JACIII Vol.8 No.6 pp. 566-572
doi: 10.20965/jaciii.2004.p0566


Application of Kernel Trick to Fuzzy c-Means with Regularization by K-L Information

Hidetomo Ichihashi, and Katsuhiro Honda

Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan

July 13, 2004
September 12, 2004
November 20, 2004
fuzzy clustering, entropy regularization, kernel trick, Gaussian mixture models

Support vector machines (SVM), kernel principal component analysis (KPCA), and kernel Fisher discriminant analysis (KFD), are examples of successful kernel-based learning methods. By the addition of a regularizer and the kernel trick to a fuzzy counterpart of Gaussian mixture models (GMM), this paper proposes a clustering algorithm in an extended high dimensional feature space. Unlike the global nonlinear approaches, GMM or its fuzzy counterpart is to model nonlinear structure with a collection, or mixture, of local linear sub-models of PCA. When the number of feature vectors and clusters are n and c respectively, this kernel approach can find up to c × n nonzero eigenvalues. A way to control the number of parameters in the mixture of probabilistic principal component analysis (PPCA) is adopted to reduce the number of parameters. The algorithm provides a partitioning with flexible shape of clusters in the original input data space.

Cite this article as:
Hidetomo Ichihashi and Katsuhiro Honda, “Application of Kernel Trick to Fuzzy c-Means with Regularization by K-L Information,” J. Adv. Comput. Intell. Intell. Inform., Vol.8, No.6, pp. 566-572, 2004.
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