A self-organizing network for hyperellipsoidal clustering (HEC)

We propose a self-organizing network (HEC) for hyper-ellipsoidal clustering. The HEC network performs a partitional clustering using the regularized Mahalanobis distance. This regularized Mahalanobis distance measure is proposed 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 in clustering multidimensional data. 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 Kolmogrov-Smirnov test on the distribution of the Mahalanobis distances of patterns in a cluster to the cluster center under the multivariate Gaussian assumption is used as a measure of cluster compactness. The HEC network has been tested on a number of artificial data sets and real data sets. Experiments show that the HEC network gives better clustering results compared to the well-known K-means algorithm with the Euclidean distance metric