Fuzzy Clustering by Particle Swarm Optimization

This paper deals with fuzzy clustering by minimizing the fuzzy c-means (FCM) model. We introduce two new methods for minimizing the two reformulated versions of the FCM objective function by particle swarm optimization (PSO). In PSO-V each particle represents a component of a cluster center. In PSO-U each particle represents an unsealed and unnormalized membership value. PSO-V and PSO-U are compared with alternating optimization (AO) and with ant colony optimization (ACO) on two benchmark data sets: the single outlier and the lung cancer data sets. The stochastic methods ACO, PSO-V, and PSO-U are slower than AO, but in each experiment one of the two PSO variants significantly outperforms the other algorithms.

[1]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[2]  James C. Bezdek,et al.  Optimization of fuzzy clustering criteria using genetic algorithms , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[3]  Lawrence O. Hall,et al.  Fuzzy ant clustering by centroid positioning , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[4]  James C. Bezdek,et al.  Optimization of clustering criteria by reformulation , 1995, IEEE Trans. Fuzzy Syst..

[5]  Jing-Yu Yang,et al.  Optimal discriminant plane for a small number of samples and design method of classifier on the plane , 1991, Pattern Recognit..

[6]  Raghuveer M. Rao,et al.  Particle swarm optimization for the clustering of wireless sensors , 2003, SPIE Defense + Commercial Sensing.

[7]  Thomas A. Runkler.  Ant colony optimization of clustering models , 2005, Int. J. Intell. Syst..

[8]  John W. Sammon,et al.  A Nonlinear Mapping for Data Structure Analysis , 1969, IEEE Transactions on Computers.

[9]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[10]  Andries Petrus Engelbrecht,et al.  Data clustering using particle swarm optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[11]  Frank Klawonn,et al.  Fuzzy clustering with evolutionary algorithms , 1998, Int. J. Intell. Syst..

[12]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[13]  Marco Dorigo,et al.  Strategies for the Increased Robustness of Ant-Based Clustering , 2003, Engineering Self-Organising Systems.

[14]  James M. Keller,et al.  Taxonomy-based soft similarity measures in bioinformatics , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[15]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[16]  Parag M. Kanade,et al.  Fuzzy ants as a clustering concept , 2003, 22nd International Conference of the North American Fuzzy Information Processing Society, NAFIPS 2003.

[17]  V. J. Rayward-Smith,et al.  Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition , 1999 .

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

[19]  Yangyang Zhang,et al.  Particle swarm optimization for mobile ad hoc networks clustering , 2004, IEEE International Conference on Networking, Sensing and Control, 2004.

[20]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..