Fuzzy min-max neural networks - Part 2: Clustering

Abstract

In an earlier companion paper (56) a supervised learning neural network pattern classifier called the fuzzy min- max classification neural network was described. In this sequel, the unsupervised learning pattern clustering sibling called the fuzzy min-max clustering neural network is presented. Pattern clusters are implemented here as fuzzy sets using a membership function with a hyperbox core that is constructed from a min point and a max point. The min-max points are determined using the fuzzy min-max learning algorithm, an expansion-contraction process that refines the author's earlier Fuzzy Adaptive Reso- nance Theory neural network (50). The fuzzy min-max clustering neural network stabilizes into pattern clusters in only a few passes through a data set; it can be reduced to hard cluster boundaries that are easily examined without sacrificing the fuzzy boundaries; it provides the ability to incorporate new data and add new clusters without retraining; and it inherently provides degree of membership information that is extremely useful in higher level decision making and information processing. This paper will provide some background concerning the development of the fuzzy min-max clustering neural network and provide a comparison with similar work that has recently emerged. A brief description of fuzzy sets, pattern clustering, and their synergistic combination is presented. The fuzzy min- max clustering neural network will be explained in detail and examples of its clustering performance will be given. The paper will conclude with a description of problems that need to be addressed and a list of some potential applications.