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
Received:July 13, 2004Accepted:September 12, 2004Published:November 20, 2004
Keywords: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:H. Ichihashi and K. 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.Data files: