A self-organizing network for hyperellipsoidal clustering (HEC).

We propose a self-organizing network for hyperellipsoidal clustering (HEC). It consists of two layers. The first employs a number of principal component analysis subnetworks to estimate the hyperellipsoidal shapes of currently formed clusters. The second performs competitive learning using the cluster shape information from the first. The network performs partitional clustering using the proposed regularized Mahalanobis distance, which was designed to deal with the problems in estimating the Mahalanobis distance when the number of patterns in a cluster is less than or not considerably larger than the dimensionality of the feature space during clustering. This distance also achieves a tradeoff between hyperspherical and hyperellipsoidal cluster shapes so as to prevent the HEC network from producing unusually large or 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. 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.