Fuzzy c-means algorithms for data with tolerance using kernel functions

Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In this paper, two new clustering algorithms based on fuzzy c-means 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 entropy-based 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, Karush-Kuhn-Tucker conditions of two objective functions are considered, respectively, and these conditions are re-expressed 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.

Original languageEnglish
Pages (from-to)2520-2534
Number of pages15
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number9
Publication statusPublished - 2008 Sept


  • Clustering
  • Fuzzy c-means
  • Kernel functions
  • Tolerance

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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