Randomized Self Organizing Map

TL;DR

This paper introduces a randomized variation of the self-organizing map that uses a blue noise distribution for neuron placement, enhancing flexibility and robustness in high-dimensional data organization.

Contribution

It presents a novel randomized SOM algorithm with controllable topological discontinuities, validated on multiple datasets and capable of adaptive reorganization.

Findings

Effective on 1D, 2D, 3D tasks and MNIST dataset

Spectral and topological analysis validate the approach

Demonstrates robustness to neural lesion and neurogenesis

Abstract

We propose a variation of the self organizing map algorithm by considering the random placement of neurons on a two-dimensional manifold, following a blue noise distribution from which various topologies can be derived. These topologies possess random (but controllable) discontinuities that allow for a more flexible self-organization, especially with high-dimensional data. The proposed algorithm is tested on one-, two- and three-dimensions tasks as well as on the MNIST handwritten digits dataset and validated using spectral analysis and topological data analysis tools. We also demonstrate the ability of the randomized self-organizing map to gracefully reorganize itself in case of neural lesion and/or neurogenesis.