Properties of learning of a fuzzy ART variant

Abstract

This paper discusses a variation of the Fuzzy ART algorithm referred to as the Fuzzy ART Variant. The Fuzzy ART Variant is a Fuzzy ART algorithm that uses a very large choice parameter value. Based on the geometrical interpretation of the weights in Fuzzy ART, useful properties of learning associated with the Fuzzy ART Variant are presented and proven. One of these properties establishes an upper bound on the number of list presentations required by the Fuzzy ART Variant to learn an arbitrary list of input patterns. This bound is small and demonstrates the short-training time property of the Fuzzy ART Variant. Through simulation, it is shown that the Fuzzy ART Variant is as good a clustering algorithm as a Fuzzy ART algorithm that uses typical (i.e. small) values for the choice parameter.