Non-Euclidean Self-Organizing Maps

TL;DR

This paper extends Self-Organizing Maps to non-Euclidean geometries, enhancing their applicability in dimension reduction, clustering, and similarity analysis in complex data spaces.

Contribution

It introduces a generalized framework for non-Euclidean SOMs with topology-related extensions, broadening their use beyond traditional Euclidean settings.

Findings

Enhanced SOM algorithm with non-Euclidean topology

Effective in dimension reduction and clustering tasks

Applicable to big data with complex geometries

Abstract

Self-Organizing Maps (SOMs, Kohonen networks) belong to neural network models of the unsupervised class. In this paper, we present the generalized setup for non-Euclidean SOMs. Most data analysts take it for granted to use some subregions of a flat space as their data model; however, by the assumption that the underlying geometry is non-Euclidean we obtain a new degree of freedom for the techniques that translate the similarities into spatial neighborhood relationships. We improve the traditional SOM algorithm by introducing topology-related extensions. Our proposition can be successfully applied to dimension reduction, clustering or finding similarities in big data (both hierarchical and non-hierarchical).