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Metaheuristic Pattern Clustering – An Overview

Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 178)

Abstract

This chapter provides a comprehensive overview to the data clustering techniques, based on naturally-inspired metaheuristic algorithms. At first the clustering problem, similarity and dissimilarity measures between patterns and the methods of cluster validation are presented in a formal way. A few classical clustering algorithms are also addressed. The chapter then discusses the relevance of population-based approach with a focus on evolutionary computing in pattern clustering and outlines the most promising evolutionary clustering methods. The chapter ends with a discussion on the automatic clustering problem, which remains largely unsolved by most of the traditional clustering algorithms.

Keywords

Particle Swarm Optimization Cluster Algorithm Cluster Center Fuzzy Cluster Cluster Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. John Wiley and Sons, Chichester (1973)zbMATHGoogle Scholar
  2. 2.
    Everitt, B.S.: Cluster Analysis, 3rd edn. Halsted Press (1993)Google Scholar
  3. 3.
    Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs (1988)zbMATHGoogle Scholar
  4. 4.
    Arabie, P., Hubert, L.J., De Soete, G. (eds.): Clustering and Classification, River Edge. World Scientific Publishing, Singapore (1996)Google Scholar
  5. 5.
    Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Computing Surveys 31(3), 264–323 (1999)CrossRefGoogle Scholar
  6. 6.
    Forgy, E.W.: Cluster Analysis of Multivariate Data: Efficiency Versus Interpretability of classification. Biometrics 21, 768–769 (1965)Google Scholar
  7. 7.
    Zahn, C.T.: Graph-theoretical methods for detecting and describing gestalt clusters. IEEE Transactions on Computers C-20, 68–86 (1971)zbMATHCrossRefGoogle Scholar
  8. 8.
    Mitchell, T.: Machine Learning. McGraw-Hill, Inc., New York (1997)zbMATHGoogle Scholar
  9. 9.
    Mao, J., Jain, A.K.: Artificial neural networks for feature extraction and multivariate data projection. IEEE Trans. Neural Network 6, 296–317 (1995)CrossRefGoogle Scholar
  10. 10.
    Pal, N.R., Bezdek, J.C., Tsao, E.C.-K.: Generalized clustering networks and Kohonen’s self-organizing scheme. IEEE Trans. Neural Networks 4, 549–557 (1993)CrossRefGoogle Scholar
  11. 11.
    Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, Heidelberg (1995)Google Scholar
  12. 12.
    Falkenauer, E.: Genetic Algorithms and Grouping Problems. John Wiley and Son, Chichester (1998)Google Scholar
  13. 13.
    Paterlini, S., Minerva, T.: Evolutionary approaches for bluster analysis. In: Bonarini, A., Masulli, F., Pasi, G. (eds.) Soft Computing Applications, pp. 167–178. Springer, Berlin (2003)Google Scholar
  14. 14.
    Brucker, P.: On the complexity of clustering problems. In: Beckmenn, M., Kunzi, H.P. (eds.) Optimization and Operations Research. Lecture Notes in Economics and Mathematical Systems, vol. 157, pp. 45–54. Springer, Berlin (1978)Google Scholar
  15. 15.
    Hamerly, G., Elkan, C.: Learning the k in k-means. In: Proceedings of the Seventeenth Annual Conference on Neural Information Processing Systems (NIPS), pp. 281–288 (December 2003)Google Scholar
  16. 16.
    Theodoridis, S., Koutroumbas, K.: Pattern Recognition, 2nd edn. Elsevier Academic Press, Amsterdam (2003)Google Scholar
  17. 17.
    Halkidi, M., Vazirgiannis, M.: Clustering validity assessment: Finding the optimal partitioning of a data set. In: Proceedings of the 2001 IEEE International Conference on Data Mining (ICDM 2001), San Jose, California, USA, pp. 187–194 (2001)Google Scholar
  18. 18.
    Dunn, J.C.: Well Separated Clusters and Optimal Fuzzy Partitions. J. Cybern. 4, 95–104 (1974)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Calinski, R.B., Harabasz, J.: Adendrite Method for Cluster Analysis. Commun. Statistics, 1–27 (1974)Google Scholar
  20. 20.
    Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 224–227 (1979)CrossRefGoogle Scholar
  21. 21.
    Pakhira, M.K., Bandyopadhyay, S., Maulik, U.: Validity index for crisp and fuzzy clusters. Pattern Recognition Letters 37, 487–501 (2004)zbMATHGoogle Scholar
  22. 22.
    Chou, C.H., Su, M.C., Lai, E.: A new cluster validity measure and its application to image compression. Pattern Analysis and Applications 7(2), 205–220 (2004)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Bezdek, J.C.: Numerical taxonomy with fuzzy sets. Journal of Math. Biol., 157–171 (1974)Google Scholar
  24. 24.
    Bezdek, J.C.: Cluster validity with fuzzy sets. Journal of Cybernetics (3), 58–72 (1974)Google Scholar
  25. 25.
    Xie, X., Beni, G.: Validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Machine Learning 3, 841–846 (1991)CrossRefGoogle Scholar
  26. 26.
    Pal, N.R., Biswas, J.: Cluster validation using graph theoretic concepts. Pattern Recognition 30(6), 847–857 (1997)CrossRefGoogle Scholar
  27. 27.
    Su, M.-C., Chou, C.-H., Lai, E.: A new cluster validity measure for clusters with different densities. In: IASTED International Conference on Intelligent Systems & Control, Salzburg, Austria, pp. 276–281 (2003)Google Scholar
  28. 28.
    Su, M.-C., Chou, C.-H.: A competitive learning algorithm using symmetry. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E82-A(4), 680–687 (1999)Google Scholar
  29. 29.
    Su, M.-C., Liu, Y.-C.: A new approach to clustering data with arbitrary shapes. Pattern Recognition 38, 1887–1901 (2005)zbMATHCrossRefGoogle Scholar
  30. 30.
    Su, M.-C., Chou, C.-H.: A modified version of the K-means algorithm with a distance based on cluster symmetry. IEEE Trans. on Pattern Analysis and Machine Intelligence 23(6), 674–680 (2001)CrossRefGoogle Scholar
  31. 31.
    Pakhira, M.K., Bandyopadhyay, S., Maulik, U.: A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification. Fuzzy Sets and Systems 155, 191–214 (2005)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Chou, C.H., Su, M.C., Lai, E.: A new cluster validity measure and its application to image compression. Pattern Analysis and Applications 7(2), 205–220 (2004)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Zhang, T., Ramakrishnman, R., Linvy, M.: BIRCH: An efficient method for very large databases. In: ACM SIGMOD, Montreal, Canada (1996)Google Scholar
  34. 34.
    Guha, S., Rastogi, R., Shim, K.: CURE: An efficient clustering algorithm for large databases. In: Proceedings of the ACM SIGMOD Conference (1998)Google Scholar
  35. 35.
    Guha, S., Rastogi, R., Shim, K.: ROCK: A robust clustering algorithm for categorical attributes. In: Proceedings of the IEEE Conference on Data Engineering (1999)Google Scholar
  36. 36.
    Hammerly, G., Elkan, C.: Alternatives to the k-means algorithm that find better clusterings. In: Proc. ACM on Information and Knowledge Management, pp. 600–607 (November 2002)Google Scholar
  37. 37.
    Zhang, T.: Convergence of large margin separable linear classification. In: NIPS 2000, pp. 357–363 (2001)Google Scholar
  38. 38.
    MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkely Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)Google Scholar
  39. 39.
    Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)Google Scholar
  40. 40.
    Huang, Z.: A Fast Clustering Algorithm to Cluster very Large Categorical Data Sets in Data Mining. DMKD (1997)Google Scholar
  41. 41.
    Ng, R., Han, J.: Efficient and effective clustering methods for spatial data mining. In: Proceeding’s of the 20th VLDB Conference, Santiago, Chile (1994)Google Scholar
  42. 42.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms, New York, Plenum (1981)Google Scholar
  43. 43.
    Wang, X., Wang, Y., Wang, L.: Improving fuzzy c-means clustering based on feature-weight learning. Pattern Recognition Letters 25, 1123–1132 (2004)CrossRefGoogle Scholar
  44. 44.
    Krishnapuram, R., Keller, J.: The possibilistic c-means algorithm: insights and recommendations. IEEE Trans. on Fuzzy Systems 4, 385–393 (1996)CrossRefGoogle Scholar
  45. 45.
    Bezdek, J.C., Keller, J., Krishnampuram, R., Pal, N.R.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer Academic Publishers, Dordercht (1999)zbMATHGoogle Scholar
  46. 46.
    Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B 39(1), 1–38 (1977)zbMATHMathSciNetGoogle Scholar
  47. 47.
    McLachlan, G., Krishnan, T.: The EM algorithm and extensions. Wiley series in probability and statistics. John Wiley & Sons, Chichester (1997)zbMATHGoogle Scholar
  48. 48.
    Hamerly, G., Elkan, C.: Alternatives to the k-Means algorithm that find better clustering (pdf). In: Proceedings of the Eleventh International Conference on Information and Knowledge Management (CIKM 2002), pp. 600–607 (November 2002)Google Scholar
  49. 49.
    Veenman, C.J., Reinders, M.J.T., Backer, E.: A maximum variance cluster algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(9), 1273–1280 (2002)CrossRefGoogle Scholar
  50. 50.
    Alldrin, N., Smith, A., Turnbull, D.: Clustering with EM and K-means, unpublished Manuscript (2003), http://louis.ucsd.edu/~nalldrin/research/cse253\_wi03.pdf
  51. 51.
    Turi, R.H.: Clustering-based colour image segmentation. PhD Thesis. Monash University, Australia (2001)Google Scholar
  52. 52.
    Ng, A., Jordan, M., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: Proceedings of eural Information Processing Systems (NIPS 2001) (2001)Google Scholar
  53. 53.
    Zhang, B., Hsu, M., Dayal, U.: K-Harmonic means - A data clustering algorithm. Technical Report HPL-1999-124. Hewlett-Packard Labs (1999)Google Scholar
  54. 54.
    Zhang, B.: Generalized K-Harmonic means - boosting in unsupervised learning. Technical Report HPL-2000-137. Hewlett-Packard Labs (2000)Google Scholar
  55. 55.
    Bradley, P.S., Fayyad, U.M.: Refining Initial Points for K-Means Clustering. In: ICML 1998, pp. 91–99 (1998)Google Scholar
  56. 56.
    Ester, M., Kriegel, H.-P., Sander, J., Xu, X.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceeding of 2nd Int. Conf. on Knowledge Discovery and Data Mining, Portland, pp. 226–23 (1996)Google Scholar
  57. 57.
    Hinneburg, A., Keim, D.: An efficient approach to clustering in large multimedia databases with noise. In: Proceedings of KDD Conference (1998)Google Scholar
  58. 58.
    Comaniciu, D., Meer, P.: Mean shift: A robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 603–619 (2002)CrossRefGoogle Scholar
  59. 59.
    Wang, W., Yang, J., Muntz, R.: STING: A statistical Information grid approach to spatial data mining. In: Proceedings of 23rd VLDB Conference (1997)Google Scholar
  60. 60.
    Sheikholeslami, C., Chatterjee, S., Zhang, A.: WaveCluster: A-multi resolution clustering approach for very large spatial database. In: Proceedings of 24th VLDB Conference, New York, USA (1998)Google Scholar
  61. 61.
    Han, J., Kamber, M.: Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers, USA (2001)Google Scholar
  62. 62.
    Back, T., Fogel, D.B., Michalewicz, Z. (eds.): Handbook of Evolutionary Computation. Oxford University Press, Oxford (1997)Google Scholar
  63. 63.
    De Jong, K.A.: Evolutionary Computation: A Unified Approach. MIT Press, Cambridge (2006)zbMATHGoogle Scholar
  64. 64.
    Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  65. 65.
    Fogel, D.B.: Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. IEEE Press, Piscataway (1995)Google Scholar
  66. 66.
    Fogel, L.J., Owens, A.J., Walsh, M.J.: Artificial Intelligence through Simulated Evolution. John Wiley, New York (1966)zbMATHGoogle Scholar
  67. 67.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  68. 68.
    Rechenberg, I.: Evolutionsstrategie - Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution (PhD thesis, 1971); Reprinted by Fromman-Holzboog (1973)Google Scholar
  69. 69.
    Schwefel, H.-P.: Numerische Optimierung von Computer-Modellen (PhD thesis) (1974); Reprinted by Birkhäuser (1977)Google Scholar
  70. 70.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Evolution. MIT Press, Massachusetts (1992)Google Scholar
  71. 71.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press Inc., Oxford (1999)zbMATHGoogle Scholar
  72. 72.
    Martinetz, T.M., Schulten, K.J.: A neural-gas network learns topologies. In: Kohonen, T., Mäkisara, K., Simula, O., Kangas, J. (eds.) Artificial Neural Networks, pp. 397–402. North-Holland, Amsterdam (1991)Google Scholar
  73. 73.
    Langton, C.G. (ed.): Artificial Life: An Overview. MIT Press, Cambridge (1995)Google Scholar
  74. 74.
    Kobti, Z., Reynolds, R., Kohler, T.: A multi-agent simulation using cultural algorithms: The effect of culture on the resilience of social systems. In: IEEE Congress on Evolutionary Computation, Canberra, Australia, December 5-12 (2003)Google Scholar
  75. 75.
    Lee, K.S., Geem, Z.W.: A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Computer Methods in Applied Mechanics and Engineering (2005)Google Scholar
  76. 76.
    Dasgupta, D. (ed.): Artificial Immune Systems and Their Applications. Springer, Berlin (1999)zbMATHGoogle Scholar
  77. 77.
    Wojtusiak, J., Michalski, R.S.: The LEM3 Implementation of learnable evolution model and Its testing on complex function optimization problems. In: Proceedings of Genetic and Evolutionary Computation Conference, GECCO 2006, Seattle, WA, July 8-12 (2006)Google Scholar
  78. 78.
    Michalewicz, Z., Fogel, D.B.: How to Solve It: Modern Heuristics. Springer, Heidelberg (2000)zbMATHGoogle Scholar
  79. 79.
    Beyer, H.-G., Schwefel, H.-P.: Evolution Strategies: A Comprehensive Introduction. Journal Natural Computing 1(1), 3–52 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  80. 80.
    Beyer, H.-G.: The Theory of Evolution Strategies. Springer, Heidelberg (2001)Google Scholar
  81. 81.
    Kita, H.: A comparison study of self-adaptation in volution etrategies and real-coded genetic algorithms. Evolutionary Computation 9(2), 223–241 (2001)MathSciNetCrossRefGoogle Scholar
  82. 82.
    Hansen, N., Ostermeier, A.: Completely de-randomized self-adaptation in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)CrossRefGoogle Scholar
  83. 83.
    Fogel, D.B.: Evolving Artificial Intelligence, Ph.D. dissertation, Univ. California, San Diego, CA (1992)Google Scholar
  84. 84.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)zbMATHGoogle Scholar
  85. 85.
    DeJong, K.A.: An analysis of behavior of a class of genetic adaptive systems. Doctoral Dissertation, University of Michigan (1975)Google Scholar
  86. 86.
    Davis, T.E., Principa, J.C.: A Markov chain framework for the simple genetic algorithm. Evolutionary Computation 1(3), 269–288 (1993)CrossRefGoogle Scholar
  87. 87.
    Muehlenbein, H., Chakraborty, U.K.: Gene pool recombination genetic algorithm and the onemax function. Journal of Computing and Information Technology 5(3), 167–182 (1997)Google Scholar
  88. 88.
    Vose, M.D., Liepins, G.E.: Punctuated equilibrium in genetic search. Complex Systems 5, 31–44 (1991)zbMATHMathSciNetGoogle Scholar
  89. 89.
    Filho, J.L.R., Treleven, P.C.: Genetic Algorithm Programming Environment, pp. 28–43. IEEE Computer Society Press, Los Alamitos (1994)Google Scholar
  90. 90.
    Smith, S.F.: A Learning System Based on Genetic Adaptive Algorithms, PhD dissertation (University of Pittsburgh) (1980)Google Scholar
  91. 91.
    Cramer, N.L.: A representation for the adaptive generation of simple sequential programs. In: John, J. (ed.) Proceedings of an International Conference on Genetic Algorithms and the Applications, Grefenstette, Carnegie Mellon University (1985)Google Scholar
  92. 92.
    Banzhaf, W., Nordin, P., Keller, R.E., Francone, F.D.: Genetic programming: An Introduction: On the Automatic Evolution of Computer Programs and Its Applications. Morgan Kaufmann, San Francisco (1998)zbMATHGoogle Scholar
  93. 93.
    Nordin, J.P.: Evolutionary Program Induction of Binary Machine Code and its Application. Krehl Verlag, Muenster, Germany (1997)Google Scholar
  94. 94.
    Beni, G., Wang, U.: Swarm intelligence in cellular robotic systems. In: NATO Advanced Workshop on Robots and Biological Systems, Il Ciocco, Tuscany, Italy (1989)Google Scholar
  95. 95.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proc. of the IEEE Int. Conf. on Neural Networks, Piscataway, NJ, pp. 1942–1948 (1995)Google Scholar
  96. 96.
    Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)Google Scholar
  97. 97.
    Dorigo, M.: Optimization, Learning and Natural Algorithms, PhD thesis, Politecnico di Milano, Italy (1992)Google Scholar
  98. 98.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant System: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics–Part B 26(1), 29–41 (1996)CrossRefGoogle Scholar
  99. 99.
    Dorigo, M., Gambardella, L.M.: Ant Colony System: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)CrossRefGoogle Scholar
  100. 100.
    Johnson, D.S., Mc Geoch, L.A.: The Traveling Salesman Problem: A Case Study in Local Optimization. In: Aarts, E.H.L., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization, pp. 215–310. John Wiley and Sons Ltd., Chichester (1997)Google Scholar
  101. 101.
    Abraham, A., Das, S., Roy, S.: Swarm intelligence algorithms for data clustering. In: Maimon, O., Rokach, L. (eds.) Soft Computing for Knowledge Discovery and Data Mining, pp. 279–313. Springer, Germany (2007)Google Scholar
  102. 102.
    Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science 220(4598), 671–680 (1983)Google Scholar
  103. 103.
    Raghavan, V.V., Birchand, K.: A clustering strategy based on a formalism of the reproductive process in a natural system. In: Proceedings of the Second International Conference on Information Storage and Retrieval, pp. 10–22Google Scholar
  104. 104.
    Murthy, C.A., Chowdury, N.: search of optimal clusters using genetic algorithm. Pattern Recognition Letters 17, 825–832 (1996)CrossRefGoogle Scholar
  105. 105.
    Falkenauer, E.: Genetic Algorithms and Grouping Problems. John Wiley and Son, Chichester (1998)Google Scholar
  106. 106.
    Bandyopadhyay, S., Murthy, C.A., Pal, S.K.: Pattern classification with genetic algorithms. Pattern Recognition Letters 16, 801–808 (1995)CrossRefGoogle Scholar
  107. 107.
    Bandyopadhyay, S., Murthy, C.A., Pal, S.K.: Pattern classification using genetic algorithm: determination of H. Pattern Recognition Letters 19, 1171–1181 (1998)zbMATHCrossRefGoogle Scholar
  108. 108.
    Bandyopadhyay, S., Murthy, C.A., Pal, S.K.: Theoretic performance of genetic pattern classifier. Journal of the Franklin Institute 336, 387–422 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  109. 109.
    Bandyopadhyay, S., Maulik, U.: Genetic clustering for automatic evolution of clusters and application to image classification. Pattern Recognition 35, 1197–1208 (2002)zbMATHCrossRefGoogle Scholar
  110. 110.
    Srikanth, R., George, R., Warsi, N., Prabhu, D., Petri, F.E., Buckles, B.P.: A variable-length genetic algorithm for clustering and classification. Pattern Recognition Letters 16, 789–800 (1995)CrossRefGoogle Scholar
  111. 111.
    Maulik, U., Bandyopadhyay, S.: Genetic algorithm-based clustering technique. Pattern Recognition 33, 1455–1465 (2000)CrossRefGoogle Scholar
  112. 112.
    Chiou, Y.C., Lan, L.W.: Theory and methodology genetic clustering algorithms. European Journal of operational Research 135, 413–427 (2001)zbMATHMathSciNetCrossRefGoogle Scholar
  113. 113.
    Bandyopadhyay, S., Maulik, U.: An evolutionary technique based on K-means algorithm for optimal clustering in RN. Information Sciences 146, 221–237 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  114. 114.
    Paterlini, S., Minerva, T.: Evolutionary approaches for cluster analysis. In: Bonarini, A., Masulli, F., Pasi, G. (eds.) Soft Computing Applications, pp. 167–178. Springer, Berlin (2003)Google Scholar
  115. 115.
    Krishna, K., Murty, M.N.: Genetic K-means algorithm. IEEE Transaction on Systems, Man and Cybernetics 29 (1999)Google Scholar
  116. 116.
    Lee, C.-Y., Antonsson, E.K.: Dynamic partitional clustering using evolution strategies. In: Proceedings of the Third Asia Pacific Conference on Simulated Evolution and Learning (2000), http://citeseer.ist.psu.edu/501113.html
  117. 117.
    Sarkar, M., Yegnanarayana, B., Khemani, D.: A clustering algorithm using an evolutionary programming-based approach. Pattern Recognition Letters 18, 975–986 (1997)CrossRefGoogle Scholar
  118. 118.
    Deneubourg, J.L., Goss, S., Franks, N., Sendova-Franks, A., Detrain, C., Chetien, L.: The dynamics of collective sorting: Robot-like ants and ant-like robots. In: Meyer, J.A., Wilson, S.W. (eds.) Proceedings of the First International Conference on Simulation of Adaptive Behaviour: From Animals to Animats 1, pp. 356–363. MIT Press, Cambridge (1991)Google Scholar
  119. 119.
    Handl, J., Knowles, J., Dorigo, M.: Ant-based clustering: a comparative study of its relative performance with respect to k-means, average link and 1D-SOM., Technical Report TR/IRIDIA/2003-24, IRIDIA, Universite Libre de Bruxelles, Belgium (2003)Google Scholar
  120. 120.
    Lumer, E., Faieta, B.: Diversity and adaptation in populations of clustering ants. In: Proceedings Third International Conference on Simulation of Adaptive Behavior: from Animals to Animates 3, pp. 499–508. MIT Press, Cambridge (1994)Google Scholar
  121. 121.
    Lumer, E., Faieta, B.: Exploratory Database Analysis via Self-Organization, unpublished manuscript (1995)Google Scholar
  122. 122.
    Emergent colonization and graph partitioning. In: Proceedings of the Third International Conference on Simulation of Adaptive Behaviour: From Animals to Animats 3, pp. 494–500. MIT Press, Cambridge (1994)Google Scholar
  123. 123.
    Kuntz, P., Snyers, D.: New results on an ant-based heuristic for highlighting the organization of large graphs. In: Proceedings of the 1999 Congress on Evolutionary Computation, pp. 1451–1458. IEEE Press, Piscataway (1999)CrossRefGoogle Scholar
  124. 124.
    Kuntz, P., Snyers, D., Layzell, P.: A Stochastic Heuristic for Visualizing Graph Clusters in a bi-dimensional Space Prior to Partitioning. Journal of Heuristics 5(3), 327–351 (1998)CrossRefGoogle Scholar
  125. 125.
    Handl, J., Meyer, B.: Improved ant-based clustering and sorting. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, p. 913. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  126. 126.
    Hoe, K.M., Lai, W.-K., Tai, T.S.Y.: Homogeneous ants for web document similarity modeling and categorization. In: Dorigo, M., Di Caro, G.A., Sampels, M. (eds.) Ant Algorithms 2002. LNCS, vol. 2463, p. 256. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  127. 127.
    Ramos, V., Merelo, J.J.: Self-organized stigmergic document maps: Environments as a mechanism for context learning. In: Proceedings of the First Spanish Conference on Evolutionary and Bio-Inspired Algorithms (AEB 2002), pp. 284–293. Centro Univ. M´erida, Merida, Spain (2002)Google Scholar
  128. 128.
    Ramos, V., Muge, F., Pina, P.: Self-organized data and image retrieval as a consequence of inter-dynamic synergistic relationships in artificial ant colonies. Soft Computing Systems: Design, Management and Applications 87, 500–509 (2002)Google Scholar
  129. 129.
    Monmarche, N., Slimane, M., Venturini, G.: Ant class: discovery of clusters in numeric data by a hybridization of an ant colony with the k means algorithm. Internal Report No. 213, E3i, Laboratoire d’Informatique, Universite de Tours (1999)Google Scholar
  130. 130.
    Kanade, P.M., Hall, L.O.: Fuzzy ants as a clustering concept. In: Proceedings of the 22nd International Conference of the North American Fuzzy Information Processing Society (NAFIPS 2003), pp. 227–232 (2003)Google Scholar
  131. 131.
    Tsang, W., Kwong, S.: Ant colony clustering and feature extraction for anomaly intrusion detection. In: Abraham, A., Grosan, C., Ramos, V. (eds.) Swarm Intelligence in Data Mining, pp. 101–121. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  132. 132.
    Omran, M., Salman, A., Engelbrecht, A.P.: Image classification using particle swarm optimization. In: Conference on Simulated Evolution and Learning, vol. 1, pp. 370–374 (2002)Google Scholar
  133. 133.
    Omran, M., Engelbrecht, A.P., Salman, A.: Particle swarm optimization method for image clustering. International Journal of Pattern Recognition and Artificial Intelligence 19(3), 297–322 (2005)CrossRefGoogle Scholar
  134. 134.
    van der Merwe, D.W., Engelbrecht, A.P.: Data clustering using particle swarm optimization. In: Proceedings of the 2003 IEEE Congress on Evolutionary Computation, Piscataway, NJ, pp. 215–220 (2003)Google Scholar
  135. 135.
    Xiao, X., Dow, E.R., Eberhart, R.C., Miled, Z.B., Oppelt, R.J.: Gene clustering using self-organizing maps and particle swarm optimization. In: Proc. of the 17th International Symposium on Parallel and Distributed Processing (PDPS 2003), IEEE Computer Society, Washington (2003)Google Scholar
  136. 136.
    Cui, X., Potok, T.E.: Document clustering analysis based on hybrid PSO + K-means algorithm. Journal of Computer Sciences (Special Issue), 27–33 (2005) ISSN 1549-3636Google Scholar
  137. 137.
    Halkidi, M., Batistakis, Y., Vazirgiannis, M.: On clustering validation techniques. Journal of Intelligent Information Systems (JIIS) 17(2-3), 107–145 (2001)zbMATHCrossRefGoogle Scholar
  138. 138.
    Rosenberger, C., Chehdi, K.: Unsupervised clustering method with optimal estimation of the number of clusters: Application to image segmentation. In: Proc. IEEE International Conference on Pattern Recognition (ICPR), vol. 1, Barcelona, pp. 1656–1659 (2000)Google Scholar
  139. 139.
    Ball, G., Hall, D.: A clustering technique for summarizing multivariate data. Behavioral Science 12, 153–155 (1967)CrossRefGoogle Scholar
  140. 140.
    Huang, K.: A synergistic automatic clustering technique (Syneract) for multispectral image analysis. Photogrammetric Engineering and Remote Sensing 1(1), 33–40 (2002)Google Scholar
  141. 141.
    Pelleg, D., Moore, A.: X-means: Extending K-means with efficient estimation of the number of clusters. In: Proceedings of the 17th International Conference on Machine Learning, pp. 727–734. Morgan Kaufmann, San Francisco (2000)Google Scholar
  142. 142.
    Kass, R., Wasserman, L.: A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association 90(431), 928–934 (1995)zbMATHMathSciNetCrossRefGoogle Scholar
  143. 143.
    Wallace, C.S., Dowe, D.L.: Intrinsic classification by MML – the snob program. In: Proceedings 7th Australian Joint Conference on Artificial Intelligence, UNE, Armidale, NSW, Australia, pp. 37–44 (1994)Google Scholar
  144. 144.
    Wallace, C.S., Boulton, D.M.: An information measure for classification. The Computer Journal 11, 185–194 (1968)zbMATHGoogle Scholar
  145. 145.
    Oliver, J.J., Hand, D.: Introduction to minimum encoding inference. Technical Report No. 94/205, Department of Computer Science, Monash University, Australia (1994)Google Scholar
  146. 146.
    Bischof, H., Leonardis, A., Selb, A.: MDL principle for robust vector quantization. Pattern Analysis and Applications 2, 59–72 (1999)zbMATHCrossRefGoogle Scholar
  147. 147.
    Gath, I., Geva, A.: Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(7), 773–781 (1989)CrossRefGoogle Scholar
  148. 148.
    Lorette, A., Descombes, X., Zerubia, J.: Fully unsupervised fuzzy clustering with entropy criterion. In: International Conference on Pattern Recognition (ICPR 2000), vol. 3, pp. 3998–4001 (2000)Google Scholar
  149. 149.
    Frigui, H., Krishnapuram, R.: A robust competitive clustering algorithm with applications in computer vision. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(5), 450–465 (1999)CrossRefGoogle Scholar
  150. 150.
    Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, N.Y. (1995)Google Scholar
  151. 151.
    Vesanto, J., Alhoniemi, E.: Clustering of the self organizing map. IEEE Transactions on Neural Networks 11(3), 586–600 (2000), http://citeseer.ist.psu.edu/vesanto00clustering.html Google Scholar
  152. 152.
    Ultsch, A.: Emergence in Self-organizing feature maps. In: Proceedings Workshop on Self-Organizing Maps (WSOM 2007), Bielefeld, Germany (2007)Google Scholar
  153. 153.
    Mehrotra, K., Mohan, C.: Rakka: Elements of Artificial Neural Networks. MIT Press, Cambridge (1997)Google Scholar
  154. 154.
    Pandya, A., Macy, R.: Pattern Recognition with Neural Networks in C++. CRC Press, Boca Raton (1996)Google Scholar
  155. 155.
    Maulik, U., Bandyopadhyay, S.: Fuzzy partitioning using real coded variable length genetic algorithm for pixel classification. IEEE Transactions on Geosciences and Remote Sensing 41(5), 1075–1081 (2003)CrossRefGoogle Scholar
  156. 156.
    Omran, M.G., Engelbrecht, A.P., Salman, A.: Dynamic clustering using particle swarm optimization with application in unsupervised image classification. In: Proceedings of World Academy of Science, Engineering and Technology, vol. 9 (November 2005)Google Scholar
  157. 157.
    Sawaragi, Y., Nakayama, H., Tanino, T.: Theory of multiobjective optimization. Mathematics in Science and Engineering, vol. 176. Academic Press Inc., Orlando (1985)zbMATHGoogle Scholar
  158. 158.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)zbMATHGoogle Scholar
  159. 159.
    Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  160. 160.
    Abraham, A., Jain, L.C., Goldberg, R. (eds.): Evolutionary Multiobjective Optimization: Theoretical Advances and Applications. Springer, London (2005)zbMATHGoogle Scholar
  161. 161.
    Knowles, J.D., Corne, D.W.: Approxmating the nondominated front using the pareto archived evolution strategy. Evolutionary Computation 8(2), 149–172 (2000)CrossRefGoogle Scholar
  162. 162.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2) (2002)Google Scholar
  163. 163.
    Minaei-Bidgoli, B., Topchy, A., Punch, W.F.: Ensembles of partitions via data resampling. In: Proc. Int. Conf. Inf. Technol. Coding Comput., pp. 188–192 (2004)Google Scholar
  164. 164.
    Topchy, A., Jain, A.K., Punch, W.: Clustering ensembles: Models of consensus and weak partitions. IEEE Trans. Pattern Anal. Mach. Intell. 27(12), 1866–1881 (2005)CrossRefGoogle Scholar
  165. 165.
    Topchy, A., Minaei, B., Jain, A.K., Punch, W.: Adaptive clustering ensembles. In: Proc. Int. Conf. Pattern Recognit., pp. 272–275 (2004)Google Scholar
  166. 166.
    Strehl, A., Ghosh, J.: Cluster ensembles—A knowledge reuse framework for combining multiple partitions. J. Machine Learn. Res. 3, 583–617 (2002)MathSciNetCrossRefGoogle Scholar
  167. 167.
    Topchy, A., Jain, A.K., Punch, W.: A mixture model for clustering ensembles. In: Proc. SIAM Int. Conf. Data Mining, pp. 379–390 (2004)Google Scholar
  168. 168.
    Law, M., Topchy, A., Jain, A.K.: Multiobjective Data Clustering. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 424–430 (2004)Google Scholar
  169. 169.
    Bandyopadhyay, S., Maulik, U., Mukhopadhyay, A.: Multiobjective genetic clustering for pixel classification in remote sensing imagery, IEEE Transactions Geoscience and Remote Sensing (2006)Google Scholar
  170. 170.
    Handl, J., Knowles, J.: Evolutionary multiobjective clustering. In: Proc. 8th Int. Conf. Parallel Problem Solving from Nature, pp. 1081–1091 (2004)Google Scholar
  171. 171.
    Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J.: PESA-II: Region-based selection in evolutionary multiobjective optimization. In: Proc. Genetic Evol. Comput. Conf., pp. 283–290 (2001)Google Scholar
  172. 172.
    Handl, J., Knowles, J.: An evolutionary approach to multiobjective clustering. IEEE Transactions on Evolutionary Computation 11(1), 56–76 (2007)CrossRefGoogle Scholar
  173. 173.
    Handl, J., Knowles, J.: Exploiting the tradeoff—the benefits of multiple objectives in data clustering. In: Proc. 3rd Int. Conf. Evol. Multicriterion Optim., pp. 547–560 (2005)Google Scholar
  174. 174.
    Handl, J., Knowles, J.: Improvements to the scalability of multiobjective clustering. In: Proc. IEEE Congr. Evol. Comput., vol. 3, pp. 2372–2379 (2005)Google Scholar
  175. 175.
    Handl, J., Knowles, J.: Multiobjective clustering around medoids. In: Proc. IEEE Congr. Evol. Comput., vol. 1, pp. 632–639 (2005)Google Scholar
  176. 176.
    Storn, R., Price, K.V.: Differential evolution - a simple and efficient adaptive scheme for global optimization over continuous spaces., Technical Report TR-95-012, ICSI (1995), http://http.icsi.berkeley.edu/~storn/litera.html
  177. 177.
    Storn, R., Price, K.V., Lampinen, J.: Differential Evolution - A Practical Approach to Global Optimization. Springer, Berlin (2005)zbMATHGoogle Scholar
  178. 178.
    Snyman, J.A.: Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms. Springer Publishing, Heidelberg (2005)zbMATHGoogle Scholar
  179. 179.
    Hahn, W.: Theory and Application of Liapunov’s Direct Method. Prentice-Hall, Englewood Cliffs (1963)zbMATHGoogle Scholar
  180. 180.
    Blake, C., Keough, E., Merz, C.J.: UCI Repository of Machine Learning Database (1998), http://www.ics.uci.edu/~mlearn/MLrepository.html
  181. 181.
    Muller, K.R., Mika, S., Ratsch, G., Tsuda, K., Scholkopf, B.: An introduction to kernel-based learning algorithms. IEEE Trans. Neural Networks 12(2), 181–202 (2001)CrossRefGoogle Scholar
  182. 182.
    Girolami, M.: Mercer kernel-based clustering in feature space. IEEE Trans. Neural Networks 13(3), 780–784 (2002)CrossRefGoogle Scholar
  183. 183.
    Scholkopf, B., Smola, A.J.: Learning with Kernels. The MIT Press, Cambridge (2002)Google Scholar

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