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JACIII Vol.13 No.4 pp. 421-428
doi: 10.20965/jaciii.2009.p0421
(2009)

Paper:

On Tolerant Fuzzy c -Means Clustering

Yukihiro Hamasuna*, Yasunori Endo**, and Sadaaki Miyamoto**

*Doctoral Program in Risk Engineering, University of Tsukuba

** Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

Received:
November 22, 2008
Accepted:
March 10, 2009
Published:
July 20, 2009
Keywords:
fuzzy c -means clustering, uncertainty, tolerance, fuzzy classification function, optimization
Abstract

This paper presents a new type of clustering algorithms by using a tolerance vector called tolerant fuzzy c -means clustering (TFCM). In the proposed algorithms, the new concept of tolerance vector plays very important role. In the original concept of tolerance, a tolerance vector attributes to each data. This concept is developed to handle data flexibly, that is, a tolerance vector attributes not only to each data but also each cluster. Using the new concept, we can consider the influence of clusters to each data by the tolerance. First, the new concept of tolerance is introduced into optimization problems based on conventional fuzzy c -means clustering (FCM). Second, the optimization problems with tolerance are solved by using Karush-Kuhn-Tucker conditions. Third, new clustering algorithms are constructed based on the explicit optimal solutions of the optimization problems. Finally, the effectiveness of the proposed algorithms is verified through numerical examples by fuzzy classification function.

Cite this article as:
Yukihiro Hamasuna, Yasunori Endo, , and Sadaaki Miyamoto, “On Tolerant Fuzzy c -Means Clustering,” J. Adv. Comput. Intell. Intell. Inform., Vol.13, No.4, pp. 421-428, 2009.
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