An efficient optimality test for the fuzzy c-means algorithm

Author

Yu, Jim ; Huang, Houkuan ; Tian, ShengFeng

Author_Institution

Dept. Comput. Sci. & Technol., Northern Jiaotong Univ., Beijing, China

Volume

1

fYear

2002

fDate

6/24/1905 12:00:00 AM

Firstpage

98

Lastpage

103

Abstract

The fuzzy c-means algorithm (FCM) is proved to converge to either local minimum or saddle point by Bezdek et al.(1987). However, it is problematical to judge the local minimum of a solution of the FCM in an easy way. In this paper, the Hessian matrix of one reduced objective function of the FCM is obtained and analyzed. Based on this study, a new optimality test of fixed points of the FCM is given, and its efficacy is verified by the examples in the paper. Moreover, a new stopping criterion for the FCM is also proposed

Keywords

Hessian matrices; fuzzy set theory; pattern clustering; Hessian matrix; fixed points; fuzzy c-means algorithm; fuzzy clustering; local minimum; optimality test; reduced objective function; saddle point; stopping criterion; Algorithm design and analysis; Clustering algorithms; Computer science; Convergence; Image analysis; Image converters; Image processing; Image recognition; Process design; Testing;

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Systems, 2002. FUZZ-IEEE'02. Proceedings of the 2002 IEEE International Conference on

Conference_Location

Honolulu, HI

Print_ISBN

0-7803-7280-8

Type

conf

DOI

10.1109/FUZZ.2002.1004967

Filename

1004967