SOM which Maps Set of SOMs: from Self-Organizing Map to Self-Organizing Homotopy

Abstract

Kohonen's self-organizin map (SOM) is an architecture that generates a map of a given dataset. In this paper, a novel extension of SOM called SOM2 is proposed. The mapping objects of SOM2 are SOMs themselves, each of which represents a set of data vectors. Thus, the entire SOM2 represents a set of data distributions. In terms of topology, SOM2 organizes a homotopy rather than a map in self-organizing manner. SOM2 is expected to be a powerful tool for the classification, estimation and recongnition tasks relevant to nonlinear manifolds.