Optimality test for generalized FCM and its application to parameter selection

Authors:
Jian Yu;Miin-Shen Yang
Affiliations:
Dept. of Comput. Sci. Technol., Northern Jiaotong Univ., Beijing, China;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2005

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Abstract

In cluster analysis, the fuzzy c-means (FCM) clustering algorithm is the best known and most widely used method. It was proven to converge to either a local minimum or saddle points by Bezdek et al. Wei and Mendel produced efficient optimality tests for FCM fixed points. Recently, a weighting exponent selection for FCM was proposed by Yu et al. Inspired by these results, we unify several alternative FCM algorithms into one model, called the generalized fuzzy c-means (GFCM). This GFCM model presents a wide variation of FCM algorithms and can easily lead to new and interesting clustering algorithms. Moreover, we construct a general optimality test for GFCM fixed points. This is applied to theoretically choose the parameters in the GFCM model. The experimental results demonstrate the precision of the theoretical analysis.