(np.sqrt(v_C_inv)) @ U_C.T + + C_pca = C + + C_lr = np.linalg.pinv(C + self.regularization * np.eye(C.shape[0])) + C_lr = iCsqrt @ phi_active.T @ phi_active @ C_lr @ phi_active.T + + if len(Y.shape) == 1: + C_lr = C_lr @ Y.reshape(-1, 1) + else: + C_lr = C_lr @ Y + + C_lr = C_lr @ C_lr.T + + Ct = self.alpha * C_pca + (1 - self.alpha) * C_lr + + v_Ct, U_Ct = sorted_eig(Ct, thresh=0) + + PPT = iCsqrt @ U_Ct[:, :self.n_PC] @ np.diag(np.sqrt(v_Ct[:self.n_PC])) + + PKT = Umm[:, :self.n_active - 1] @ np.diagflat(np.sqrt(vmm_inv)) + + self.PKT = PKT @ PPT + + T = self.Knm @ self.PKT + + PT = np.linalg.pinv(T.T @ T) @ T.T + self.PTY = PT @ Y + self.PTX = PT @ X + + def transform(self, X, Knm=None): + X, _, Knm = self.preprocess(X=X, K=Knm) + + if self.PKT is None: + raise Exception("Error: must fit the PCovR model before transforming") + else: + if Knm is None: + Knm = self.kernel(X, self.X_sparse) + _, _, Knm = self.preprocess(K=Knm) + + T = Knm @ self.PKT + Yp = T @ self.PTY + Xr = T @ self.PTX + + Xr, Yp = self.postprocess(X=Xr, Y=Yp) + + return T, Yp, Xr + + def loss(self, X, Y, Knm=None): + if Knm is None: + Knm = self.kernel(X, self.X_sparse) + Knm -= np.mean(self.K_ref, axis=0) + + T, Yp, Xr = self.transform(X, Knm=Knm) + + Lkpca = np.linalg.norm(Xr - X)**2 / np.linalg.norm(X)**2 + Lkrr = np.linalg.norm(Y - Yp)**2 / np.linalg.norm(Y)**2 + + return Lkpca, Lkrr + + def statistics(self, X, Y, Knm=None): + if Knm is None: + Knm = self.kernel(X, self.X_sparse) + Knm -= np.mean(self.K_ref, axis=0) + + T, Yp, Xr = self.transform(X, Knm=Knm) + + return get_stats(x=X, y=Y, yp=Yp, t=T, xr=Xr) diff --git a/utilities/deprecated/deprecated.py b/utilities/deprecated/deprecated.py new file mode 100644 index 0000000..bf0671d --- /dev/null +++ b/utilities/deprecated/deprecated.py @@ -0,0 +1,70 @@ +from ase.io import read, write + +# Librascal +from rascal.representations import SphericalInvariants as SOAP + + +def load_xyz(N=10, input_file="../datasets/CSD-1000R.xyz", property = "CS_local"): + """ + Loads the data from the xyz file + """ + + # Read the first N frames of CSD-500 + frames = read(input_file, index=":") + if(Nthresh else 0.0) for vv in v]) + + +def normalize_matrix(A, scale=None): + """ Normalize a matrix so that its entries have unit variance """ + if scale is None: + scale = np.linalg.norm(A) / np.sqrt(len(A)) + return A / scale + + +def center_matrix(A, center=None): + """ Removes the mean to "center" a feature matrix """ + if (center is None): + center = np.mean(A, axis=0) + return A - center + + +def FPS(X, n=0, idx=None): + """ + Does Farthest Point Selection on a set of points X + Adapted from a routine by Michele Ceriotti + """ + N = X.shape[0] + + # If desired number of points less than or equal to zero, + # select all points + if n <= 0: + n = N + + # Initialize arrays to store distances and indices + fps_idxs = np.zeros(n, dtype=np.int) + d = np.zeros(n) + + if idx is None: + # Pick first point at random + idx = np.random.randint(0, N) + fps_idxs[0] = idx + + # Compute distance from all points to the first point + d1 = np.linalg.norm(X - X[idx], axis=1)**2 + + # Loop over the remaining points... + for i in range(1, n): + + # Get maximum distance and corresponding point + fps_idxs[i] = np.argmax(d1) + d[i - 1] = np.amax(d1) + + # Compute distance from all points to the selected point + d2 = np.linalg.norm(X - X[fps_idxs[i]], axis=1)**2 + + # Set distances to minimum among the last two selected points + d1 = np.minimum(d1, d2) + + if np.abs(d1).max() == 0.0: + print("Only {} FPS Possible".format(i)) + return fps_idxs[:i], d[:i] + + return fps_idxs, d + + +def quick_inverse(mat): + """ Does a quick(er) matrix inverse """ + U_mat, v_mat = sorted_eig(mat, thresh=0) + + return np.matmul(np.matmul(U_mat, np.diagflat(eig_inv(v_mat))), U_mat.T) + + +def sorted_eig(mat, thresh=0.0, n=None, sps=True): + """ + Returns n eigenvalues and vectors sorted + from largest to smallest eigenvalue + """ + + if(sps): + from scipy.sparse.linalg import eigs as speig + if(n is None): + k = mat.shape[0] - 1 + else: + k = n + val, vec = speig(mat, k=k, tol=thresh) + val = np.real(val) + vec = np.real(vec) + + idx = sorted(range(len(val)), key=lambda i: -val[i]) + + val = val[idx] + vec = vec[:, idx] + + else: + val, vec = np.linalg.eigh(mat) + val = np.flip(val, axis=0) + vec = np.flip(vec, axis=1) + + if(n is not None and len(val[val=thresh] + val = val[val>=thresh] + + + return val[:n], vec[:, :n] + + +def get_stats(y=None, yp=None, x=None, t=None, xr=None, k=None, kapprox=None, **kwargs): + """Returns available statistics given provided data""" + stats = {} + if y is not None and yp is not None: + stats["Coefficient of Determination
($R^2$)"] = calc_R2(y, yp) + stats[r"$\ell_{regr}$"] = np.linalg.norm(y - yp) / y.shape[0] + if x is not None and t is not None: + stats[r"Dataset Variance
$\sigma_X^2$"] = x.var(axis=0).sum() + stats[r"Projection Variance
$\sigma_T^2$"] = t.var(axis=0).sum() + error = x.var(axis=0).sum() - t.var(axis=0).sum() + stats[r"Residual Variance
$\sigma_X^2 - \sigma_T^2$"] = error + if x is not None and xr is not None: + stats[r"$\ell_{proj}$"] = ((x - xr)**2).mean(axis=0).sum() + if k is not None and kapprox is not None: + error = np.linalg.norm(kapprox - k)**2 / np.linalg.norm(k)**2.0 + stats[r"$\ell_{gram}$"] = error + + # allow for manual input of statistics (for kpcovr error) + for k in kwargs: + stats[k] = kwargs[k] + + return stats + + +def split_data(N, n_train=0): + """Returns indices for the training and tests data sets""" + global n_test + # Splits in train and test sets + if n_train <= 0: # defaults 50-50 split + n_train = int(N / 2) + n_test = N - n_train + r_train = np.asarray(range(N)) + np.random.shuffle(r_train) + i_test = list(sorted(r_train[n_train:])) + i_train = list(sorted(r_train[:n_train])) + + return i_test, i_train + + +def load_variables(cache_file="../datasets/precomputed.npz", **kwargs): + """Loads the cache holding the soap vectors for CSD""" + return calculate_variables(**dict(np.load(cache_file)), **kwargs) + + +def calculate_variables( + X, + Y, + indices, + n_atoms, + N=10, + n_FPS=200, + kernel_func=gaussian_kernel, + i_train=None, + i_test=None, + **kwargs): + """Loads necessary data for the tutorials""" + + print(len(indices), "frames in total.") + print("Shape of Input Data is ", X.shape, ".") + + if n_FPS is not None: + fps_idxs, _ = FPS(X.T, n_FPS) + print("Taking a subsampling of ", n_FPS, "features") + X = X[:, fps_idxs] + + try: + print("Shape of testing data is: ", i_train.shape, ".") + except: + print("Splitting Data Set") + try: + i_test, i_train = split_data(len(Y), n_train) + except: + n_train = int(len(Y) / 2) + i_test, i_train = split_data(len(Y), n_train) + + n_train = len(i_train) + n_test = len(i_test) + + Y_train = Y[i_train] + Y_test = Y[i_test] + + Y_center = Y_train.mean(axis=0) + Y_scale = np.linalg.norm(Y_train - Y_center, axis=0) / np.sqrt(n_train / Y_train.shape[1]) + + Y = center_matrix(Y, center=Y_center) + Y_train = center_matrix(Y_train, center=Y_center) + Y_test = center_matrix(Y_test, center=Y_center) + Y_train = normalize_matrix(Y_train, scale=Y_scale) + Y_test = normalize_matrix(Y_test, scale=Y_scale) + + if len(Y) == len(indices): + print("Computing training/testing sets from summed environment-centered soap vectors.") + frame_starts = [sum(nat[:i]) for i in range(len(n_atoms) + 1)] + X_split = [ + X[frame_starts[i]:frame_starts[i + 1]] + for i in range(len(indices)) + ] + + X = np.array([np.mean(xs, axis=0) for xs in X_split]) + X_train = X[i_train] + X_test = X[i_test] + + else: + X_split = X.copy() + + X_train = X[i_train] + X_test = X[i_test] + + X_center = X_train.mean(axis=0) + X_scale = np.linalg.norm(X_train - X_center) / np.sqrt(n_train) + + X_train = center_matrix(X_train, center=X_center) + X_test = center_matrix(X_test, center=X_center) + X = center_matrix(X, center=X_center) + + X_train = normalize_matrix(X_train, scale=X_scale) + X_test = normalize_matrix(X_test, scale=X_scale) + X = normalize_matrix(X, scale=X_scale) + + try: + print("Shape of kernel is: ", K_train.shape, ".") + except: + if len(Y) == len(indices): + print("Computing kernels from summing kernels of environment-centered soap vectors.") + + K_train = kernel_func([X_split[i] for i in i_train], + [X_split[i] for i in i_train]) + K_test = kernel_func([X_split[i] for i in i_test], + [X_split[i] for i in i_train]) + + else: + + K_train = kernel_func(X_split[i_train], X_split[i_train]) + K_test = kernel_func(X_split[i_test], X_split[i_train]) + + K_test = center_kernel(K_test, reference=K_train) + K_train = center_kernel(K_train) + + K_scale = np.trace(K_train) / K_train.shape[0] + + K_train = normalize_matrix(K_train, scale=K_scale) + K_test = normalize_matrix(K_test, scale=K_scale) + + n_train = len(X_train) + n_test = len(X_test) + n_PC = 2 + + return dict(X=X, Y=Y, + X_split=X_split, + X_center=X_center, Y_center=Y_center, + X_scale=X_scale, Y_scale=Y_scale, + X_train=X_train, Y_train=Y_train, + X_test=X_test, Y_test=Y_test, + K_train=K_train, K_test=K_test, + i_train=i_train, i_test=i_test, + n_PC=n_PC, n_train=n_train, n_test=n_test) diff --git a/utilities/kernel_pcovr.mplstyle b/utilities/kernel_pcovr.mplstyle new file mode 100644 index 0000000..636138d --- /dev/null +++ b/utilities/kernel_pcovr.mplstyle @@ -0,0 +1,67 @@ + + +# AXES +axes.edgecolor : (0.1,0.1,0.1) #Normalized RGB colours (from 0 to 1 instead of 0 to 255) +axes.grid : False +axes.labelcolor : (0.1,0.1,0.1) +axes.labelsize : 12 +axes.linewidth : 1.0 +axes.prop_cycle : cycler('color', [ '0046b8', '2464c9', '4d87e3', '7899cf', '8ea1bf']) #hex colours +axes.spines.bottom : True +axes.spines.left : True +axes.spines.right : True +axes.spines.top : True +axes.titlesize : 16 + +# TEXT OPTIONS +font.size : 12 +legend.fontsize : 12 +figure.titlesize : large ## size of the figure title (Figure.suptitle()) + ## when plotting very large data sets, + +# FIGURE OUTPUT +text.color : black +figure.dpi : 150 +figure.figsize : 6, 5 +savefig.dpi : 200 + +# GRID +grid.alpha : 0.7 +grid.linestyle : -- +grid.linewidth : 0.6 +hatch.linewidth : 1.0 + +# LINES +lines.linewidth : 1.0 +lines.markeredgewidth : 0.5 +lines.markeredgecolor : black +lines.markersize : 10 +patch.linewidth : 0.4 +patch.edgecolor : black +patch.force_edgecolor : True +patch.antialiased : True + +# SCATTER PLOT +scatter.marker : o + +# TICKS +xtick.bottom : True +xtick.color : black +xtick.direction : in +xtick.labelsize : 12 +xtick.major.pad : 5.0 +xtick.major.size : 4.0 +xtick.minor.pad : 5.0 +xtick.minor.size : 2.0 +xtick.minor.visible : True +xtick.top : True +ytick.color : black +ytick.direction : in +ytick.labelsize : 12 +ytick.left : True +ytick.major.pad : 5.0 +ytick.major.size : 4.0 +ytick.minor.pad : 5.0 +ytick.minor.size : 2.0 +ytick.minor.visible : True +ytick.right : True diff --git a/utilities/kernels.py b/utilities/kernels.py new file mode 100644 index 0000000..e5573dc --- /dev/null +++ b/utilities/kernels.py @@ -0,0 +1,210 @@ +import numpy as np +from scipy.spatial.distance import cdist + +def self_linear_kernel(XA): + """ + Build a dot product kernel between all samples in XA + + ---Arguments--- + XA: vectors of data from which to build the kernel, + where each row is a sample and each column is a feature. + If XA is a list, the kernel is averaged over the list + + ---Returns--- + K: dot product kernel matrix between XA samples + """ + + K = np.zeros((len(XA), len(XA))) + + flag_A = isinstance(XA, list) + + # XA structures + if flag_A: + for idx_i in range(len(XA)): + for idx_j in range(idx_i, len(XA)): + kij = np.matmul(XA[idx_i], XA[idx_j].T) + K[idx_i, idx_j] = K[idx_j, idx_i] = kij.mean() + + # XA environments + else: + K = np.matmul(XA, XA.T) + + return K + +def linear_kernel(XA, XB=None): + """ + Builds a dot product kernel + + ---Arguments--- + XA, XB: vectors of data from which to build the kernel, + where each row is a sample and each column is a feature. + If XA or XB is a list, the kernel is averaged over the list + + ---Returns--- + K: dot product kernel between XA (and XB) + """ + + flag_A = isinstance(XA, list) + flag_B = isinstance(XB, list) + + if XB is None: + return self_linear_kernel(XA) + + else: + K = np.zeros((len(XA), len(XB))) + + # XA and XB structures + if flag_A and flag_B: + for idx_i in range(len(XA)): + for idx_j in (range(len(XB))): + ki = np.matmul(XA[idx_i], XB[idx_i].T) + K[idx_i, idx_j] = ki.mean() + + # XA structures, XB environments + elif flag_A: + for idx_i in range(len(XA)): + ki = np.matmul(XA[idx_i], XB.T) + K[idx_i, :] = ki.mean(axis=0) + + # XA environments, XB structures + elif flag_B: + for idx_j in range(len(XB)): + kj = np.matmul(XA, XB[idx_j].T) + K[:, idx_j] = ki.mean(axis=1) + + # XA and XB environments + else: + K = np.matmul(XA, XB.T) + + return K + + +def self_gaussian_kernel(XA, gamma=1.0): + """ + Build a Gaussian kernel between all samples in XA + + ---Arguments--- + XA: vectors of data from which to build the kernel, + where each row is a sample and each column is a feature. + If XA is a list, the kernel is averaged over the list + gamma: kernel width + + ---Returns--- + K: gaussian kernel matrix between XA samples + """ + + K = np.zeros((len(XA), len(XA))) + + flag_A = isinstance(XA, list) + + # XA structures + if flag_A: + for idx_i in range(len(XA)): + for idx_j in range(idx_i, len(XA)): + kij = np.exp(-gamma*cdist(XA[idx_i], XA[idx_j], metric="sqeuclidean")) + K[idx_i, idx_j] = K[idx_j, idx_i] = kij.mean() + + # XA environments + else: + K = np.exp(-gamma*cdist(XA, XA, metric="sqeuclidean")) + + return K + + +def gaussian_kernel(XA, XB=None, gamma=1.0): + """ + Build a Gaussian kernel between all samples in XA and XB + + ---Arguments--- + XA, XB: vectors of data from which to build the kernel, + where each row is a sample and each column is a feature. + If XA or XB is a list, the kernel is averaged over the list + gamma: kernel width + + ---Returns--- + K: gaussian kernel matrix between XA (and XB) + """ + + flag_A = isinstance(XA, list) + flag_B = isinstance(XB, list) + + if XB is None: + return self_gaussian_kernel(XA, gamma=gamma) + + else: + K = np.zeros((len(XA), len(XB))) + + # XA and XB structures + if flag_A and flag_B: + for idx_i in range(len(XA)): + for idx_j in (range(len(XB))): + ki = np.exp(-gamma*cdist(XA[idx_i], XB[idx_j], metric="sqeuclidean")) + K[idx_i, idx_j] = ki.mean() + + # XA structures, XB environments + elif flag_A: + for idx_i in range(len(XA)): + ki = np.exp(-gamma*cdist(XA[idx_i], XB, metric="sqeuclidean")) + K[idx_i, :] = ki.mean(axis=0) + + # XA environments, XB structures + elif flag_B: + for idx_j in range(len(XB)): + kj = np.exp(-gamma*cdist(XA, XB[idx_j], metric="sqeuclidean")) + K[:, idx_j] = ki.mean(axis=1) + + # XA and XB environments + else: + K = np.exp(-gamma*cdist(XA, XB, metric="sqeuclidean")) + + return K + + +def center_kernel(K, reference=None, ref_cmean=None, ref_rmean=None, ref_mean=None): + """ + Centers a kernel + + ---Arguments--- + K: kernel to center + reference: kernel relative to whos RKHS one should center + defaults to K + + ---Returns--- + Kc: centered kernel + + ---References--- + 1. https://en.wikipedia.org/wiki/Kernel_principal_component_analysis + 2. M. Welling, 'Kernel Principal Component Analysis', + https://www.ics.uci.edu/~welling/classnotes/papers_class/Kernel-PCA.pdf + """ + + K_ref = reference + if K_ref is None: + K_ref = K + else: + if K.shape[1] != K_ref.shape[0]: + raise ValueError( + "The kernel to be centered and the reference have inconsistent sizes") + if K_ref.shape[0] != K_ref.shape[1]: + raise ValueError( + "The reference kernel is not square, and does not define a RKHS") + # oneMN = np.ones((K.shape[0], K.shape[1]))/K.shape[1] + # oneNN = np.ones((K.shape[1], K.shape[1]))/K.shape[1] + # + # Kc = K - np.matmul(oneMN, K_ref) - np.matmul(K, oneNN) + \ + # np.matmul(np.matmul(oneMN, K_ref), oneNN) + + if(ref_cmean is None): + ref_cmean = K_ref.mean(axis=0) + + if(ref_rmean is None): + ref_rmean = K.mean(axis=1) + + if(ref_mean is None): + ref_mean = K_ref.mean() + + Kc = K - np.broadcast_arrays(K, ref_cmean)[1] \ + - ref_rmean.reshape((K.shape[0], 1)) \ + + np.broadcast_arrays(K, ref_mean)[1] + + return Kc diff --git a/utilities/kpcovr.py b/utilities/kpcovr.py new file mode 100644 index 0000000..ceda4a2 --- /dev/null +++ b/utilities/kpcovr.py @@ -0,0 +1,447 @@ +import numpy as np +from scipy.spatial.distance import cdist +from .general import get_stats, FPS, sorted_eig, eig_inv +from .kernels import linear_kernel, gaussian_kernel, center_kernel + +kernels = {"gaussian": gaussian_kernel, + "linear": linear_kernel + } + + +class KPCovR: + + """ + Performs KPCovR, as described in Helfrecht (2020), + which combines Kernel Principal Components Analysis (KPCA) + and Kernel Ridge Regression (KRR) + + ---Arguments--- + X: independent (predictor) variable + Y: dependent (response) variable + alpha: tuning parameter + n_PC: number of principal components to retain + kernel_type: kernel function, may be either type str or function, + defaults to a linear kernel + + ---Returns--- + Xp: X values projected into the latent (PCA-like) space + Yp: predicted Y values + Xr: Reconstructed X values from the latent (PCA-like) space + Lx: KPCA loss + Ly: KR loss + + ---References--- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligent + Laboratory Systems 14(1): 155-164, 1992 + 2. M. Vervolet, H. A. L. Kiers, W. Noortgate, E. Ceulemans, + 'PCovR: An R Package for Principal Covariates Regression', + Journal of Statistical Software 65(1):1-14, 2015 + """ + + def __init__(self, alpha=0.0, n_PC=2, + kernel_type='linear', regularization=1e-12): + + self.alpha = alpha + self.n_PC = n_PC + self.regularization = regularization + + self.PKT = None + self.PTK = None + self.PTY = None + self.X = None # To save the X which was used to train the model + + if(isinstance(kernel_type, str)): + if(kernel_type in kernels): + self.kernel = kernels[kernel_type] + else: + raise Exception('Kernel Error: \ + Please specify either {}\ + or pass a suitable kernel function.\ + '.format(kernels.keys())) + elif(callable(kernel_type)): + self.kernel = kernel_type + else: + raise Exception('Kernel Error: \ + Please specify either {}\ + or pass a suitable kernel function.\ + '.format(kernels.keys())) + + def fit(self, X, Y, K=None, Yhat=None): + """ + Fits the KPCovR to the training inputs and outputs + + ---Arguments--- + X: independent (predictor) variable + Y: dependent (response) variable + + ---Returns--- + PKT: Weights projecting kernel into latent PCA-space + T: Projection of kernel in latent PCA-space + PTY: Projector from latent PCA-space to Y-space + PTK: Projector from latent PCA-space to kernel-space + """ + + if(K is None): + K = self.kernel(X, X) + self.K = K + K = center_kernel(K) + else: + self.K = K + + if(X is not None): + self.X = X + else: + print("No input data supplied during fitting." + + "\nTransformations and statistics only" + + "available with pre-computed kernels.") + + # Compute maximum eigenvalue of kernel matrix + + if(Yhat is None): + Yhat = K @ np.linalg.pinv(K, rcond=self.regularization) @ Y + + if(len(Y.shape) == 1): + Yhat = Yhat.reshape(-1, 1) + + K_pca = K #/ (np.trace(K) / X.shape[0]) + K_lr = np.matmul(Yhat, Yhat.T) + + Kt = (self.alpha * K_pca) + (1.0 - self.alpha) * K_lr + self.Kt = Kt + + self.v, self.U = sorted_eig( + Kt, thresh=self.regularization, n=self.n_PC) + + P_krr = np.linalg.solve(K + np.eye(len(K)) * self.regularization, Yhat) + P_krr = np.matmul(P_krr, Yhat.T) + + P_kpca = np.eye(K.shape[0]) #/ (np.trace(K) / K.shape[0]) + + P = (self.alpha * P_kpca) + (1.0 - self.alpha) * P_krr + + v_inv = np.diagflat(eig_inv(self.v[:self.n_PC])) + + self.PKT = np.matmul(P, np.matmul(self.U[:, :self.n_PC], + np.sqrt(v_inv))) + T = np.matmul(K, self.PKT) + + PT = np.matmul(T.T, T) + PT = np.linalg.pinv(PT) + PT = np.matmul(PT, T.T) + self.PTK = np.matmul(PT, K) + self.PTY = np.matmul(PT, Y) + self.PTX = np.matmul(PT, X) + + def transform(self, X=None, K=None): + """ + Transforms a set of inputs using the computed KPCovR + + ---Arguments--- + X: independent (predictor) variable + + ---Returns--- + Xp: X values projected into the latent (PCA-like) space + Yp: predicted Y values + + """ + if self.PKT is None: + print("Error: must fit the PCovR model before transforming") + elif(X is None and K is None): + print("Either the kernel or input data must be specified.") + else: + + if(K is None and self.X is not None): + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.K) + elif(K is None): + print("This functionality is not available.") + return + + T = np.matmul(K, self.PKT) + Yp = np.matmul(T, self.PTY) + Xr = np.matmul(T, self.PTX) + + if(T.shape[1] == 1): + T = np.array((T.reshape(-1), np.zeros(T.shape[0]))).T + return T, Yp, Xr + + def loss(self, X=None, Y=None, K=None): + """ + Computes the loss values for KPCovR on the given predictor and + response variables + + ---Arguments--- + X: independent (predictor) variable + Y: dependent (response) variable + + ---Returns--- + Lx: KPCA loss + Ly: KR loss + + """ + + if(K is None and self.X is not None): + K = self.kernel(X, self.X) + + K = center_kernel(K, reference=self.K) + elif(K is None): + raise ValueError( + "Must provide a kernel or a feature vector, in which case the train features should be available in the class") + + Tp, Yp, Xr = self.transform(X=X, K=K) + Kapprox = np.matmul(Tp, self.PTK) + + Lkpca = np.linalg.norm(K - Kapprox)**2/np.linalg.norm(K)**2 + Lkrr = np.linalg.norm(Y - Yp)**2/np.linalg.norm(Y)**2 + + return Lkpca, Lkrr + + def statistics(self, X, Y, K=None): + """ + Computes the loss values and reconstruction errors for + KPCovR for the given predictor and response variables + + ---Arguments--- + X: independent (predictor) variable + Y: dependent (response) variable + + ---Returns--- + dictionary of available statistics + + """ + + if(K is None and self.X is not None): + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.K) + + Tp, Yp, Xr = self.transform(X=X, K=K) + + Kapprox = np.matmul(Tp, self.PTK) + + return get_stats(x=X, y=Y, yp=Yp, t=Tp, xr=Xr, + k=K, kapprox=Kapprox) + + +class SparseKPCovR: + + """ + Performs KPCovR, as described in Helfrecht (2020) + which combines Kernel Principal Components Analysis (KPCA) + and Kernel Ridge Regression (KRR), on a sparse active set + of variables + + ---Arguments--- + X: independent (predictor) variable + Y: dependent (response) variable + alpha: tuning parameter + n_PC: number of principal components to retain + kernel_type: kernel function, may be either type str or function, + defaults to a linear kernel + + ---Returns--- + Xp: X values projected into the latent (PCA-like) space + Yp: predicted Y values + Lx: KPCA loss + Ly: KR loss + + ---References--- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligent + Laboratory Systems 14(1): 155-164, 1992 + 2. M. Vervolet, H. A. L. Kiers, W. Noortgate, E. Ceulemans, + 'PCovR: An R Package for Principal Covariates Regression', + Journal of Statistical Software 65(1):1-14, 2015 + """ + + def __init__(self, alpha, n_PC, n_active=100, regularization=1e-6, kernel_type="linear"): + + self.alpha = alpha + self.n_active = n_active + self.n_PC = n_PC + self.regularization = regularization + + self.PKT = None + self.PTY = None + self.PTX = None + self.X = None # To save the X which was used to train the model + + if(isinstance(kernel_type, str)): + if(kernel_type in kernels): + self.kernel = kernels[kernel_type] + else: + raise Exception('Kernel Error: \ + Please specify either {}\ + or pass a suitable kernel function.\ + '.format(kernels.keys())) + elif(callable(kernel_type)): + self.kernel = kernel_type + else: + raise Exception('Kernel Error: \ + Please specify either {}\ + or pass a suitable kernel function.\ + '.format(kernels.keys())) + + def fit(self, X, Y, X_sparse=None, Kmm=None, Knm=None): + """ + Fits the KPCovR to the training inputs and outputs + + ---Arguments--- + X: independent (predictor) variable + Y: dependent (response) variable + + ---Returns--- + PKT: Weights projecting K into latent PCA-space + T: Projection of K in latent PCA-space + PTY: Projector from latent PCA-space to Y-space + PTX: Projector from latent PCA-space to X-space + """ + + if(X_sparse is None): + fps_idxs, _ = FPS(X, self.n_active) + self.X_sparse = X[fps_idxs, :] + else: + self.X_sparse = X_sparse + + if(Kmm is None): + Kmm = self.kernel(self.X_sparse, self.X_sparse) + self.Kmm = Kmm + Kmm = center_kernel(Kmm) + else: + self.Kmm = Kmm + + if(Knm is None): + Knm = self.kernel(X, self.X_sparse) + Knm = center_kernel(Knm, reference=self.Kmm) + self.Knm = Knm + + vmm, Umm = sorted_eig( + Kmm, thresh=self.regularization, n=self.n_active) + vmm_inv = eig_inv(vmm[:self.n_active-1]) + + self.barKM = np.mean(self.Knm, axis=0) + + phi_active = np.matmul(self.Knm, Umm[:, :self.n_active-1]) + phi_active = np.matmul(phi_active, np.diagflat(np.sqrt(vmm_inv))) + barPhi = np.mean(phi_active, axis=0) + phi_active -= barPhi + + C = np.dot(phi_active.T, phi_active) + + v_C, U_C = sorted_eig(C, thresh=0) + U_C = U_C[:, v_C > 0] + v_C = v_C[v_C > 0] + v_C_inv = eig_inv(v_C) + + Csqrt = np.matmul(np.matmul(U_C, np.diagflat(np.sqrt(v_C))), U_C.T) + iCsqrt = np.matmul( + np.matmul(U_C, np.diagflat(np.sqrt(v_C_inv))), U_C.T) + + C_pca = C #/ (np.trace(C)/C.shape[0]) + + C_lr = np.linalg.pinv(C + self.regularization*np.eye(C.shape[0])) + C_lr = np.matmul(phi_active, C_lr) + C_lr = np.matmul(phi_active.T, C_lr) + C_lr = np.matmul(iCsqrt, C_lr) + C_lr = np.matmul(C_lr, phi_active.T) + + if(len(Y.shape) == 1): + C_lr = np.matmul(C_lr, Y.reshape(-1, 1)) + else: + C_lr = np.matmul(C_lr, Y) + + C_lr = np.matmul(C_lr, C_lr.T) + + Ct = self.alpha*C_pca + (1-self.alpha)*C_lr + + v_Ct, U_Ct = sorted_eig(Ct, thresh=0) + + PPT = np.matmul(iCsqrt, U_Ct[:, :self.n_PC]) + PPT = np.matmul(PPT, np.diag(np.sqrt(v_Ct[:self.n_PC]))) + + PKT = np.matmul(Umm[:, :self.n_active-1], + np.diagflat(np.sqrt(vmm_inv))) + self.PKT = np.matmul(PKT, PPT) + self.barT = np.matmul(barPhi, PPT) + + T = np.matmul(self.Knm, self.PKT) - self.barT + + PT = np.matmul(T.T, T) + PT = np.linalg.pinv(PT) + PT = np.matmul(PT, T.T) + self.PTY = np.matmul(PT, Y) + self.PTX = np.matmul(PT, X) + + def transform(self, X, Knm=None): + """ + Transforms a set of inputs using the computed Sparse KPCovR + + ---Arguments--- + X: independent (predictor) variable + + ---Returns--- + Xp: X values projected into the latent (PCA-like) space + Yp: predicted Y values + + """ + + if self.PKT is None: + print("Error: must fit the PCovR model before transforming") + else: + + if(Knm is None): + Knm = self.kernel(X, self.X_sparse) + Knm = center_kernel(Knm, reference=self.Kmm) + + T = np.matmul(Knm, self.PKT) - self.barT + Yp = np.matmul(T, self.PTY) + Xr = np.matmul(T, self.PTX) + return T, Yp, Xr + + def loss(self, X, Y, Knm=None): + """ + Computes the loss values for KPCovR on the given predictor and + response variables + + ---Arguments--- + X: independent (predictor) variable + Y: dependent (response) variable + + ---Returns--- + Lx: KPCA loss + Ly: KR loss + + """ + + if(Knm is None): + Knm = self.kernel(X, self.X_sparse) + Knm = center_kernel(Knm, reference=self.Kmm) + + T, Yp, Xr = self.transform(X, Knm=Knm) + + Lkpca = np.linalg.norm(Xr - X)**2/np.linalg.norm(X)**2 + Lkrr = np.linalg.norm(Y - Yp)**2/np.linalg.norm(Y)**2 + + return Lkpca, Lkrr + + def statistics(self, X, Y, Knm=None): + """ + Computes the loss values and reconstruction errors for + KPCovR for the given predictor and response variables + + ---Arguments--- + X: independent (predictor) variable + Y: dependent (response) variable + + ---Returns--- + dictionary of available statistics + + """ + + if(Knm is None): + Knm = self.kernel(X, self.X_sparse) + Knm = center_kernel(Knm, reference=self.Kmm) + + T, Yp, Xr = self.transform(X, Knm=Knm) + + return get_stats(x=X, y=Y, yp=Yp, t=T, xr=Xr) diff --git a/utilities/old_classes.py b/utilities/old_classes.py new file mode 100644 index 0000000..1f258cf --- /dev/null +++ b/utilities/old_classes.py @@ -0,0 +1,728 @@ +import numpy as np +from .general import FPS, get_stats, sorted_eig, eig_inv +from .kernels import linear_kernel, center_kernel, gaussian_kernel + +kernels = { + "gaussian": gaussian_kernel, + "linear": linear_kernel +} + + +class PCA: + """ + Performs principal component analysis + + ---Attributes--- + n_PC: number of PCA components to retain + (`None` retains all components) + C: covariance matrix of the data + self.U: eigenvalues of the covariance matrix + V: eigenvectors of the covariance matrix + + ---Methods--- + fit: fit the PCA + transform: transform data based on the PCA fit + + ---References--- + 1. https: / / en.wikipedia.org / wiki / Principal_component_analysis + 2. M. E. Tipping 'Sparse Kernel Principal Component Analysis', + Advances in Neural Information Processing Systems 13, 633 - 639, 2001 + """ + + def __init__(self, n_PC=None, regularization=1e-12): + + # Initialize attributes + + self.n_PC = n_PC + self.C = None + self.PXT = None + self.PTX = None + self.regularization = regularization + + def fit(self, X): + """ + Fits the PCA + + ---Arguments--- + X: centered data on which to build the PCA + """ + + # Compute covariance + self.C = np.matmul(X.T, X) / (X.shape[0] - 1) + + # Compute eigendecomposition of covariance matrix + v, U = sorted_eig(self.C, thresh=self.regularization, n=self.n_PC) + + self.PXT = U[:, :self.n_PC] + self.PTX = self.PXT.T + + def transform(self, X): + """ + Transforms the PCA + + ---Arguments--- + X: centered data to transform based on the PCA + """ + + if self.PXT is None: + print("Error: must fit the PCA before transforming") + else: + + # Compute PCA scores + T = np.matmul(X, self.PXT) + return T + + def statistics(self, X): + T = self.transform(X) + X_PCA = np.matmul(T, self.PTX) + return get_stats(x=X, t=T, xr=X_PCA) + + +class LR: + """ + Performs linear regression + + ---Attributes--- + w: regression weights + + ---Methods--- + fit: fit the linear regression model by computing regression weights + transform: compute predicted Y values + + ---References--- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligents + Laboratory Systems 14(1): 155-164, 1992 + 2. https://en.wikipedia.org/wiki/Linear_regression + """ + + def __init__(self, regularization=1e-12): + self.PXY = None + self.regularization = regularization + + def fit(self, X, Y): + """ + Fits the linear regression model + + ---Arguments--- + X: centered, independent (predictor) variable + Y: centered, dependent (response) variable + """ + + # Compute inverse of covariance + XTX = np.matmul(X.T, X) + XTX = XTX + self.regularization * np.eye(X.shape[1]) + XTX = np.linalg.pinv(XTX) + + # Compute LR solution + self.PXY = np.matmul(XTX, X.T) + self.PXY = np.matmul(self.PXY, Y) + + def transform(self, X): + """ + Computes predicted Y values + + ---Arguments--- + X: centered, independent (predictor) variable + """ + + # Compute predicted Y + Yp = np.matmul(X, self.PXY) + + return Yp + + def statistics(self, X, Y): + Yp = self.transform(X) + return get_stats(x=X, y=Y, yp=Yp) + + +class KPCA: + """ + Performs kernel principal component analysis on a dataset + based on a kernel between all of the constituent data points + + ---Arguments--- + K: kernel matrix + n_PC: number of principal components to retain in the decomposition + + ---Returns--- + T: KPCA scores + + ---References--- + 1. https: / / en.wikipedia.org / wiki / Kernel_principal_component_analysis + 2. M. E. Tipping, 'Sparse Kernel Principal Component Analysis', + Advances in Neural Information Processing Systems 13, 633 - 639, 2001 + """ + + def __init__(self, n_PC, regularization=1e-12, kernel_type="linear"): + self.n_PC = n_PC + self.PTX = None + self.PKT = None + self.PTK = None + self.regularization = regularization + self.v, self.U = None, None + + if(isinstance(kernel_type, str)): + self.kernel = kernels[kernel_type] + else: + self.kernel = kernel_type + + def fit(self, X=None, K=None): + + if(K is None): + K = self.kernel(X, X) + K = center_kernel(K) + + if(X is not None): + self.X = X + else: + print("No input data supplied during fitting. \ + \nTransformations/statistics only available for kernel inputs.") + + # Compute eigendecomposition of kernel + self.v, self.U = sorted_eig( + K, thresh=self.regularization, n=self.n_PC) + + v_inv = eig_inv(self.v[:self.n_PC]) + + self.PKT = np.matmul(self.U[:, :self.n_PC], + np.diagflat(np.sqrt(v_inv))) + self.T = np.matmul(K, self.PKT) + self.PTK = np.matmul(np.diagflat(v_inv), + np.matmul(self.T.T, K)) + if(X is not None): + self.PTX = np.matmul(np.diagflat(v_inv), + np.matmul(self.T.T, X)) + + def transform(self, X=None, K=None): + if self.PKT is None: + print("Error: must fit the KPCA before transforming") + elif X is None and K is None: + print("Either the kernel or input data must be specified.") + else: + + # Compute KPCA transformation + if(K is None): + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.kernel(self.X, self.X)) + + T = np.matmul(K, self.PKT) + + return T + + def statistics(self, X=None, Y=None, K=None): + if X is None and K is None: + print("Either the kernel or input data must be specified.") + else: + # Compute KPCA transformation + + if(K is None): + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.kernel(self.X, self.X)) + + T = np.matmul(K, self.PKT) + Kapprox = np.matmul(T, self.PTK) + if(self.PTX is not None): + Xr = np.matmul(T, self.PTX) + else: + Xr = None + + return get_stats(k=K, kapprox=Kapprox, x=X, xr=Xr, + t=T) + + +class KRR: + """ + Performs kernel ridge regression + + ---Arguments--- + K: kernel matrix + Y: property values + regularization: regularization factor to ensure positive definiteness + + ---Returns--- + w: regression weights + + ---References--- + 1. M. Ceriotti, M. J. Willatt, G. Csanyi, + 'Machine Learning of Atomic - Scale Properties + Based on Physical Principles', Handbook of Materials Modeling, + Springer, 2018 + """ + + def __init__(self, regularization=1.0E-16, kernel_type="linear"): + + self.regularization = regularization + self.PKY = None + self.X = None + + if(isinstance(kernel_type, str)): + self.kernel = kernels[kernel_type] + else: + self.kernel = kernel_type + + def fit(self, X=None, Y=None, K=None): + + if(K is None): + K = self.kernel(X, X) + self.K = K.copy() + K = center_kernel(K, self.K) + + if(X is not None): + self.X = X + else: + print("No input data supplied during fitting. \ + \nTransformations/statistics only available for kernel inputs.") + + # Regularize the model + Kreg = K + np.eye(K.shape[0]) * self.regularization + + # Solve the model + self.PKY = np.linalg.solve(Kreg, Y) + + def transform(self, X=None, K=None): + if self.PKY is None: + print("Error: must fit the KPCA before transforming") + elif X is None and K is None: + print("Either the kernel or input data must be specified.") + else: + + # Compute KPCA transformation + if(K is None): + K = self.kernel(X, self.X) + K = center_kernel(K, reference=self.K) + + Yp = np.matmul(K, self.PKY) + + return Yp + + def statistics(self, X=None, Y=None, K=None): + + Yp = self.transform(X=X, K=K) + + return get_stats(x=X, y=Y, yp=Yp, k=K) + + +class SparseKPCA: + """ + Performs kernel principal component analysis on a dataset + based on a kernel between furthest point sampling of the constituent + data points + + ---Arguments--- + K: kernel matrix + n_PC: number of principal components to retain in the decomposition + + ---Returns--- + T: KPCA scores + + ---References--- + 1. https: / / en.wikipedia.org / wiki / Kernel_principal_component_analysis + 2. M. E. Tipping, 'Sparse Kernel Principal Component Analysis', + Advances in Neural Information Processing Systems 13, 633 - 639, 2001 + """ + + def __init__(self, n_PC, n_active=100, regularization=1e-12, + kernel_type="linear"): + + self.n_PC = n_PC + self.n_active = n_active + self.PKT = None + self.X = None + self.regularization = regularization + + if(isinstance(kernel_type, str)): + self.kernel = kernels[kernel_type] + else: + self.kernel = kernel_type + + def fit(self, X, i_sparse=None, X_sparse=None, Kmm=None, Knm=None): + + if(i_sparse is None): + i_sparse, _ = FPS(X, self.n_active) + + if(X_sparse is None): + self.X_sparse = X[i_sparse, :] + else: + self.X_sparse = X_sparse + + if(Kmm is None): + Kmm = self.kernel(self.X_sparse, self.X_sparse) + Kmm = center_kernel(Kmm) + self.Kmm = Kmm + + if(Knm is None): + Knm = self.kernel(X, self.X_sparse) + Knm = center_kernel(Knm, Kmm) + self.barKM = np.mean(Knm, axis=0) + + # Compute eigendecomposition of kernel + self.vmm, self.Umm = sorted_eig( + Kmm, thresh=self.regularization, n=self.n_active) + + U_active = self.Umm[:, :self.n_active - 1] + v_invsqrt = np.diagflat(np.sqrt(eig_inv(self.vmm[0:self.n_active - 1]))) + self.U_active = np.matmul(U_active, v_invsqrt) + + phi_active = np.matmul(Knm - self.barKM, self.U_active) + + C = np.dot(phi_active.T, phi_active) + + self.v_C, self.U_C = sorted_eig( + C, thresh=self.regularization, n=self.n_active) + + self.PKT = np.matmul(self.U_active, self.U_C[:, :self.n_PC]) + self.T = np.matmul(Knm - self.barKM, self.PKT) + self.PTX = np.matmul(np.diagflat( + eig_inv(self.v_C[:self.n_PC])), np.matmul(self.T.T, X)) + + def transform(self, X, Knm=None): + if self.PKT is None: + print("Error: must fit the KPCA before transforming") + else: + if(Knm is None): + Knm = self.kernel(X, self.X_sparse) + + # Compute KPCA transformation + T = np.matmul(Knm - self.barKM, self.PKT) + + return T + + def statistics(self, X, Knm=None, K_test=None): + + T = self.transform(X, Knm=Knm) + Kapprox = np.matmul(T, T.T) + + if(K_test is None): + K_test = self.kernel(X, X) + K_test = center_kernel(K_test) + + Xr = np.matmul(T, self.PTX) + + return get_stats(k=K_test, kapprox=Kapprox, x=X, xr=Xr, + t=T) + + +class SparseKRR: + """ + Performs sparsified kernel ridge regression + + TODO: Put in terms of X, Y + ---Arguments--- + Knm: kernel between the whole dataset and the 'representative' data points + Kmm: kernel between the 'representative' data points and themselves + Y: property values + sigma: regularization parameter + regularization: additional regularization scale based on + the maximum eigenvalue of sigma * Kmm + Knm.T x Knm + + ---Returns--- + Yp: predicted property values + + ---References--- + 1. M. Ceriotti, M. J. Willatt, G. Csanyi, + 'Machine Learning of Atomic - Scale Properties + Based on Physical Principles', Handbook of Materials Modeling, + Springer, 2018 + 2. A. J. Smola, B. Scholkopf, 'Sparse Greedy Matrix Approximation + for Machine Learning', Proceedings of the 17th International + Conference on Machine Learning, 911 - 918, 2000 + """ + + def __init__(self, regularization=1.0E-16, + n_active=100, kernel_type='linear'): + + self.regularization = regularization + self.n_active = n_active + self.w = None + + if(isinstance(kernel_type, str)): + self.kernel = kernels[kernel_type] + else: + self.kernel = kernel_type + + def fit(self, X, Y, i_sparse=None, X_sparse=None, Kmm=None, Knm=None): + + if(i_sparse is None): + i_sparse, _ = FPS(X, self.n_active) + + if(X_sparse is None): + self.X_sparse = X[i_sparse, :] + else: + self.X_sparse = X_sparse + + if(Kmm is None): + Kmm = self.kernel(self.X_sparse, self.X_sparse) + Kmm = center_kernel(Kmm) + self.Kmm = Kmm + + if(Knm is None): + Knm = self.kernel(X, self.X_sparse) + Knm = center_kernel(Knm, Kmm) + + # Compute max eigenvalue of regularized model + PKY = np.linalg.pinv(np.matmul(Knm.T, Knm) + self.regularization * Kmm) + PKY = np.matmul(PKY, Knm.T) + self.PKY = np.matmul(PKY, Y) + + def transform(self, X, Knm=None): + if self.PKY is None: + print("Error: must fit the KRR model before transforming") + else: + if(Knm is None): + Knm = self.kernel(X, self.X_sparse) + + Yp = np.matmul(Knm, self.PKY) + + return Yp + + def statistics(self, X, Y, Knm=None): + P = self.transform(X, Knm=Knm) + + return get_stats(x=X, y=Y, yp=P) + + +class MDS: + """ + Performs multidimensional scaling + + ---Attributes--- + n_MDS: number of PCA components to retain + (`None` retains all components) + K: inner product of the data, hereon kernel + U: eigenvalues of the kernel matrix + V: eigenvectors of the kernel matrix + + ---Methods--- + fit: fit the MDS + transform: transform data based on the MDS fit + + ---References--- + 1. https: / / en.wikipedia.org / wiki / Multidimensional_scaling + 2. Torgerson, W.S. 'Multidimensional scaling: I. Theory and method', + Psychometrika 17, 401 - 419, 1952 + https: / / doi.org / 10.1007 / BF02288916 + """ + + def __init__(self, n_MDS=None, regularization=1e-12): + + # Initialize attributes + + self.n_MDS = n_MDS + self.K = None + self.PXT = None + self.regularization = regularization + + def fit(self, X): + """ + Fits the PCA + + ---Arguments--- + X: centered and normalized data on which to build the MDS + """ + + # Compute covariance + self.K = np.matmul(X, X.T) + + # Compute eigendecomposition of covariance matrix + v, U = sorted_eig(self.K, thresh=self.regularization, n=self.n_MDS) + + T = np.matmul(U[:, :self.n_MDS], np.diagflat(np.sqrt(v[:self.n_MDS]))) + self.PXT = np.linalg.lstsq(X, T, rcond=None)[0] + self.PTX = np.linalg.lstsq(T, X, rcond=None)[0] + + def transform(self, X): + """ + Transforms using MDS + + ---Arguments--- + X: centered data to transform based on MDS + """ + + if self.PXT is None: + print("Error: must fit the MDS before transforming") + else: + + # Compute PCA scores + T = np.matmul(X, self.PXT) + return T + + def statistics(self, X): + T = self.transform(X) + Xr = np.matmul(T, self.PTX) + stats = get_stats(x=X, t=T, xr=Xr) + kernel_error = np.linalg.norm(np.matmul(X, X.T) - np.matmul(T, T.T)) ** 2.0 + stats['Strain'] = kernel_error / np.linalg.norm(np.matmul(X, X.T)) + return stats + + +class PCovR: + """ + Performs PCovR, detecting whether the data set is in Structure or + Feature Space + + ---Arguments--- + X: independent (predictor) variable, centered and normalized + Y: dependent (response) variable, centered and normalized + alpha: tuning parameter + n_PC: number of principal components to retain + loss: compute individual PCA and linear regression loss terms + + ---Returns--- + Xp: X values projected into the latent (PCA - like) space + Xr: reconstructed X values from the PCA + Yp: predicted Y values + B: regression coefficients for predicting Y + Lx: PCA loss + Ly: linear regression loss + + ---References--- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligent + Laboratory Systems 14(1): 155-164, 1992 + 2. M. Vervolet, H. A. L. Kiers, W. Noortgate, E. Ceulemans, + 'PCovR: An R Package for Principal Covariates Regression', + Journal of Statistical Software 65(1):1-14, 2015 + """ + + def __init__(self, alpha=0.0, n_PC=None, regularization=1e-12, space='auto'): + self.alpha = alpha + self.n_PC = n_PC + self.regularization = regularization + + self.v = None + self.U = None + self.PXT = None + self.PTX = None + self.PTY = None + + self.space = space + + def compute_K(self, X, Y, Yhat=None): + + # Compute K + if(Yhat is None): + lr = LR(regularization=self.regularization) + lr.fit(X, Y) + + self.Yhat = lr.transform(X) + + else: + self.Yhat = Yhat + + if(len(Y.shape) == 1): + self.Yhat = self.Yhat.reshape(-1, 1) + + K_pca = np.matmul(X, X.T) + K_lr = np.matmul(self.Yhat, self.Yhat.T) + + self.K = (self.alpha * K_pca) + (1.0 - self.alpha) * K_lr + + def fit_feature_space(self, X, Y, Yhat=None): + + self.compute_K(X, Y, Yhat=Yhat) + + # Compute the inverse square root of the covariance of X + C = np.matmul(X.T, X) + v_C, U_C = sorted_eig(C, thresh=self.regularization) + U_C = U_C[:, v_C > self.regularization] + v_C = v_C[v_C > self.regularization] + + Csqrt = np.matmul(np.matmul(U_C, np.diagflat(np.sqrt(v_C))), U_C.T) + iCsqrt = np.matmul( + np.matmul(U_C, np.diagflat(np.sqrt(eig_inv(v_C)))), U_C.T) + + Ct = np.matmul(iCsqrt, X.T) + Ct = np.matmul(np.matmul(Ct, self.K), Ct.T) + + v_Ct, U_Ct = sorted_eig(Ct, thresh=self.regularization, n=self.n_PC) + + v_inv = eig_inv(v_Ct[:self.n_PC]) + + PXV = np.matmul(iCsqrt, U_Ct[:, :self.n_PC]) + + self.PXT = np.matmul(PXV, + np.diagflat(np.sqrt(v_Ct[:self.n_PC]))) + self.PTX = np.matmul(np.diagflat(np.sqrt(v_inv)), + np.matmul(U_Ct[:, :self.n_PC].T, Csqrt)) + PTY = np.matmul(np.diagflat(np.sqrt(v_inv)), + U_Ct[:, :self.n_PC].T) + PTY = np.matmul(PTY, iCsqrt) + self.PTY = np.matmul(np.matmul(PTY, X.T), Y) + + def fit_structure_space(self, X, Y, Yhat=None): + + self.compute_K(X, Y, Yhat=Yhat) + self.v, self.U = sorted_eig( + self.K, thresh=self.regularization, n=self.n_PC) + + v_inv = eig_inv(self.v[:self.n_PC]) + self.T = np.matmul(self.U[:, :self.n_PC], + np.diagflat(np.sqrt(self.v[:self.n_PC]))) + + P_lr = np.matmul(X.T, X) + np.eye(X.shape[1]) * self.regularization + P_lr = np.linalg.pinv(P_lr) + P_lr = np.matmul(P_lr, X.T) + P_lr = np.matmul(P_lr, Y) + + if(len(Y.shape) == 1): + P_lr = P_lr.reshape((-1, 1)) + + P_lr = np.matmul(P_lr, self.Yhat.T) + + P_pca = X.T + + P = (self.alpha * P_pca) + (1.0 - self.alpha) * P_lr + self.PXT = np.matmul(P, np.matmul(self.U[:, :self.n_PC], + np.diag(np.sqrt(v_inv)))) + self.PTY = np.matmul(np.diagflat(v_inv), + np.matmul(self.T.T, Y)) + + self.PTX = np.matmul(np.diagflat(v_inv), + np.matmul(self.T.T, X)) + + def fit(self, X, Y, Yhat=None): + + sample_heavy = X.shape[0] > X.shape[1] + if((self.space == 'feature' or sample_heavy) and self.space != 'structure'): + if(X.shape[0] > X.shape[1] and self.space != 'feature'): + print("# samples > # features, computing in feature space") + self.fit_feature_space(X, Y, Yhat=Yhat) + elif(self.space == 'structure' or not sample_heavy): + if(sample_heavy and self.space != 'structure'): + print("# samples < # features, computing in structure space") + self.fit_structure_space(X, Y, Yhat=Yhat) + else: + raise Exception('Space Error: \ + Please specify either space = "structure",\ + "feature", or "auto" to designate the space to \ + compute in.\ + ') + + def transform(self, X): + if self.PXT is None or self.PTY is None: + print("Error: must fit the PCovR model before transforming") + else: + # self.Undo whitening of PCA scores and scale by norm + # Xp = np.linalg.norm(X)* + + T = np.matmul(X, self.PXT) + + Yp = np.matmul(np.matmul(X, self.PXT), self.PTY) + + Xr = np.matmul(T, self.PTX) + + return T, Yp, Xr + + def loss(self, X, Y): + T, Yp, Xr = self.transform(X) + + Lpca = np.linalg.norm(X - Xr) ** 2 / np.linalg.norm(X) ** 2 + Llr = np.linalg.norm(Y - Yp) ** 2 / np.linalg.norm(Y) ** 2 + + return Lpca, Llr + + def statistics(self, X, Y): + T, Yp, Xr = self.transform(X) + + return get_stats(x=X, y=Y, yp=Yp, t=T, xr=Xr) diff --git a/utilities/plotting.py b/utilities/plotting.py new file mode 100644 index 0000000..52ccc91 --- /dev/null +++ b/utilities/plotting.py @@ -0,0 +1,297 @@ +import numpy as np +import matplotlib.pyplot as plt +from IPython.display import display, Markdown +import os +import datetime + +utils_dir = os.path.dirname(os.path.realpath(__file__)) +plt.style.use('{}/kernel_pcovr.mplstyle'.format(utils_dir)) + + +def plot_base(scatter_points, fig, ax, title, x_label, y_label, cbar=True, + cbar_title="", cb_orientation='vertical', cb_ax = None, rasterized=True, + font_scaled=False, + **kwargs): + """ + Base class for all plotting utilities + Author: Rose K. Cersonsky + + ---Variables--- + scatter_points: (array) n-dimensional data to plot + first two components are plotted + fig, ax: figure and axis to plot on, as generated by plt.subplots() + title: (str) title for plot + x_label, y_label: (str) labels for x-axis and y-axis + cbar_title: (str) label for colorbar + kwargs: arguments to pass to plt.scatter + + """ + + # print(kwargs) + if(ax is None or fig is None): + fig, ax = plt.subplots(1, figsize=plt.rcParams['figure.figsize']) + + cb_args = kwargs.get('cb_args', {}) + if('cb_args' in kwargs): + kwargs.pop('cb_args') + + p = ax.scatter(scatter_points[:, 0], + scatter_points[:, 1], + rasterized=rasterized, + **kwargs + ) + + if('cmap' in kwargs and cbar==True): + + if(cb_ax is None): + cb_args['ax'] = ax + cb_args['fraction'] = cb_args.get('fraction', 0.4) + else: + cb_args['cax'] = cb_ax + cb_args['fraction'] = cb_args.get('fraction', 1.0) + + cbar = fig.colorbar(p, **cb_args, + orientation=cb_orientation, + ) + + if(cb_orientation=='horizontal'): + cbar.ax.set_xlabel(cbar_title) + else: + cbar.ax.set_ylabel(cbar_title) + + if(font_scaled): + size = min(fig.get_size_inches())*fig.dpi + fontsize = size/100. + ax.set_title(title, fontsize=fontsize) + ax.set_xlabel(x_label, fontsize=fontsize, labelpad=0.0) + ax.set_ylabel(y_label, fontsize=fontsize, labelpad=0.0) + else: + ax.set_title(title) + ax.set_xlabel(x_label) + ax.set_ylabel(y_label) + + return fig, ax + + +def plot_simple(X, fig=None, ax=None, title=None, labels=[r"$X_1$", r"$X_2$"], **kwargs): + """ + Create simple plot of 2+ dimensional data + Author: Rose K. Cersonsky + + ---Variables--- + X: (array) n-dimensional data to plot + first two components will be plotted + fig, ax: figure and axis to plot on, as generated by plt.subplots() + title: (str) title for plot + labels: (str) labels for x-axis and y-axis + kwargs: arguments to pass to plt.scatter + """ + + if('cmapY' in kwargs): + kwargs.pop('cmapY') + if('cmapX' in kwargs): + kwargs.pop('cmapX') + if('color' not in kwargs): + kwargs['color'] = 'b' + + fig, ax = plot_base(scatter_points=X, fig=fig, ax=ax, title=title, + alpha=1.0, + x_label=labels[0], + y_label=labels[1], + **kwargs + ) + return ax + + +def plot_projection(Y, T, fig=None, ax=None, Y_scale=1.0, Y_center=0.0, **kwargs): + """ + Create a plot of a latent-space projection of data + Author: Rose K. Cersonsky + + ---Variables--- + Y: (array) property to use for the colorbar + T: (array) latent-space projection + fig, ax: figure and axis to plot on, as generated by plt.subplots() + kwargs: arguments to pass to plt.scatter, + may contain cbar_title, x_label, y_label, and title + for non-typical plots + """ + + Y = Y.reshape(Y.shape[0], -1) + if(len(T.shape)==1 or T.shape[-1]==1): + T = np.array([T[:,0], np.zeros(T.shape[0])]).T + + if('color' not in kwargs): + if Y.shape[-1] != 1: + if('cmap2D' in kwargs and 'colormap' not in kwargs): + if('vmin' not in kwargs or 'vmax' not in kwargs): + bounds = np.array([np.mean(Y, axis=0)-np.std(Y, axis=0), + np.mean(Y, axis=0)+np.std(Y, axis=0)]).T + else: + bounds = np.array([kwargs['vmin'], kwargs['vmax']]).T + kwargs.pop('vmin'); kwargs.pop('vmax'); + + bounds = bounds[:2] + colormap = kwargs['cmap2D'](*bounds) + kwargs['c'] = [colormap(y) for y in Y] + elif('colormap' in kwargs): + kwargs['c'] = [kwargs['colormap'](y) for y in Y] + kwargs.pop('colormap') + else: + Y = Y[:, 0] + if isinstance(Y_scale, np.ndarray) or isinstance(Y_scale, list): + Y_scale = Y_scale[0] + if isinstance(Y_center, np.ndarray) or isinstance(Y_center, list): + Y_center = Y_center[0] + kwargs['c'] = Y * Y_scale + Y_center + if('cmap' in kwargs): + kwargs.pop('cmap') + if('vmin' in kwargs): + kwargs.pop('vmin'); kwargs.pop('vmax') + elif('c' not in kwargs): + Y = Y[:, 0] + Y_center = np.array([Y_center]) + Y_center = Y_center.reshape(Y_center.shape[0], -1) + Y_center = Y_center[0] + + if('colormap' in kwargs): + kwargs['c'] = [kwargs['colormap']( (y-min(Y)) / (max(Y) - min(Y))) for y in Y] + kwargs.pop('colormap') + else: + kwargs['c'] = Y * Y_scale + Y_center + kwargs['cmap'] = kwargs.get('cmapX', "viridis") + + if('cmap2D' in kwargs): + kwargs.pop('cmap2D') + if('colormap' in kwargs): + kwargs.pop('colormap') + + if('cmapY' in kwargs): + kwargs.pop('cmapY') + if('cmapX' in kwargs): + kwargs.pop('cmapX') + + kwargs['cbar_title'] = kwargs.get('cbar_title', "CS") + kwargs['x_label'] = kwargs.get('x_label', r'$PC_1$') + kwargs['y_label'] = kwargs.get('y_label', r'$PC_2$') + kwargs['title'] = kwargs.get('title', None) + + fig, ax = plot_base(scatter_points=T, fig=fig, ax=ax, **kwargs) + return ax + + +def plot_regression(Y, Yp, fig=None, ax=None, Y_scale=1.0, Y_center=0.0, **kwargs): + """ + Create a plot of a regressed data + Author: Rose K. Cersonsky + + ---Variables--- + Y: (array) property to compare against + Yp: (array) predicted property + fig, ax: figure and axis to plot on, as generated by plt.subplots() + kwargs: arguments to pass to plt.scatter, + may contain cbar_title, x_label, y_label, and title + for non-typical plots + """ + if len(Y.shape) != 1: + # print("Only plotting first column of Y") + Y = Y[:, 0] + Yp = Yp[:, 0] + if isinstance(Y_scale, np.ndarray) or isinstance(Y_scale, list): + Y_scale = Y_scale[0] + if isinstance(Y_center, np.ndarray) or isinstance(Y_center, list): + Y_center = Y_center[0] + kwargs['cmap'] = kwargs.get('cmapY', 'Greys') + + if('cmapY' in kwargs): + kwargs.pop('cmapY') + if('cmapX' in kwargs): + kwargs.pop('cmapX') + if('cmap2D' in kwargs): + kwargs.pop('cmap2D') + + if('color' not in kwargs): + kwargs['c'] = Y_scale * np.abs(Y - Yp) + + kwargs['cbar_title'] = kwargs.get('cbar_title', "Loss") + kwargs['x_label'] = kwargs.get('x_label', r'$Y$') + kwargs['y_label'] = kwargs.get('y_label', r'$\hat{Y}$') + kwargs['title'] = kwargs.get('title', None) + + plot_points = np.add(np.multiply(Y_scale, [Y, Yp]), Y_center) + + fig, ax = plot_base(scatter_points=plot_points.T, fig=fig, ax=ax, **kwargs) + + cm = np.mean(plot_points, axis=1) + bound = max(np.abs(plot_points[0]-cm[0]).max(), + np.abs(plot_points[1]-cm[1]).max()) + ax.set_xlim([cm[0]-bound, cm[0]+bound]) + ax.set_ylim([cm[1]-bound, cm[1]+bound]) + ax.plot([cm[0]-bound, cm[0]+bound], [cm[1]-bound, + cm[1]+bound], + 'r--', zorder=4, linewidth=0.25) + + return ax + + +def get_cmaps(): + from .colorbars import load + + load() + + return dict( + cmapY='Greys', + cmapX='cbarHot', + edgecolor='k' + ) + + +def markdown_table(data, headers, columns, title, precision=1e-3): + + return display(Markdown(f'
{title}

\ +
' + + ''.join([f'\ + ' for c, d in zip(columns, data)]) + + "
' + + '
'.join(headers) + + '
{c} {" ".join([dd for dd in d])}
")) + + +def table_from_dict(dictionaries, headers, title='', precision=1e-6): + columns = [] + for d in dictionaries: + for k in d: + if k not in columns: + columns.append(k) + data = [["{:g}".format(d[k]) if k in d else '' for d in dictionaries] + for k in columns] + return markdown_table(data, headers, columns, title, precision=precision) + + +def check_mirrors(X1, X2): + # Checking if the PCs of the sparse kernel are reflections of those for the full kernel + def hist_dist(x, xr): + hp, bp = np.histogramdd(x, bins=20, normed=True) + hq, bq = np.histogramdd(xr, bins=20, normed=True) + return np.linalg.norm(hp-hq) + + X = X1.copy() + Xref = X2.copy() + + X = np.subtract(X, np.mean(X, axis=0)) + Xref = np.subtract(Xref, np.mean(Xref, axis=0)) + + Xscale = np.linalg.norm(X) + X = X / Xscale + Xref = Xref / np.linalg.norm(Xref) + + if(hist_dist(X[:, 0], Xref[:, 0]) > hist_dist(-X[:, 0], Xref[:, 0])): + xflip = -1 + else: + xflip = 1 + if(hist_dist(X[:, 1], Xref[:, 1]) > hist_dist(-X[:, 1], Xref[:, 1])): + yflip = -1 + else: + yflip = 1 + + return (xflip, yflip)*X1[:, :2] diff --git a/utilities/scalers.py b/utilities/scalers.py new file mode 100644 index 0000000..3f6f9b5 --- /dev/null +++ b/utilities/scalers.py @@ -0,0 +1,52 @@ +import numpy as np +import sklearn as sk +from sklearn.base import TransformerMixin, BaseEstimator + +class NormalizeScaler(TransformerMixin, BaseEstimator): + """ A more flexible scaler for features and data, that mimics + sklearn.preprocessing.StandardScaler but makes the mean norm of the rows + equal to one. """ + + + def __init__(self, *, with_mean=True, with_norm=True, per_feature=False): + """ Initialize NormalizeScaler. Defines whether it will subtract mean + (with_mean=True), apply normalization (with_norm=True) and whether it will + normalize each feature separately (per_feature=True). """ + + self.__with_mean = with_mean + self.__with_norm = with_norm + self.__per_feature = per_feature + self.n_samples_seen_ = 0 + + def fit(self, X, y=None): + """ Compute mean and scaling to be applied for subsequent normalization. """ + + + self.n_samples_seen_, self.n_features_ = X.shape + self.mean_ = np.zeros(self.n_features_) + + if self.__with_mean: + self.mean_ = X.mean(axis=0) + centred_X = X - self.mean_ + else: + centred_X = X + + self.scale_ = 1.0 + if self.__with_norm: + var = (centred_X**2).mean(axis=0) + + if self.__per_feature: + if np.any(var==0): + raise ValueError("Cannot normalize a feature with zero variance") + self.scale_ = np.sqrt(1.0/(self.n_features_*var)) + else: + self.scale_ = 1.0/np.sqrt(var.sum()) + + return self + + def transform(self, X, y=None): + """ Normalize a vector based on previously computed mean and scaling. """ + + if self.n_samples_seen_ == 0 : + raise sk.exceptions.NotFittedError("This "+type(self).__name__+" instance is not fitted yet. Call 'fit' with appropriate arguments before using this estimator.") + return self.scale_*(X-self.mean_) diff --git a/utilities/sklearn_covr/_base.py b/utilities/sklearn_covr/_base.py new file mode 100644 index 0000000..480f5cb --- /dev/null +++ b/utilities/sklearn_covr/_base.py @@ -0,0 +1,101 @@ +import numpy as np +from abc import abstractmethod +from sklearn.utils import check_array +from sklearn.utils.validation import check_is_fitted + +class _BasePCovR(): + """ + Super-class defined for PCovR style methods + # """ + + def __init__(self, alpha, n_components, regularization, tol): + # TODO + self.alpha = alpha + self.n_components = n_components + self.regularization = regularization + self.tol = tol + + @abstractmethod + def fit(self, X, Y, Yhat=None): + """Placeholder for fit. Subclasses should implement this method! + + Fit the model with X. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples and + n_features is the number of features. + Y : array-like, shape (n_samples, n_properties) + Training data, where n_samples is the number of samples and + n_properties is the number of properties + Yhat : array-like, shape (n_samples, n_properties), optional + Regressed training data, where n_samples is the number of samples and + n_properties is the number of properties. If not supplied, computed + by ridge regression. + + Returns + ------- + self : object + Returns the instance itself. + """ + + @abstractmethod + def transform(self, X): + """Placeholder for transform. Subclasses should implement this method! + + Transforms the model with X. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples and + n_features is the number of features. + + Returns + ------- + self : object + Returns the instance itself. + """ + + @abstractmethod + def predict(self, X): + """Placeholder for transform. Subclasses should implement this method! + + Predicts the outputs given X. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples and + n_features is the number of features. + + Returns + ------- + self : object + Returns the instance itself. + """ + + def _project(self, A, projector): + """Apply a projector to matrix A + + + Parameters + ---------- + A : array-like, shape (n, a) + projector: string corresponding to the named projection matrix of shape (a, p) + + Returns + ------- + A' : array-like, shape (n, p) + + Examples + -------- + + >>> todo + """ + check_is_fitted(self) + + A = check_array(A) + A_transformed = np.dot(A, self.__dict__[projector]) + return A_transformed diff --git a/utilities/sklearn_covr/pcovr.py b/utilities/sklearn_covr/pcovr.py new file mode 100644 index 0000000..0e924e7 --- /dev/null +++ b/utilities/sklearn_covr/pcovr.py @@ -0,0 +1,189 @@ +import numpy as np +from sklearn.linear_model import LinearRegression as LR +from sklearn.utils.validation import check_X_y +from scipy.sparse.linalg import eigs + +from ._base import _BasePCovR + +class PCovR(_BasePCovR): + """ + Performs PCovR, detecting whether the data set is in Sample or Feature Space + + ----Attributes---- + space: whether to compute in feature or sample space + n_components: number of latent space components for dimensionality reduction + regularization: regularization parameter for linear models + tol: tolerance for small eigenvalues in eigendecompositions + alpha: (float) mixing parameter between decomposition and regression + ptx_: projector from latent space to input space + pty_: projector from latent space to property space + pxt_: projector from input space to latent space + Yhat: regressed properties + + ----References---- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligent + Laboratory Systems 14(1): 155-164, 1992 + 2. M. Vervolet, H. A. L. Kiers, W. Noortgate, E. Ceulemans, + 'PCovR: An R Package for Principal Covariates Regression', + Journal of Statistical Software 65(1):1-14, 2015 + """ + + def __init__(self, alpha=0.0, n_components=None, + regularization=1e-6, tol=1e-12, + eig_solver="sparse", + space=None, lr_args={}, *args, **kwargs, + ): + super().__init__(alpha=alpha, n_components=n_components, + regularization=regularization, tol=tol, + *args, **kwargs) + self.space = space + self.lr_args = lr_args + self.eig_solver = eig_solver + self.n_components = n_components + self.Yhat = None + self.W = None + + def fit(self, X, Y, Yhat=None, W=None): + # as required by the superclass + + X, Y = check_X_y(X, Y, y_numeric=True, multi_output=True) + + if Yhat is None or W is None: + self._compute_Yhat(X, Y) + else: + self.Yhat = Yhat + self.W = W + + # Sparse eigensolvers will not work when seeking N-1 eigenvalues + if min(X.shape) <= self.n_components: + self.eig_solver = 'full' + + self._fit(X, Y) + + def _fit(self, X, Y): + """ + Method for computing the PCovR projectors + """ + if self.space is None: + if X.shape[0] > X.shape[1]: + self.space = 'feature' + else: + self.space = 'structure' + + if self.space == 'feature': + self._fit_feature_space(X, Y) + else: + self._fit_sample_space(X, Y) + + self.mean_ = np.mean(X, axis =0) + + def _compute_Yhat(self, X, Y): + """ + Method for computing the approximation of Y + """ + + if self.Yhat is None: + lr = LR(self.lr_args) # some sort of args + lr.fit(X, Y) + self.Yhat = lr.predict(X) + self.W = lr.coef_.T + + if self.W is None: + W = np.linalg.pinv(np.dot(X.T, X), rcond=self.regularization) + W = np.linalg.multi_dot([W, X.T, Y]) + self.W = W + + def _fit_feature_space(self, X, Y): + """ + In sample-space PCovR, the projectors are determined by: + + C̃ = α X.T X + (1 - α) (X.T X)^(-1/2) X.T Ŷ Ŷ.T X (X.T X)^(-1/2) + + where + + P_XT = (X.T X)^(-1/2) U_C̃.T Λ_C̃^(1/2) + P_TX = Λ_C̃^(-1/2) U_C̃.T (X.T X)^(1/2) + P_TY = Λ_C̃^(-1/2) U_C̃.T (X.T X)^(-1/2) X.T Y + + """ + + C = np.dot(X.T, X) + + # it is necessary to use the full SVD to decompose C + v, U = self._eig_solver(C, full_matrix=True) + S = v ** 0.5 + S_inv = np.linalg.pinv(np.diagflat(S)) + + Csqrt = np.linalg.multi_dot([U, np.diagflat(S), U.T]) + iCsqrt = np.linalg.multi_dot([U, S_inv, U.T]) + + C_lr = iCsqrt @ X.T @ self.Yhat + C_lr = C_lr @ C_lr.T + + # note about Ctilde definition + Ct = self.alpha * C + (1.0 - self.alpha) * C_lr + + v, U = self._eig_solver(Ct) + S = v ** 0.5 + + self.pxt_ = np.linalg.multi_dot([iCsqrt, U, np.diagflat(S)]) + self.ptx_ = np.linalg.multi_dot([S_inv, U.T, Csqrt]) + self.pty_ = np.linalg.multi_dot( + [S_inv, U.T, iCsqrt, X.T, Y]) + + def _fit_sample_space(self, X, Y): + """ + In sample-space PCovR, the projectors are determined by: + + K̃ = α X X.T + (1 - α) Ŷ Ŷ.T + + where + + P_XT = α X.T + (1 - α) P_XY Ŷ.T + P_TX = Λ_K̃^(-1/2) U_K̃.T X + P_TY = Λ_K̃^(-1/2) U_K̃.T Y + + """ + + + Kt = (self.alpha * np.dot(X, X.T)) + \ + (1.0 - self.alpha) * np.dot(self.Yhat, self.Yhat.T) + + v, U = self._eig_solver(Kt) + S = v ** 0.5 + + T = np.dot(U, np.diagflat(S)) + + P = (self.alpha * X.T) + (1.0 - self.alpha) * \ + np.dot(self.W, self.Yhat.T) + self.pxt_ = np.linalg.multi_dot([P, U, np.diagflat(1/S)]) + self.pty_ = np.linalg.multi_dot([np.diagflat(1/S**2.0), T.T, Y]) + self.ptx_ = np.linalg.multi_dot([np.diagflat(1/S**2.0), T.T, X]) + + def _eig_solver(self, matrix, full_matrix=False): + if(self.eig_solver=='sparse' and full_matrix==False): + v, U= eigs(matrix, k=self.n_components, tol=self.tol) + else: + v, U = np.linalg.eig(matrix) + + U = np.real(U[:, np.argsort(v)]) + v = np.real(v[np.argsort(v)]) + + U = U[:, v > self.tol] + v = v[v > self.tol] + + if(len(v)==1): + U = U.reshape(-1,1) + + return v, U + + def transform(self, X): + return super()._project(X, 'pxt_') + + def inverse_transform(self, T): + return super()._project(T, 'ptx_') + + def predict(self, X): + # Predict based on X only + return super()._project(self.transform(X), 'pty_') diff --git a/utilities/sklearn_sparse/SparseKPCA.py b/utilities/sklearn_sparse/SparseKPCA.py new file mode 100644 index 0000000..c5138cf --- /dev/null +++ b/utilities/sklearn_sparse/SparseKPCA.py @@ -0,0 +1,91 @@ +from .Sparsified import _Sparsified +import numpy as np +from sklearn.preprocessing import KernelCenterer + + +class SparseKPCA(_Sparsified): + """ + #TODO make a description + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PKY: projector from kernel space to property space + PKY: projector from kernel space to property space (null) + PTK: projector from latent space to kernel space + PXT: projector from input space to latent space + X: input used to train the model, if further kernels need be constructed + X_sparse: active set used to train the model, if further kernels need be + constructed + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + n_PC (int) number of principal components to store + n_active: (int) size of the active set + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Methods---- + fit: fit the KPCA + statistics: provide available statistics for the decomposition + transform: transform data based on the KPCA fit + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and + center attributes + preprocess: centers and scales provided inputs according to scale and + center attributes + + ----References---- + 1. https://en.wikipedia.org/wiki/Kernel_principal_component_analysis + 2. M. E. Tipping, 'Sparse Kernel Principal Component Analysis', + Advances in Neural Information Processing Systems 13, 633 - 639, 2001 + """ + + def __init__(self, n_components, mixing=0.0, kernel="linear", gamma=None, degree=3, + coef0=1, kernel_params=None, n_active=None, + regularization=1E-12, tol=0, center=True): + super().__init__(mixing=mixing, kernel=kernel, gamma=gamma, degree=degree, + coef0=coef0, kernel_params=kernel_params, n_active=n_active, + regularization=regularization, tol=tol, n_components=n_components, center=center) + + def fit(self, X,y=None, Kmm=None, Knm=None): + self._define_Kmm_Knm(X, Kmm, Knm) + # Compute eigendecomposition of kernel + vmm, Umm = self._eig_solver(self.Kmm, k=self.n_active) + + U_active = Umm[:, :self.n_active ] + vmm_inv = np.linalg.pinv(np.diagflat(vmm)) + v_invsqrt = np.sqrt(vmm_inv) + U_active = U_active @ v_invsqrt + + phi_active = self.Knm @ U_active + + C = phi_active.T @ phi_active + + v_C, U_C = self._eig_solver(C) + + self.pkt_ = U_active @ U_C[:, :self.n_components] + T = self.Knm @ self.pkt_ + v_C_inv = np.linalg.pinv( np.diagflat(v_C[:self.n_components]) ) + self.ptx_ = v_C_inv @ T.T @ X + + def predict(self, X): + pass + #TODO deside, wgat we should with predict in this case. We should realize predict(abs of Sparcified) + + def transform(self, X=None, Knm=None): + + if X is None and Knm is None: + raise Exception( "Error: required feature or kernel matrices" ) + + if self.pkt_ is None: + raise Exception("Error: must fit the KPCA before transforming") + else: + if Knm is None: + Knm = self._get_kernel(X, self.X_sparse) + Knm = KernelCenterer().fit_transform(Knm) + + return self._project( Knm, 'pkt_' ) + + def fit_transform(self, X, y=None,Kmm=None, Knm=None): + self.fit(X,y,Kmm,Knm) + self.transform(X,self.Knm) diff --git a/utilities/sklearn_sparse/SparseKPCovR.py b/utilities/sklearn_sparse/SparseKPCovR.py new file mode 100644 index 0000000..1218c9c --- /dev/null +++ b/utilities/sklearn_sparse/SparseKPCovR.py @@ -0,0 +1,149 @@ +from .Sparsified import _Sparsified +import numpy as np +from sklearn.preprocessing import KernelCenterer +from sklearn.utils.validation import check_X_y +from sklearn.preprocessing import Normalizer + + +class SparseKPCovR(_Sparsified): + """ + Performs KPCovR, as described in Helfrecht (2020) + which combines Kernel Principal Components Analysis (KPCA) + and Kernel Ridge Regression (KRR), on a sparse active set + of variables + + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PKY: projector from kernel space to property space + PTK: projector from latent space to kernel space + PTX: projector from latent space to input space + PTY: projector from latent space to property space + PXT: projector from input space to latent space + PXY: projector from input space to property space + X: input used to train the model, if further kernels need be constructed + X_sparse: active set used to train the model, if further kernels need be + constructed + Yhat: regressed properties + alpha: (float) mixing parameter between decomposition and regression + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + n_PC (int) number of principal components to store + n_active: (int) size of the active set + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and + center attributes + preprocess: centers and scales provided inputs according to scale and + center attributes + + ---References--- + 1. S. de Jong, H. A. L. Kiers, 'Principal Covariates + Regression: Part I. Theory', Chemometrics and Intelligent + Laboratory Systems 14(1): 155-164, 1992 + 2. M. Vervolet, H. A. L. Kiers, W. Noortgate, E. Ceulemans, + 'PCovR: An R Package for Principal Covariates Regression', + Journal of Statistical Software 65(1):1-14, 2015 + """ + + def __init__(self, n_components, mixing=0.0, kernel="linear", gamma=None, degree=3, + coef0=1, kernel_params=None, n_active=None, + regularization=1E-12, tol=0, center=True): + super().__init__(mixing=mixing, kernel=kernel, gamma=gamma, degree=degree, + coef0=coef0, kernel_params=kernel_params, n_active=n_active, + regularization=regularization, tol=tol, n_components=n_components, center=center) + + def fit(self, X, Y, X_sparse=None, Kmm=None, Knm=None): + + X, Y = check_X_y( X, Y, y_numeric=True, multi_output=True ) + if X_sparse is None: + fps_idxs, _ = self.FPS(X, self.n_active) + self.X_sparse = X[fps_idxs, :] + else: + self.X_sparse = X_sparse + + if Kmm is None: + Kmm = self._get_kernel(self.X_sparse, self.X_sparse) + + if self.center: + Kmm = KernelCenterer().fit_transform(Kmm) + self.Kmm = Kmm + + if Knm is None: + Knm = self._get_kernel(X, self.X_sparse) + Knm = KernelCenterer().fit_transform(Knm) + self.Knm = Knm + vmm, Umm = self._eig_solver(self.Kmm, k=self.n_active) + vmm_inv = np.linalg.pinv( np.diagflat(vmm[:self.n_active - 1]) ) + phi_active = self.Knm @ Umm[:, :self.n_active - 1] @ np.sqrt(vmm_inv) + C = phi_active.T @ phi_active + + v_C, U_C = self._eig_solver(C, tol=0, k = self.n_active) + U_C = U_C[:, v_C > 0] + v_C = v_C[v_C > 0] + v_C_inv = np.linalg.pinv( np.diagflat(v_C)) + Csqrt = U_C @ np.diagflat(np.sqrt(v_C)) @ U_C.T + iCsqrt = U_C @ np.sqrt(v_C_inv) @ U_C.T + + C_pca = C + + C_lr = np.linalg.pinv(C + self.regularization * np.eye(C.shape[0])) + C_lr = iCsqrt @ phi_active.T @ phi_active @ C_lr @ phi_active.T + + if len(Y.shape) == 1: + C_lr = C_lr @ Y.reshape(-1, 1) + else: + C_lr = C_lr @ Y + + C_lr = C_lr @ C_lr.T + + Ct = self.mixing * C_pca + (1 - self.mixing) * C_lr + + v_Ct, U_Ct = self._eig_solver(Ct, tol=0, k=self.n_active) + PPT = iCsqrt @ U_Ct[:, :self.n_components] @ np.diag(np.sqrt(v_Ct[:self.n_components])) + + PKT = Umm[:, :self.n_active - 1] @ np.sqrt(vmm_inv) + + self.pkt_ = PKT @ PPT + + T = self.Knm @ self.pkt_ + + PT = np.linalg.pinv(T.T @ T) @ T.T + self.pty_ = PT @ Y + self.ptx_ = PT @ X + + def transform(self, X=None, Knm=None): + + if X is None and Knm is None: + raise Exception( "Error: required feature or kernel matrices" ) + + if self.pkt_ is None: + raise Exception("Error: must fit the KPCovR before transforming") + else: + if Knm is None: + Knm = self._get_kernel(X, self.X_sparse) + Knm = KernelCenterer().fit_transform(Knm) + + return self._project( Knm, 'pkt_') + + def predict(self, X=None, K=None): + T = self.transform(X, K) + return self._project(T,'pty_') + + def fit_transform(self, X, Y=None, X_sparse=None, Kmm=None, Knm=None): + self.fit(X,Y, X_sparse, Kmm, Knm) + return self.transform(X, Knm) + + def fit_predict(self, X, Y=None, X_sparse=None, Kmm=None, Knm=None, K=None): + self.fit( X, Y, X_sparse, Kmm, Knm ) + return self.predict(X, K) + + def inverse_transform(self, T): + if T is None: + raise Exception( "Error: required feature matrix" ) + + if self.ptx_ is None: + raise Exception("Error: must fit the KPCovR before transforming") + return self._project(T,'ptx_') diff --git a/utilities/sklearn_sparse/SparseKRR.py b/utilities/sklearn_sparse/SparseKRR.py new file mode 100644 index 0000000..bc182a7 --- /dev/null +++ b/utilities/sklearn_sparse/SparseKRR.py @@ -0,0 +1,85 @@ +from .Sparsified import _Sparsified +import numpy as np +from sklearn.preprocessing import KernelCenterer + + +class SparseKRR(_Sparsified): + """ + TODO make a description + Performs sparsified kernel ridge regression + + ----Inherited Attributes---- + PKT: projector from kernel space to latent space + PTK: projector from latent space to kernel space + PTX: projector from latent space to input space + PXY: projector from input space to property space + X: input used to train the model, if further kernels need be constructed + X_sparse: active set used to train the model, if further kernels need be + constructed + center: (boolean) whether to shift all inputs to zero mean + kernel: function to construct the kernel of the input data + n_active: (int) size of the active set + regularization: (float) parameter to offset all small eigenvalues for + regularization + scale: (boolean) whether to scale all inputs to unit variance + + ----Inherited Methods---- + postprocess: un-centers and un-scales outputs according to scale and + center attributes + preprocess: centers and scales provided inputs according to scale and + center attributes + + ----Methods---- + fit: fit the kernel ridge regression model by computing regression weights + statistics: provide available statistics for the regression + transform: compute predicted Y values + + ----References---- + 1. M. Ceriotti, M. J. Willatt, G. Csanyi, + 'Machine Learning of Atomic - Scale Properties + Based on Physical Principles', Handbook of Materials Modeling, + Springer, 2018 + 2. A. J. Smola, B. Scholkopf, 'Sparse Greedy Matrix Approximation + for Machine Learning', Proceedings of the 17th International + Conference on Machine Learning, 911 - 918, 2000 + """ + + def __init__(self, mixing=0.0, kernel="linear", gamma=None, degree=3, + coef0=1, kernel_params=None, n_active=None, + regularization=1E-12, tol=0, center=True): + super().__init__(mixing=mixing, kernel=kernel, gamma=gamma, degree=degree, + coef0=coef0, kernel_params=kernel_params, n_active=n_active, + regularization=regularization, tol=tol, center=center) + def fit(self, X, Y, Kmm=None, Knm=None): + self._define_Kmm_Knm(X, Kmm, Knm) + + # Compute max eigenvalue of regularized model + PKY = np.linalg.pinv(self.Knm.T @ self.Knm + (self.regularization * self.Kmm)) + self.pky_ = PKY @ self.Knm.T @ Y + + def predict(self, X=None, Knm=None): + if X is None and Knm is None: + raise Exception( "Error: required feature or kernel matrices" ) + if self.pky_ is None: + raise Exception("Error: must fit the KRR model before transforming") + else: + if Knm is None: + Knm = self._get_kernel(X, self.X_sparse) + Knm = KernelCenterer().fit_transform(Knm) + + Yp = Knm @ self.pky_ + return Yp + + def transform(self, X): + #return Knm matrix + Knm = self._get_kernel( X, self.X_sparse ) + Knm = KernelCenterer().fit_transform(Knm) + return Knm + + def fit_transform(self, X, y=None,Kmm=None, Knm=None): + self.fit(X, y, Kmm, Knm) + return self.Knm + + def fit_predict(self, X, Y, Kmm=None, Knm=None): + self.fit(X,Y, Kmm, Knm) + self.predict(self.Knm) diff --git a/utilities/sklearn_sparse/Sparsified.py b/utilities/sklearn_sparse/Sparsified.py new file mode 100644 index 0000000..14db204 --- /dev/null +++ b/utilities/sklearn_sparse/Sparsified.py @@ -0,0 +1,195 @@ +import numpy as np +from abc import abstractmethod, ABCMeta +from sklearn.utils import check_array +from sklearn.utils.validation import check_is_fitted +from sklearn.base import BaseEstimator, TransformerMixin, RegressorMixin +from scipy.sparse.linalg import eigs +from sklearn.preprocessing import KernelCenterer +from sklearn.metrics.pairwise import pairwise_kernels + + +class _Sparsified(TransformerMixin, RegressorMixin, BaseEstimator, metaclass=ABCMeta): + """ + Super-class defined sparcified methods + """ + + def __init__(self, mixing, kernel="linear", gamma=None, degree=3, + coef0=1, kernel_params=None, n_active=None, + regularization=1E-12, tol=0, center=True, n_jobs=None, n_components=None): + # TODO + self.mixing = mixing + self.kernel = kernel + self.gamma = gamma + self.degree = degree + self.coef0 = coef0 + self.kernel_params = kernel_params + self.n_active = n_active + self.regularization = regularization + self.tol = tol + self.center = center + self.n_jobs = n_jobs + self.n_components = n_components #TODO solve, where we should define it + + + @abstractmethod + def fit(self, X, Y, Yhat=None): + """Placeholder for fit. Subclasses should implement this method! + Fit the model with X. + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples and + n_features is the number of features. + Y : array-like, shape (n_samples, n_properties) + Training data, where n_samples is the number of samples and + n_properties is the number of properties + Yhat : array-like, shape (n_samples, n_properties), optional + Regressed training data, where n_samples is the number of samples and + n_properties is the number of properties. If not supplied, computed + by ridge regression. + Returns + ------- + self : object + Returns the instance itself. + """ + + @abstractmethod + def transform(self, X): + """Placeholder for transform. Subclasses should implement this method! + Transforms the model with X. + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples and + n_features is the number of features. + Returns + ------- + self : object + Returns the instance itself. + """ + + @abstractmethod + def predict(self, X): + """Placeholder for transform. Subclasses should implement this method! + Predicts the outputs given X. + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples and + n_features is the number of features. + Returns + ------- + self : object + Returns the instance itself. + """ + + def _project(self, A, projector): + """Apply a projector to matrix A + Parameters + ---------- + A : array-like, shape (n, a) + projector: string corresponding to the named projection matrix of shape (a, p) + Returns + ------- + A' : array-like, shape (n, p) + Examples + -------- + >>> todo + """ + check_is_fitted(self, projector) + + A = check_array(A) + A_transformed = np.dot(A, self.__dict__[projector]) + return A_transformed + + def _get_kernel(self, X, Y=None): + if callable(self.kernel): + params = self.kernel_params or {} + else: + params = {"gamma": self.gamma, + "degree": self.degree, + "coef0": self.coef0} + return pairwise_kernels(X, Y, metric=self.kernel, + filter_params=True, n_jobs=self.n_jobs, + **params) + + def _eig_solver(self, matrix, full_matrix=False, tol =None, k = None): + if tol is None: + tol=self.tol + if k is None: + k = self.n_components + if(full_matrix == False): + v, U = eigs(matrix, k=k, tol=tol) + else: + v, U = np.linalg.eig(matrix) + + U = np.real(U[:, np.argsort(-v)]) + v = np.real(v[np.argsort(-v)]) + + U = U[:, v > tol] + v = v[v > tol] + + if(len(v) == 1): + U = U.reshape(-1, 1) + + return v, U + + def _define_Kmm_Knm(self,X, Kmm=None, Knm=None): + if Kmm is None or Knm is None: + i_sparse, _ = self.FPS(X, self.n_active) + + self.X_sparse = X[i_sparse, :] + Kmm = self._get_kernel(self.X_sparse, self.X_sparse) + + Knm = self._get_kernel(X, self.X_sparse) + + if self.center: + Kmm = KernelCenterer().fit_transform(Kmm) + Knm = KernelCenterer().fit_transform( Knm ) + self.Kmm = Kmm + self.Knm = Knm + + + def FPS(self, X, n=0, idx=None): + """ + #TODO Deside, where this function should be + Does Farthest Point Selection on a set of points X + Adapted from a routine by Michele Ceriotti + """ + N = X.shape[0] + + # If desired number of points less than or equal to zero, + # select all points + if n <= 0: + n = N + + # Initialize arrays to store distances and indices + fps_idxs = np.zeros( n, dtype=np.int ) + d = np.zeros( n ) + + if idx is None: + # Pick first point at random + idx = np.random.randint( 0, N ) + fps_idxs[0] = idx + + # Compute distance from all points to the first point + d1 = np.linalg.norm( X - X[idx], axis=1 ) ** 2 + + # Loop over the remaining points... + for i in range( 1, n ): + + # Get maximum distance and corresponding point + fps_idxs[i] = np.argmax( d1 ) + d[i - 1] = np.amax( d1 ) + + # Compute distance from all points to the selected point + d2 = np.linalg.norm( X - X[fps_idxs[i]], axis=1 ) ** 2 + + # Set distances to minimum among the last two selected points + d1 = np.minimum( d1, d2 ) + + if np.abs( d1 ).max() == 0.0: + print( "Only {} FPS Possible".format( i ) ) + return fps_idxs[:i], d[:i] + + return fps_idxs, d diff --git a/utilities/sklearn_sparse/sparse_tests/.DS_Store b/utilities/sklearn_sparse/sparse_tests/.DS_Store new file mode 100644 index 0000000..5008ddf Binary files /dev/null and b/utilities/sklearn_sparse/sparse_tests/.DS_Store differ diff --git a/utilities/sklearn_sparse/sparse_tests/SparseKPCA_tests.py b/utilities/sklearn_sparse/sparse_tests/SparseKPCA_tests.py new file mode 100644 index 0000000..d7e76b4 --- /dev/null +++ b/utilities/sklearn_sparse/sparse_tests/SparseKPCA_tests.py @@ -0,0 +1,20 @@ +import numpy as np +from sklearn import exceptions +from sklearn.utils.validation import check_X_y +import unittest +from .Sparse_Base_Tests import Sparse_Base_Tests + +class SparseKPCA_tests(Sparse_Base_Tests): + def __init__(self, *args, **kwargs): + super().__init__(model = 'KPCA', *args, **kwargs ) + + # Basic Test of model PCA Errors, that None return np.nan + def test_pca_errors(self): + + for i, mixing in enumerate(self.alphas): + with self.subTest(error=self.pca_errors[i]): + self.assertFalse(np.isnan(self.pca_errors[i])) + + +if __name__ == '__main__': + unittest.main() diff --git a/utilities/sklearn_sparse/sparse_tests/SparseKPCovR_tests.py b/utilities/sklearn_sparse/sparse_tests/SparseKPCovR_tests.py new file mode 100644 index 0000000..eaf29d9 --- /dev/null +++ b/utilities/sklearn_sparse/sparse_tests/SparseKPCovR_tests.py @@ -0,0 +1,85 @@ +import numpy as np +from sklearn import exceptions +from sklearn.utils.validation import check_X_y +import unittest +from sklearn_sparse.sparse_tests.Sparse_Base_Tests import Sparse_Base_Tests + +class SparseKPCovR_tests(Sparse_Base_Tests): + def __init__(self,model='KPCovR', *args, **kwargs): + super().__init__(model = 'KPCovR', *args, **kwargs ) + + def add_errors(self): + for i, mixing in enumerate(self.alphas): + if(np.isnan(self.lr_errors[i]) or np.isnan(self.pca_errors[i])): + Yp, _, Xr = self.run_sparse(mixing=mixing) + self.lr_errors[i] = self.rel_error(self.Y, Yp) + self.pca_errors[i] = self.rel_error(self.X, Xr) + + # Basic Test of model PCA Errors, that None return np.nan + def test_pca_errors(self): + + for i, mixing in enumerate(self.alphas): + with self.subTest(error=self.pca_errors[i]): + self.assertFalse(np.isnan(self.pca_errors[i])) + + # Basic Test of model LR Errors, that None return np.nan + def test_krr_errors(self): + + for i, mixing in enumerate(self.alphas): + with self.subTest(error=self.lr_errors[i]): + self.assertFalse(np.isnan(self.lr_errors[i])) + + + # Test that model LR Errors are monotonic with alpha + def test_krr_monotonicity(self): + self.add_errors() + + for i, _ in enumerate(self.alphas[:-1]): + with self.subTest(i=i): + lr1 = round(self.lr_errors[i], self.rounding) + lr2 = round(self.lr_errors[i+1], self.rounding) + self.assertTrue(lr1 <= lr2, + msg=f'LR Error Non-Monotonic\n {lr1} > {lr2}' + ) + + # Test that model PCA Errors are monotonic with alpha + def test_pca_monotonicity(self): + self.add_errors() + + for i, a in enumerate(self.alphas[:-1]): + with self.subTest(i=i): + pca1 = round(self.pca_errors[i], self.rounding) + pca2 = round(self.pca_errors[i+1], self.rounding) + self.assertTrue(pca1 >= pca2, + msg=f'PCA Error Non-Monotonic\n {pca2} > {pca1}' + ) + + # Test that model PCA Errors are monotonic with n_active + def test_active_pca_monotonicity(self): + self.add_errors_active() + + for i, a in enumerate(self.n_active): + with self.subTest(i=i): + pca1 = round(self.pca_errors_active[i], self.rounding) + pca2 = round(self.pca_errors_active[i+1], self.rounding) + self.assertTrue(pca2 >= pca1, + msg=f'PCA Error Non-Monotonic\n {pca2} > {pca1}' + ) + + # Test that model LR Errors are monotonic with alpha + def test_active_krr_monotonicity(self): + self.add_errors_active() + + for i, _ in enumerate(self.alphas[:-1]): + with self.subTest(i=i): + lr1 = round(self.lr_errors_active[i], self.rounding) + lr2 = round(self.lr_errors_active[i+1], self.rounding) + self.assertTrue(lr1 <= lr2, + msg=f'LR Error Non-Monotonic\n {lr1} > {lr2}' + ) + + def test_T_shape(self): + _, T, _ = self.run_sparse(mixing=0.5) + self.assertTrue(check_X_y(self.X, T, multi_output=True)) +if __name__ == '__main__': + unittest.main() diff --git a/utilities/sklearn_sparse/sparse_tests/SparseKRR_tests.py b/utilities/sklearn_sparse/sparse_tests/SparseKRR_tests.py new file mode 100644 index 0000000..52fcd56 --- /dev/null +++ b/utilities/sklearn_sparse/sparse_tests/SparseKRR_tests.py @@ -0,0 +1,32 @@ +import numpy as np +import unittest +from sklearn_sparse.sparse_tests.Sparse_Base_Tests import Sparse_Base_Tests +from sklearn_sparse.SparseKRR import SparseKRR + +class SparseKRR_tests(Sparse_Base_Tests): + def __init__(self,model='KRR', *args, **kwargs): + super().__init__(model = 'KRR', *args, **kwargs ) + + # Basic Test of model LR Errors, that None return np.nan + + def test_krr_errors(self): + + for i, mixing in enumerate(self.alphas): + with self.subTest(error=self.lr_errors[i]): + self.assertFalse(np.isnan(self.lr_errors[i])) + + # Test that model LR Errors are monotonic with alpha + def test_active_krr_monotonicity(self): + self.add_errors_active() + + for i, _ in enumerate(self.alphas[:-1]): + with self.subTest(i=i): + lr1 = round(self.lr_errors_active[i], self.rounding) + lr2 = round(self.lr_errors_active[i+1], self.rounding) + self.assertTrue(lr1 <= lr2, + msg=f'LR Error Non-Monotonic\n {lr1} > {lr2}' + ) +if __name__ == "__main__": + suite = unittest.TestSuite() + suite = unittest.defaultTestLoader.loadTestsFromTestCase( SparseKRR_tests ) + unittest.TextTestRunner().run( suite ) \ No newline at end of file diff --git a/utilities/sklearn_sparse/sparse_tests/Sparse_Base_Tests.py b/utilities/sklearn_sparse/sparse_tests/Sparse_Base_Tests.py new file mode 100644 index 0000000..a5c5139 --- /dev/null +++ b/utilities/sklearn_sparse/sparse_tests/Sparse_Base_Tests.py @@ -0,0 +1,129 @@ +import numpy as np +from sklearn import exceptions +from sklearn.utils.validation import check_X_y +import unittest +import time + + +class Sparse_Base_Tests(unittest.TestCase): + def __init__(self,model, *args, **kwargs): + super().__init__(*args, **kwargs) + + self.data = np.load('CSD-test.npz') + self.X = self.data["X"] + self.Y = self.data["Y"] + self.Knm = None + self.model = model + + self.error_tol = 1E-3 + self.rounding = -int(round(np.log10(self.error_tol))) + + self.kernels =["linear", "poly", "rbf", "sigmoid", "cosine"] + n_mixing = 11 + n_active=10 + self.lr_errors = np.nan * np.zeros(n_mixing) + self.pca_errors = np.nan * np.zeros(n_mixing) + self.lr_errors_active = np.nan * np.zeros(n_active) + self.pca_errors_active = np.nan * np.zeros(n_active) + self.alphas = np.linspace(0, 1, n_mixing) + self.n_active = [i for i in range(10,21)] + + def setUp(self): + self.startTime = time.time() + + def tearDown(self): + t = time.time() - self.startTime + print('%s: %.3f' % (self.id(), t)) + + def rel_error(self, A, B): + return np.linalg.norm(A-B)**2.0 / np.linalg.norm(A)**2.0 + + def add_errors_active(self): + if (self.model == 'KPCovR'): + for i, n_active in enumerate(self.n_active): + if(np.isnan(self.lr_errors_active[i]))or(np.isnan(self.pca_errors_active[i])) : + Yp, _, Xr = self.run_sparse(n_active=n_active) + self.lr_errors_active[i] = self.rel_error(self.Y, Yp) + self.pca_errors_active[i] = self.rel_error(self.X, Xr) + elif(self.model=='KRR'): + for i, n_active in enumerate( self.n_active ): + if (np.isnan( self.pca_errors_active[i] )): + Yp = self.run_sparse( n_active=n_active ) + self.lr_errors_active[i] = self.rel_error( self.Y, Yp ) + + + def run_sparse(self, mixing=0.5,n_active=20, kernel='linear'): + if (self.model =='KPCovR'): + skpcovr = self.model(mixing=mixing, + n_components=2, + tol=1E-12, n_active=n_active, + kernel = kernel) + if(self.Knm is None): + skpcovr.fit(self.X, self.Y) + Yp = skpcovr.predict(self.X) + T = skpcovr.transform(self.X) + else: + skpcovr.fit(self.X, self.Y, Knm=self.Knm) + Yp = skpcovr.predict(self.X, Knm=self.Knm) + T = skpcovr.transform(self.X, Knm=self.Knm) + Xr = skpcovr.inverse_transform(T) + return Yp, T, Xr + elif(self.model =='KPCA'): + skpca = self.model( mixing=mixing, + n_components=2, + tol=1E-12, n_active=n_active, + kernel=kernel ) + if (self.Knm is None): + skpca.fit( self.X, self.Y ) + T = skpca.transform( self.X ) + else: + skpca.fit( self.X, self.Y, Knm=self.Knm ) + T = skpca.transform( self.X, Knm=self.Knm ) + return T + else: + skrr = self.model( mixing=mixing, + tol=1E-12, n_active=n_active, + kernel=kernel) + if (self.Knm is None): + skrr.fit( self.X, self.Y ) + Yp = skrr.predict( self.X ) + else: + skrr.fit( self.X, self.Y, Knm=self.Knm ) + Yp = skrr.predict( self.X, Knm=self.Knm ) + return Yp + + + + # Checks that the model will not transform before fitting + def transform_nonfitted_failure(self): + if(self.model=='KPCovR')or(self.model=='KPCA'): + model = self.model(mixing=0.5, + n_components=2, + tol=1E-12, + n_active=20) + with self.assertRaises(exceptions.NotFittedError): + if(self.Knm is not None): + _ = model.transform(self.X, Knm=self.Knm) + else: + _ = model.transform(self.X) + + + # Checks that the model will not predict before fitting + def predict_nonfitted_failure(self): + if(self.model=='KPCovR')or(self.model=='KRR'): + model = self.model(mixing=0.5, + n_components=2, + tol=1E-12, + n_active=20) + with self.assertRaises(exceptions.NotFittedError): + if(self.Knm is not None): + _ = model.predict(self.X, Knm=self.Knm) + else: + _ = model.predict(self.X) + + #Check work of the algorithm with different kernels + def test_kernel(self): + for i, kernel in enumerate( self.kernels ): + try: + self.run_sparse(kernel=kernel) + except: raise Exception(f'Kernel \'{kernel}\' doesn\'t work') \ No newline at end of file diff --git a/utilities/sklearn_sparse/sparse_tests/test.py b/utilities/sklearn_sparse/sparse_tests/test.py new file mode 100644 index 0000000..c5b2242 --- /dev/null +++ b/utilities/sklearn_sparse/sparse_tests/test.py @@ -0,0 +1,20 @@ +import unittest + +class TestStringMethods(unittest.TestCase): + + def test_upper(self): + self.assertEqual('foo'.upper(), 'FOO') + + def test_isupper(self): + self.assertTrue('FOO'.isupper()) + self.assertFalse('Foo'.isupper()) + + def test_split(self): + s = 'hello world' + self.assertEqual(s.split(), ['hello', 'world']) + # Проверим, что s.split не работает, если разделитель - не строка + with self.assertRaises(TypeError): + s.split(2) + +if __name__ == '__main__': + unittest.main() \ No newline at end of file