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Fuzzy cMeans Algorithms for Data with Tolerance Using Kernel Functions
Yuchi KANZAWA Yasunori ENDO Sadaaki MIYAMOTO
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E91A
No.9
pp.25202534 Publication Date: 2008/09/01
Online ISSN: 17451337
DOI: 10.1093/ietfec/e91a.9.2520
Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications) Category: Soft Computing Keyword: fuzzy cmeans, clustering, tolerance, kernel functions,
Full Text: PDF(598.6KB)>>
Summary:
In this paper, two new clustering algorithms based on fuzzy cmeans for data with tolerance using kernel functions are proposed. Kernel functions which map the data from the original space into higher dimensional feature space are introduced into the proposed algorithms. Nonlinear boundary of clusters can be easily found by using the kernel functions. First, two clustering algorithms for data with tolerance are introduced. One is based on standard method and the other is on entropybased one. Second, the tolerance in feature space is discussed taking account into soft margin algorithm in Support Vector Machine. Third, two objective functions in feature space are shown corresponding to two methods, respectively. Fourth, KarushKuhnTucker conditions of two objective functions are considered, respectively, and these conditions are reexpressed with kernel functions as the representation of an inner product for mapping from the original pattern space into a higher dimensional feature space. Fifth, two iterative algorithms are proposed for the objective functions, respectively. Through some numerical experiments, the proposed algorithms are discussed.

