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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages122-133
Number of pages12
Volume5285 LNAI
DOIs
Publication statusPublished - 2008
Event5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008 - Sabadell
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)03029743
ISSN (Electronic)16113349

Other

Other5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008
CitySabadell
Period08/10/3008/10/31

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Clustering algorithms

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Kanzawa, Y., Endo, Y., & Miyamoto, S. (2008). Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5285 LNAI, 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

Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function. / Kanzawa, Yuchi; Endo, Yasunori; Miyamoto, Sadaaki.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5285 LNAI 2008. p. 122-133 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5285 LNAI).

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

Kanzawa, Y, Endo, Y & Miyamoto, S 2008, Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 5285 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5285 LNAI, pp. 122-133, 5th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2008, Sabadell, 08/10/30. https://doi.org/10.1007/978-3-540-88269-5-12
Kanzawa Y, Endo Y, Miyamoto S. Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5285 LNAI. 2008. p. 122-133. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-88269-5-12
Kanzawa, Yuchi ; Endo, Yasunori ; Miyamoto, Sadaaki. / Fuzzy classification function of standard fuzzy c-means algorithm for data with tolerance using kernel function. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5285 LNAI 2008. pp. 122-133 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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