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.
[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):
[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):
@article{"International Journal of Information, Control and Computer Sciences:62415", author = "Mohanad Alata and Mohammad Molhim and Abdullah Ramini", title = "Optimizing of Fuzzy C-Means Clustering Algorithm Using GA", abstract = "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.", keywords = "Fuzzy clustering, Fuzzy C-Means, Genetic
Algorithm, Sugeno fuzzy systems.", volume = "2", number = "3", pages = "922-6", }