Construction of fuzzy membership functions using interactive self-organizing maps

Abstract

This paper presents a Kohonen-like mapping that eliminates or reduces four limitations of the Kohonen maps. The described network is invariant to scale, very resistant to 'automatic selection of feature dimensions,' results in strictly ordered clusters of ascending/descending magnitude, and may allow a greater amount of information to be gleaned from high dimensional data sets. The network treats each input component separately but each map is influenced via inter-map connections. Unfortunately, processing time increases combinatorially as the number of input components and number of neurons per component increases. As a demonstration, membership functions are constructed for a four variable data set with minimal parameter setting, the most crucial being the number of classes per input component.