Indefinite kernel fuzzy c-means clustering algorithms

Yuchi Kanzawa; Yasunori Endo; Sadaaki Miyamoto

doi:10.1007/978-3-642-16292-3_13

Indefinite kernel fuzzy c-means clustering algorithms

Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Modeling Decisions for Artificial Intelligence - 7th International Conference, MDAI 2010, Proceedings
Pages	116-128
Number of pages	13
DOIs	https://doi.org/10.1007/978-3-642-16292-3_13
Publication status	Published - 2010
Event	7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010 - Perpignan, France Duration: 2010 Oct 27 → 2010 Oct 29

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6408 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010
Country/Territory	France
City	Perpignan
Period	10/10/27 → 10/10/29

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)

Access to Document

10.1007/978-3-642-16292-3_13

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

Indefinite kernel fuzzy c-means clustering algorithms. / Kanzawa, Yuchi; Endo, Yasunori; Miyamoto, Sadaaki.
Modeling Decisions for Artificial Intelligence - 7th International Conference, MDAI 2010, Proceedings. 2010. p. 116-128 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6408 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6408 LNAI, pp. 116-128, 7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010, Perpignan, France, 10/10/27. https://doi.org/10.1007/978-3-642-16292-3_13

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

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AB - 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.

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Indefinite kernel fuzzy c-means clustering algorithms

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