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JACIII Vol.15 No.1 pp. 90-94
doi: 10.20965/jaciii.2011.p0090
(2011)

Paper:

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

Received:
January 18, 2010
Accepted:
April 22, 2010
Published:
January 20, 2011
Keywords:
positive definite kernel, completely monotone function, fuzzy clustering
Abstract

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.

Cite this article as:
Jeongsik Hwang and Sadaaki Miyamoto, “Kernel Functions Derived from Fuzzy Clustering and Their Application to Kernel Fuzzy c-Means,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.1, pp. 90-94, 2011.
Data files:
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