Diffusion Self-Organizing Map on the Hypersphere

TL;DR

This paper introduces a diffusion-based self-organizing map on the hypersphere, efficiently implemented with linear algebra, demonstrated on MNIST, offering a novel approach for data visualization and clustering on spherical domains.

Contribution

It presents a new diffusion-based method for self-organizing maps on the hypersphere, with an efficient linear algebra implementation and practical demonstration on MNIST.

Findings

Efficient linear algebra implementation of the diffusion self-organizing map.

Successful application to MNIST dataset.

Potential for spherical data visualization and clustering.

Abstract

We discuss a diffusion based implementation of the self-organizing map on the unit hypersphere. We show that this approach can be efficiently implemented using just linear algebra methods, we give a python numpy implementation, and we illustrate the approach using the well known MNIST dataset.