Data Clustering Method Using a Modified Gaussian Kernel Metric and Kernel PCA

Abstract

Most hyper-ellipsoidal clustering (BEC) approaches use the Mahalanobis distance as a distance metric. It has been proven that BEC, under this condition, cannot be realized since the cost function of partitional clustering is a constant. We demonstrate that BEC with a modified Gaussian kernel metric can be interpreted as a problem of finding condensed ellipsoidal clusters (with respect to the volumes and densities of the clusters) and propose a practical HEC algorithm that is able to efficiently handle clusters that are ellipsoidal in shape and that are of different size and density. We then try to refine the HEC algorithm by utilizing ellipsoids defined on the kernel feature space to deal with mare complex-shaped clusters. The proposed methods lead to a significant improvement in the clustering results over K-means algorithm, fuzzy C-means algorithm, GMM-EM algorithm, and EEC algorithm based on minimum-volume ellipsoids using Mahalanobis distance.