Description of Input Patterns by Linear Mixtures of SOM Models

Abstract

This paper introduces a novel way of analyzing input patterns presented to the Self-Organizing Map (SOM). Instead of identifying only the "winner," i.e., the model that matches best with the input, we determine the linear mixture of the models (reference vectors) of the SOM that approximates to the input vector best. It will be shown that if only nonnegative weights are allowed in this linear mixture, the expansion of the input pattern in terms of the models is very meaningful, contains only few terms, and provides a better insight into the input state than what the mere "winner" can give. If then the models fall into classes that are known a priori, the sums of the weights over each class can be interpreted as expressing the affiliation of the input with the due classes.