A self-organizing network for hyperellipsoidal clustering (HEC)

Abstract

We propose a self-organizing network for hyperellipsoidal clustering (HEC). The HEC network consists of two layers. The first layer employs a number of principal component analysis subnetworks which are used to estimate the hyperellipsoidal shapes of currently formed clusters. The second layer then performs a competitive learning using the cluster shape information provided by the first layer. The HEC network performs a partitional clustering using the proposed regularized Mahalanobis distance. This regularized Mahalanobis distance is designed to deal with the problems in estimating the Mahalanobis distance when the number of patterns in a cluster is less than (ill-posed problem) or not considerably larger than (poorly posed problem) the dimensionality of the feature space during the clustering procedure. This regularized distance also achieves a tradeoff between hyperspherical and hyperellipsoidal cluster shapes so as to prevent the HEC network from producing unusually large or unusually small clusters. The significance level of the Kolmogorov-Smirnov test on the distribution of the Mahalanobis distances of patterns in a cluster to the cluster center under the Gaussian cluster assumption is used as a compactness measure of the cluster. The HEC network has been tested on a number of artificial data sets and real data sets. We also apply the HEC network to texture segmentation problems. Experiments show that the HEC network leads to a significant improvement in the clustering results over the K-means algorithm with Euclidean distance. Our results on real data sets also indicate that hyperellipsoidal shaped clusters are often encountered in practice. © 1996 IEEE.