Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function

Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto

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

Abstract

In this paper, the fuzzy classification functions of the standard fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the standard fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.

Original languageEnglish
Title of host publicationModeling Decisions for Artificial Intelligence - 5th International Conference, MDAI 2008, Proceedings
Pages122-133
Number of pages12
DOIs
Publication statusPublished - 2008 Dec 31
Event5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008 - Sabadell, Spain
Duration: 2008 Oct 302008 Oct 31

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5285 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008
CountrySpain
CitySabadell
Period08/10/3008/10/31

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Kanzawa, Y., Endo, Y., & Miyamoto, S. (2008). Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function. In Modeling Decisions for Artificial Intelligence - 5th International Conference, MDAI 2008, Proceedings (pp. 122-133). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5285 LNAI). https://doi.org/10.1007/978-3-540-88269-5-12