Application of neural networks in cluster analysis

How to efficiently specify the "correct" number of clusters from a given multidimensional data set is one of the most fundamental and unsolved problems in cluster analysis. In this paper, we propose a method for automatically discovering the number of clusters and estimating the locations of the centroids of the resulting clusters. This method is based on the interpretation of a self-organizing feature map (SOFM) formed by the given data set. The other difficult problem in cluster analysis is how to choose an appropriate metric for measuring the similarity between a pattern and a cluster centroid. The performance of clustering algorithms greatly depends on the chosen measure of similarity. Clustering algorithms utilizing the Euclidean metric view patterns as a collection of hyperspherical-shaped swarms. Actually, genetic structures of real data sets often exhibit hyperellipsoidal-shaped clusters. In the second part of this paper we present a method of training a single-layer neural network composed of quadratic neurons to cluster data into hyperellipsoidal and/or hyperspherical-shaped swarms. Two data sets are utilized to illustrate the proposed methods.