This is the implementation of the paper: Topology Representing Networks : Thomas Martinetz, Klaus Schulten. Neural Networks, Vol 7, No. 3, pp. 507-522, 1994.
The authors propose two approaches for building the topology preserving map.
- Simultaneously distributing the pointers over the manifold (vector quantization procedure) using neural gas algorithm1 and creating/updating connections using competitive Hebb rule2.
- First distribute the pointers over the manifold and then create the connections between adjacent neural units with overlapping masked Voronoi polyhedra.
However, the authors have compiled the algorithm only for the first approach in the paper, I've implemented the same approach in this repository.
Topology Representing Network adaptation algorithm has been implemented in trn.py. Inputs and outputs from the adaptation function has been documented in-place.
I have simulated the adaptation of a simple 2-Dimensional Square shaped manifold. It can be found under simulations/simple_square.py. Simply follow the following steps to run the code for simulation.
- Install the requirements through PyPI
:
pip install -r requirements.txt - Run the simulation file
:
python3 simulations/simple_square.py
- Simulations that authors have used, explicitly in
Figure 6&Figure 8of the paper are yet to be implemented.
The simulation for the aforementioned 2-D square shaped manifold was carried out using N = 200 (with other parameters being the same as what was suggested for the simulations by the authors in section 5 of the paper) and the results were graphed.
Adaption iterated for 40000 steps.
Manifold
Manifold with Pointers on Initial Distribution
Manifold with Adapted Pointers
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