A new dynamic clustering approach (DCPSO), based on Particle Swarm Optimization, is proposed. This approach is applied to unsupervised image classification. The proposed approach automatically determines the "optimum" number of clusters and simultaneously clusters the data set with minimal user interference. The algorithm starts by partitioning the data set into a relatively large number of clusters to reduce the effects of initial conditions. Using binary particle swarm optimization the "best" number of clusters is selected. The centers of the chosen clusters is then refined via the Kmeans clustering algorithm. The experiments conducted show that the proposed approach generally found the "optimum" number of clusters on the tested images., {"references":["A.K. Jain, M.N. Murty, P.J. Flynn, Data Clustering: A Review, ACM\nComputing Surveys, vol. 31(3), 264-323,1999.","A.K. Jain, R. Duin, J. Mao, Statistical Pattern Recognition: A Review,\nIEEE Transactions on Pattern Analysis and Machine Intellgence, vol. 22\n(1), 4-37, 2000.","D. Judd, P. Mckinley, A.K. Jain, Large-scale Parallel Data Clustering,\nIEEE Transactions on Pattern Analysis and Machine Intellgence, vol. 20\n(8), 871-876, 1998.","H.M. Abbas, M.M. Fahmy, Neural Networks for Maximum Likelihood\nClustering, Signal Processing, vol. 36(1), 111-126, 1994.","G.B. Coleman, H.C. Andrews, Image Segmentation by Clustering, Proc.\nIEEE, vol. 67, 773-785, 1979.","A.K. Jain, R.C. Dubes, Algorithms for Clustering Data, New Jersey,\nPrentice Hall, 1988.","S. Ray, R.H. Turi, Determination of Number of Clusters in K-Means\nClustering and Application in Colour Image Segmentation, Proceedings\nof the 4th International Conference on Advances in Pattern Recognition\nand Digital Techniques (ICAPRDT'99), Calcutta, India, 137-143, 1999.","C. Carpineto, G. Romano, A Lattice Conceptual Clustering System and\nIts Application to Browsing Retrieval, Machine Learning, vol. 24(2), 95-\n122, 1996.","C.-Y. Lee, E.K. Antonsson, Dynamic Partitional Clustering Using\nEvolution Strategies, In The Third Asia-Pacific Conference on\nSimulated Evolution and Learning, 2000.\n[10] G. Hamerly, C. Elkan, Learning the K in K-means, 7th Annual\nConference on Neural Information Processing Systems, 2003.\n[11] H. Frigui and R. Krishnapuram, A Robust Competitive Clustering\nAlgorithm with Applications in Computer Vision, IEEE Transactions on\nPattern Analysis and Machine Intelligence, vol. 21(5), 450-465, 1999.\n[12] Y. Leung, J. Zhang, Z. Xu, Clustering by Space-Space Filtering, IEEE\nTransactions on Pattern Analysis and Machine Intelligence, vol. 22(12),\n1396-1410, 2000.\n[13] M. Halkidi, Y. Batistakis, M. Vazirgiannis, On Clustering Validation\nTechniques, Intelligent Information Systems Journal, Kluwer Pulishers,\nvol. 17(2-3), 107-145, 2001.\n[14] S. Theodoridis and K. Koutroubas, Pattern Recognition, Academic\nPress, 1999.\n[15] C. Rosenberger and K. Chehdi, Unsupervised Clustering Method with\nOptimal Estimation of the Number of Clusters: Application to Image\nSegmentation, International Conference on Pattern Recognition\n(ICPR'00), vol. 1, 1656-1659 (2000).\n[16] L. Kuncheva and J. Bezdek, Nearest Prototype Classification:\nClustering, Genetic Algorithms, or Random Search?, IEEE Transactions\non Systems, Man, and Cybernetics-Part C: Applications and Reviews,\nvol. 28(1), 160-164, 1998.\n[17] G. Ball and D. Hall, A Clustering Technique for Summarizing\nMultivariate Data, Behavioral Science, vol. 12, 153-155, 1967.\n[18] K. Huang, A Synergistic Automatic Clustering Technique (Syneract) for\nMultispectral Image Analysis, Photogrammetric Engineering and\nRemote Sensing, vol. 1(1), 33-40, 2002.\n[19] D. Pelleg, A. Moore, X-means: Extending K-means with efficient\nestimation of the number of clusters, Proceedings of the 17th\nInternational Conference on Machine Learning, 727-734, Morgan\nKaufmann, San Francisco, CA, 2000.\n[20] R. Kass, L. Wasserman, A reference Bayesian test for nested hypotheses\nand its relationship to the Schwarz criterion, Journal of the American\nStatistical Association, vol. 90(431), 928-934, 1995.\n[21] G. Hamerly, Learning structure and concepts in data using data\nclustering, PhD Thesis, University of California, San Diego, 2003.\n[22] C.S. Wallace, D.L. Dowe, Intrinsic classification by MML - the snob\nprogram, Proceedings 7th Australian Joint Conference on Artificial\nIntelligence, UNE, Armidale, NSW, Australia, 37-44, 1994.\n[23] C.S. Wallace, An improved program for classification, Technical Report\nNo. 47, Department of Computer Science, Monash University, Australia,\n1984.\n[24] R.H. Turi, Clustering-Based Colour Image Segmentation, PhD Thesis,\nMonash University, Australia, 2001.\n[25] C.S. Wallace, D.M. Boulton, An information measure for classification,\nThe Computer Journal, vol. 11, 185-194, 1968.\n[26] J.J. Oliver, D. Hand, Introduction to minimum encoding inference,\nTechnical Report No. 94/205, Department of Computer Science, Monash\nUniversity, Australia, 1994.\n[27] H. Bischof, A. Leonardis, A. Selb, MDL principle for robust vector\nquantization, Pattern analysis and applications, 2, 59-72, 1999.\n[28] I. Gath, A. Geva, Unsupervised Optimal Fuzzy Clustering, IEEE\nTransactions on Pattern Analysis and Machine Intelligence, vol. 11(7),\n773-781, 1989.\n[29] A. Lorette, X. Descombes, J. Zerubia, Fully Unsupervised Fuzzy\nClustering with Entropy Criterion, International Conference on Pattern\nRecognition (ICPR'00), vol. 3, 3998-4001, 2000.\n[30] N. Boujemaa, On Competitive Unsupervised Clustering, International\nConference on Pattern Recognition (ICPR'00), vol. 1, 1631-1634, 2000.\n[31] H. Frigui and R. Krishnapuram, Clustering by Competitive\nAgglomeration, Pattern Recognition Letters, vol. 30(7), 1109-1119,\n1997.\n[32] H. Frigui and R. Krishnapuram, A Robust Competitive Clustering\nAlgorithm with Applications in Computer Vision, IEEE Transactions on\nPattern Analysis and Machine Intelligence, vol. 21(5), 450-465, 1999.\n[33] T. Kohonen, Self-Organizing Maps, Springer Series in Information\nSciences, 30, Springer-Verlag, N.Y., 1995.\n[34] K. Mehrotra, C. Mohan, Rakka, Elements of Artificial Neural Networks,\nMIT Press, 1997.\n[35] A. Pandya, R. Macy, Pattern Recognition with Neural Networks in C++,\nCRC Press, 1996.\n[36] M. Halkidi, M. Vazirgiannis, Clustering Validity Assessment: Finding\nthe Optimal Partitioning of a data set, Proceedings of ICDM Conference,\nCA (USA), Nov. 2001.\n[37] J. Kennedy, R. Eberhart, Particle Swarm Optimization, Proceedings of\nIEEE International Conference on Neural Networks, Perth, Australia,\nvol. 4, 1942-1948, 1995.\n[38] J. Kennedy, R. Eberhart, Swarm Intelligence, Morgan Kaufmann, 2001.\n[39] A. Engelbrecht, Computational Intelligence: An Introduction, John\nWiley and Sons, 2002.\n[40] Y. Shi, R. Eberhart, Parameter Selection in Particle Swarm Optimization,\nEvolutionary Programming VII: Proceedings of EP 98, 591-600, 1998.\n[41] P. Suganthan, Particle Swarm Optimizer with Neighborhood Optimizer,\nProceedings of the Congress on Evolutionary Computation, 1958-1962,\n1999.\n[42] Y. Shi, R. Eberhart, A Modified Particle Swarm Optimizer, Proceedings\nof the IEEE International Conference on Evolutionary Computation,\nPiscataway, NJ, 69-73, 1998.\n[43] J. Kennedy, Small Worlds and Mega-Minds: Effects of Neighborhood\nTopology on Particle Swarm Performance, Proceedings of the Congress\non Evolutionary Computation, 1931-1938, 1999.\n[44] J. Kennedy, R. Mendes, Population Structure and Particle Performance,\nProceedings of the IEEE Congress on Evolutionary Computation,\nHonolulu, Hawaii, 2002.\n[45] F. Van den Bergh, An Analysis of Particle Swarm Optimizers, PhD\nThesis, Department of Computer Science, University of Pretoria, 2002.\n[46] F. van den Bergh, A.P. Engelbrecht, A New Locally Convergent Particle\nSwarm Optimizer, Proceedings of the IEEE Conference on Systems,\nMan, and Cybernetics, Hammamet, Tunisia, 2002.\n[47] J. Kennedy, R. Eberhart, A Discrete Binary Version of the Particle\nSwarm Algorithm, Proceedings of the Conference on Systems, Man, and\nCybernetics, 4104-4109, 1997."]}