• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.4
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• pp.300-305
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• 2002

In this paper, we use the modified gaussian kernel function as clustering distance measure and recast the given hyper-ellipsoidal clustering problem as the optimization problem that minimizes the volume of hyper-ellipsoidal clusters, respectively and solve this using EVP (eigen value problem) that is one of the LMI (linear matrix inequality) techniques.

• ETRI Journal
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• v.36 no.3
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• pp.333-342
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• 2014

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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.215-218
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• 2002

본 논문에서는 타원형 클러스터링을 위한 거리측정 함수로써 변형된 가무시안 커널 함수를 사용하며, 주어진 클러스터링 문제를 각 타원형 클러스터의 체적을 최소화하는 문제로 해석하고 이를 선형행렬 부등식 기법 중 하나인 고유값 문제로 변환하여 최적화하는 새로운 알고리즘을 제안한다.