Kernel Functions Derived from Fuzzy Clustering and Their Application to Kernel Fuzzy c-Means
Jeongsik Hwang and Sadaaki Miyamoto
Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Ibaraki 305-8573, Japan
Among widely used kernel functions, such as support vector machines, in data analysis, the Gaussian kernel is most often used. This kernel arises in entropy-based fuzzy c-means clustering. There is reason, however, to check whether other types of functions used in fuzzy c-means are also kernels. Using completely monotone functions, we show they can be kernels if a regularization constant proposed by Ichihashi is introduced. We also show how these kernel functions are applied to kernel-based fuzzy c-means clustering, which outperform the Gaussian kernel in a typical example.
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