New Cluster Validity Index with Fuzzy Functions

A new cluster validity index is introduced to validate the results obtained by the recent Improved Fuzzy Clustering (IFC), which combines two different methods, i.e., fuzzy c-means clustering and fuzzy c-regression, in a novel way. Proposed validity measure determines the optimum number of clusters of the IFC based on a ratio of the compactness to separability of the clusters. The compactness is represented with: (i) the sum of the average distances of each object to their cluster centers, and (ii) the error measure of their fuzzy functions, which utilizes membership values as additional input variables. The separability is based on the ratio between: (i) the maximum distance between the cluster representatives, and (ii) the angles between their representative fuzzy functions. The experiments exhibit that the new cluster validity index is a useful function when selecting the parameters of the IFC.

[1]  Witold Pedrycz,et al.  User-Driven Fuzzy Clustering: On the Road to Semantic Classification , 2005, RSFDGrC.

[2]  Witold Pedrycz,et al.  Collaborative Rough Clustering , 2005, PReMI.

[3]  Yu-Geng Xi,et al.  A clustering algorithm for fuzzy model identification , 1998, Fuzzy Sets Syst..

[4]  I. Burhan Türksen,et al.  Fuzzy functions with support vector machines , 2007, Inf. Sci..

[5]  I. Turksen,et al.  Comparison of Fuzzy Functions with Fuzzy Rule Base Approaches , 2006 .

[6]  Doheon Lee,et al.  Fuzzy cluster validation index based on inter-cluster proximity , 2003, Pattern Recognit. Lett..

[7]  J. Bezdek.  Cluster Validity with Fuzzy Sets , 1973 .

[8]  James C. Bezdek,et al.  On cluster validity for the fuzzy c-means model , 1995, IEEE Trans. Fuzzy Syst..

[9]  Frank Klawonn,et al.  Improved fuzzy partitions for fuzzy regression models , 2003, Int. J. Approx. Reason..

[10]  I. Burhan Türksen,et al.  Fuzzy functions with LSE , 2008, Appl. Soft Comput..

[11]  Y. Fukuyama,et al.  A new method of choosing the number of clusters for the fuzzy c-mean method , 1989 .

[12]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[13]  R.J. Hathaway,et al.  Switching regression models and fuzzy clustering , 1993, IEEE Trans. Fuzzy Syst..

[14]  S. Gunn.  Support Vector Machines for Classification and Regression , 1998 .

[15]  Mustafa Demirci.  Fuzzy functions and their fundamental properties , 1999, Fuzzy Sets Syst..

[16]  Minho Kim,et al.  New indices for cluster validity assessment , 2005, Pattern Recognit. Lett..

[17]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[18]  Chung-Chun Kung,et al.  A new cluster validity criterion for fuzzy c-regression model and its application to T-S fuzzy model identification , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[19]  Gerardo Beni,et al.  A Validity Measure for Fuzzy Clustering , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Shengrui Wang,et al.  An objective approach to cluster validation , 2006, Pattern Recognit. Lett..