Topology Preservation in Fuzzy Self-Organizing Maps

Abstract

One of the important properties of SOM is its topology preservation of the input data. The topographic error is one of the techniques proposed to measure how well the continuity of the map is preserved. However, this topographic error is only applicable to the crisp SOM algorithms and cannot be adapted to the fuzzy SOM (FSOM) since FSOM does not assign a unique winning neuron to the input patterns. In this paper, we propose a new technique to measure the topology preservation of the FSOM algorithms. The new measure relies on the distribution of the membership values on the map. A low topographic error is achieved when neighboring neurons share similar or same membership values to a given input pattern.