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

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...

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Published inETRI journal Vol. 36; no. 3; pp. 333 - 342
Main Authors Lee, Hansung, Yoo, Jang‐Hee, Park, Daihee
Format Journal Article
LanguageEnglish
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
Online AccessGet full text
ISSN1225-6463
2233-7326
2233-7326
DOI10.4218/etrij.14.0113.0553

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Abstract 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.
AbstractList 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.
Most hyper-ellipsoidal clustering (HEC) approaches usethe Mahalanobis distance as a distance metric. It has beenproven that HEC, under this condition, cannot be realizedsince the cost function of partitional clustering is aconstant. We demonstrate that HEC with a modifiedGaussian kernel metric can be interpreted as a problem offinding condensed ellipsoidal clusters (with respect to thevolumes and densities of the clusters) and propose apractical HEC algorithm that is able to efficiently handleclusters that are ellipsoidal in shape and that are ofdifferent size and density. We then try to refine the HECalgorithm by utilizing ellipsoids defined on the kernelfeature space to deal with more complex-shaped clusters. The proposed methods lead to a significant improvementin the clustering results over K-means algorithm, fuzzy Cmeansalgorithm, GMM-EM algorithm, and HECalgorithm based on minimum-volume ellipsoids usingMahalanobis distance. KCI Citation Count: 3
Author Lee, Hansung
Park, Daihee
Yoo, Jang‐Hee
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Notes This work was supported by the IT R&D program of MOTIE/KEIT, Korea (10039149, Development of Basic Technology of Human Identification and Retrieval at a Distance for Active Video Surveillance Service with Real‐time Awareness of Safety Threats).
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Snippet Most hyper‐ellipsoidal clustering (HEC) approaches use the Mahalanobis distance as a distance metric. It has been proven that HEC, under this condition, cannot...
Most hyper-ellipsoidal clustering (HEC) approaches usethe Mahalanobis distance as a distance metric. It has beenproven that HEC, under this condition, cannot...
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SubjectTerms Data clustering
Gaussian kernel
hyper‐ellipsoidal clustering
kernel PCA
minimum‐volume ellipsoids
전자/정보통신공학
Title Data Clustering Method Using a Modified Gaussian Kernel Metric and Kernel PCA
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