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

Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

In this paper, two new clustering algorithms based on fuzzy c-means for data with tolerance 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, two objective functions in feature space are shown corresponding to two methods, respectively. Third, Karush-Kuhn-Tucker 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 original pattern space into higher dimensional feature space than the original one. Last, two iterative algorithms are proposed for the objective functions, respectively.

Original languageEnglish
Title of host publication2006 IEEE International Conference on Fuzzy Systems
Pages744-750
Number of pages7
DOIs
Publication statusPublished - 2006 Dec 1
Event2006 IEEE International Conference on Fuzzy Systems - Vancouver, BC, Canada
Duration: 2006 Jul 162006 Jul 21

Publication series

NameIEEE International Conference on Fuzzy Systems
ISSN (Print)1098-7584

Conference

Conference2006 IEEE International Conference on Fuzzy Systems
CountryCanada
CityVancouver, BC
Period06/7/1606/7/21

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Artificial Intelligence
  • Applied Mathematics

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  • Cite this

    Kanzawa, Y., Endo, Y., & Miyamoto, S. (2006). Fuzzy c-means clustering for data with tolerance using kernel functions. In 2006 IEEE International Conference on Fuzzy Systems (pp. 744-750). [1681793] (IEEE International Conference on Fuzzy Systems). https://doi.org/10.1109/FUZZY.2006.1681793