Optimizing of Fuzzy C-Means Clustering Algorithm Using GA

Fuzzy C-means Clustering algorithm (FCM) is a method that is frequently used in pattern recognition. It has the advantage of giving good modeling results in many cases, although, it is not capable of specifying the number of clusters by itself. In FCM algorithm most researchers fix weighting exponent (m) to a conventional value of 2 which might not be the appropriate for all applications. Consequently, the main objective of this paper is to use the subtractive clustering algorithm to provide the optimal number of clusters needed by FCM algorithm by optimizing the parameters of the subtractive clustering algorithm by an iterative search approach and then to find an optimal weighting exponent (m) for the FCM algorithm. In order to get an optimal number of clusters, the iterative search approach is used to find the optimal single-output Sugenotype Fuzzy Inference System (FIS) model by optimizing the parameters of the subtractive clustering algorithm that give minimum least square error between the actual data and the Sugeno fuzzy model. Once the number of clusters is optimized, then two approaches are proposed to optimize the weighting exponent (m) in the FCM algorithm, namely, the iterative search approach and the genetic algorithms. The above mentioned approach is tested on the generated data from the original function and optimal fuzzy models are obtained with minimum error between the real data and the obtained fuzzy models.

Authors:

• Mohanad Alata
• Mohammad Molhim
• Abdullah Ramini

Keywords:

• Fuzzy clustering
• Fuzzy C-Means
• Genetic Algorithm
• Sugeno fuzzy systems.

References:

[1] Li-Xin Wang, A Course in Fuzzy Systems and Control, (Prentice Hall,
Inc.) Upper Saddle River, NJ 07458; 1997: 342-353.
[2] J. C. Dunn, A Fuzzy Relative of the ISODATA Process and Its Use in
Detecting Compact Well-Separated Clusters, Journal of Cybernetics 3;
1973: 32-57.
[3] Bezdek, J. C., Pattern Recognition with Fuzzy Objective Function
Algorithms, Plenum Press, NY, 1981.
[4] Beightler, C. S., Phillips, D. J., & Wild, D. J., Foundations of
optimization (2nd ed.). (Prentice-Hall) Englewood Cliffs, NJ, 1979.
[5] Luus, R. and Jaakola T. H. I., Optimization by Direct Search and
Systematic Reduction of the Size of Search Region, AIChE Journal
1973; 19(4): 760 - 766.
[6] Hall, L. O., Ozyurt, I. B. and Bezdek, J. C., Clustering with a genetically
optimized approach, IEEE Trans. Evolutionary Computation 1999; 3(2),
103-112.
[7] Chiu S. Fuzzy model identification based on cluster estimation. 1994,
Journal of Intelligent and Fuzzy Systems; 2:267-78.
[8] Yager, R. and D. Filev, Generation of Fuzzy Rules by Mountain
Clustering, Journal of Intelligent & Fuzzy Systems, 1994; 2 (3): 209-
219.
[9] Ginat, D., Genetic Algorithm - A Function Optimizer, NSF Report,
Department of Computer Science, University of Maryland, College Park,
MD20740, 1988.
[10] Wang, Q. J., Using Genetic Algorithms to Optimize Model Parameters,
Journal of Environmental Modeling and Software 1997; 12(1):