Indefinite kernel fuzzy c-means clustering algorithms

Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto

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

6 Citations (Scopus)

Abstract

This paper proposes two types of kernel fuzzy c-means algorithms with an indefinite kernel. Both algorithms are based on the fact that the relational fuzzy c-means algorithm is a special case of the kernel fuzzy c-means algorithm. The first proposed algorithm adaptively updated the indefinite kernel matrix such that the dissimilarity between each datum and each cluster center in the feature space is non-negative, instead of subtracting the minimal eigenvalue of the given kernel matrix as its preprocess. This derivation follows the manner in which the non-Euclidean relational fuzzy c-means algorithm is derived from the original relational fuzzy c-means one. The second proposed method produces the memberships by solving the optimization problem in which the constraint of non-negative memberships is added to the one of K-sFCM. This derivation follows the manner in which the non-Euclidean fuzzy relational clustering algorithm is derived from the original relational fuzzy c-means one. Through a numerical example, the proposed algorithms are discussed.

Original languageEnglish
Title of host publicationModeling Decisions for Artificial Intelligence - 7th International Conference, MDAI 2010, Proceedings
Pages116-128
Number of pages13
DOIs
Publication statusPublished - 2010 Dec 1
Event7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010 - Perpignan, France
Duration: 2010 Oct 272010 Oct 29

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6408 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010
CountryFrance
CityPerpignan
Period10/10/2710/10/29

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Keywords

  • Indefinite kernel
  • Kernel fuzzy c-means
  • Non-Euclidean fuzzy relational clustering
  • Non-Euclidean relational fuzzy c-means

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kanzawa, Y., Endo, Y., & Miyamoto, S. (2010). Indefinite kernel fuzzy c-means clustering algorithms. In Modeling Decisions for Artificial Intelligence - 7th International Conference, MDAI 2010, Proceedings (pp. 116-128). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6408 LNAI). https://doi.org/10.1007/978-3-642-16292-3_13