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

• Published in: ETRI journal Vol. 36; no. 3; pp. 333 - 342
• Main Authors: Lee, Hansung, Yoo, Jang‐Hee, Park, Daihee
• Format: Journal Article
• Language: English
• Published: Electronics and Telecommunications Research Institute (ETRI) 01.06.2014; 한국전자통신연구원
• Subjects: Data clustering; Gaussian kernel; hyper‐ellipsoidal clustering; kernel PCA; minimum‐volume ellipsoids; 전자/정보통신공학
• ISSN: 1225-6463; 2233-7326; 2233-7326
• DOI: 10.4218/etrij.14.0113.0553

Most hyper‐ellipsoidal clustering (HEC) approaches use the Mahalanobis distance as a distance metric. It has been proven that HEC, under this condition, cannot be realized since the cost function of partitional clustering is a constant. We demonstrate that HEC 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 more 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 HEC algorithm based on minimum‐volume ellipsoids using Mahalanobis distance.