Abstract
In this article a simulated annealing based approach for automatically clustering a data set into a number of fuzzy partitions is proposed. This is in contrast to the widely used fuzzy clustering scheme, the fuzzy C-Means (FCM) algorithm, which requires the a priori knowledge of the number of clusters. The said approach uses a real-coded variable representation of the cluster centers encoded as a state of the simulated annealing, while optimizing the Xie-Beni cluster validity index. In order to automatically determine the number of clusters, the perturbation operator is defined appropriately so that it can alter the cluster centers, and increase as well as decrease the encoded number of cluster centers. The operators are designed using some domain specific information. The effectiveness of the proposed technique in determining the appropriate number of clusters is demonstrated for both artificial and real-life data sets.
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References
Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs (1988)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)
Hammah, R.E., Curran, J.H.: Validity measures for the fuzzy cluster analysis of orientations. IEEE Trans. Patt. Anal. Mach. Intell, 1467–1472 (2000)
Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J. Cyberns. 3, 32–57 (1973)
Bezdek, J.C.: Cluster validity with fuzzy sets. J. Cybernet. 3, 58–72 (1974)
Bezdek, J.C.: Mathematical models for systematics and taxonomy. In: Estabrook, G. (ed.) Proc. 8th Intl. Conf. Numerical Taxonomy, pp. 143–166. Freeman, San Francisco (1975)
Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. Patt. Anal. Mach. Intell. 1, 224–227 (1979)
Windham, M.P.: Cluster validity for the fuzzy c-means clustering algorithm. IEEE Trans. Patt. Anal. Mach. Intell. 4, 357–363 (1982)
Bensaid, A.M., Hall, L.O., Bezdek, J.C., Clarke, L.P., Silbiger, M.L., Arrington, J.A., Murtagh, R.F.: Validity-guided (re)clustering with applications to image segmentation. IEEE Trans. Fuzzy Systs. 4, 112–123 (1996)
Xie, X.L., Beni, G.: A validity measure for fuzzy clustering. IEEE Trans. Patt. Anal. Mach. Intell. 13, 841–847 (1991)
Kirkpatrik, S., Gelatt, C., Vecchi, M.: Optimization by simulated annealing. Science 220, 671–680 (1983)
van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated Annealing: Theory and Applications. Kluwer Academic Publishers, Dordrecht (1987)
Bakker, B., Heskes, T.: Model clustering by deterministic annealing. In: European Symposium on Artificial Neural Networks, Bruges, Belgium, pp. 87–92 (1999)
Lukashin, A.V., Fuchs, R.: Analysis of temporal gene expression profiles: clustering by simulated annealing and determining the optimal number of clusters. Bioinformatics 17, 405–419 (2001)
Bandyopadhyay, S., Maulik, U., Pakhira, M.K.: Clustering using simulated annealing with probabilistic redistribution. International Journal of Pattern Recognition and Artificial Intelligence 15, 269–285 (2001)
Hermes, L., Buhmann, J.M.: Semi-supervised image segmentation by parametric distributional clustering. In: Rangarajan, A., Figueiredo, M.A.T., Zerubia, J. (eds.) EMMCVPR 2003. LNCS, vol. 2683, pp. 229–245. Springer, Heidelberg (2003)
Mitra, S., Pal, S.K.: Fuzzy multi-layer perceptron, inferencing and rule generation. IEEE Trans. Neural Networks 6, 51–63 (1995)
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Bandyopadhyay, S. (2005). Automatic Determination of the Number of Fuzzy Clusters Using Simulated Annealing with Variable Representation. In: Hacid, MS., Murray, N.V., Raś, Z.W., Tsumoto, S. (eds) Foundations of Intelligent Systems. ISMIS 2005. Lecture Notes in Computer Science(), vol 3488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11425274_61
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DOI: https://doi.org/10.1007/11425274_61
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