The K-Exemplars Clustering Method

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In order to apply the concepts of k-means to deal with any specified dissimilarity measures, we propose a k-exemplars clustering method that modifies k-means by restricting the cluster centers on data points. The proposed method not only has similar clustering accuracy as k-means but also faster convergence. According to the definition of the objective function of k-exemplars, the proposed method can be used to deal with a relational data set, and the cluster centers (exemplars) of each cluster will also be extracted. Hence, the k-exemplars can work in an environment with specified dissimilarity measures.

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224-230

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August 2013

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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[1] J. MacQueen, Some methods for classification and analysis of multivariate observations, in: Proc. of 5th Berkeley Symposium, vol. 1, 1967, pp.281-297.

Google Scholar

[2] A.K. Jain, Data clustering: 50 years beyond k-means, Pattern Recog. Lett. 31 (2010) 651-666.

DOI: 10.1016/j.patrec.2009.09.011

Google Scholar

[3] J. Mao, A.K. Jain, A self-organizing network for hyper-ellipsoidal clustering (HEC). IEEE Trans. Neural Networks 7 (January 1996), 16-29.

DOI: 10.1109/72.478389

Google Scholar

[4] Y. Linde, A. Buzo, R. Gray, An algorithm for vector quantizer design. IEEE Trans. Comm. 28 (1980) 84-94.

DOI: 10.1109/tcom.1980.1094577

Google Scholar

[5] H. Kashima, J. Hu, B. Ray, M. Singh, K-means clustering of proportional data using L1 distance, in: Proc. Internat. Conf. on Pattern Recognition, 2008, pp.1-4.

DOI: 10.1109/icpr.2008.4760982

Google Scholar

[6] A. Banerjee, S. Merugu, I.S. Dhillon, J. Ghosh, Clustering with Bregman divergences, J. Mach. Learn. Res. 6 (2005) 1705-1749.

Google Scholar

[7] K.L. Wu, M.S. Yang, Alternative c-means clustering algorithms, Pattern Recog. 35 (2002) 2267-2278.

Google Scholar

[8] Z.X. Huang, Extensions to the k-means algorithm for clustering large data set with categorical values, Data Mining Knowl. Discov. 2 (1998) 283-304.

Google Scholar

[9] S. Lloyd, Least squares quantization in PCM, Bell Telephone Laboratories Papers, Marray Hill, (1957).

Google Scholar

[10] D. Pollard, Strong consistency of k-means clustering, Annal. Statistics 9 (1981) 135-140.

Google Scholar

[11] S.Z. Selim, M.A. Ismail, K-means-type algorithms: a generalized convergence theorem and characterization of local optimality, IEEE Trans. Pattern Anal. Mach. Intell. 6 (1999) 81-86.

DOI: 10.1109/tpami.1984.4767478

Google Scholar

[12] D. Pollard, A central limit theorem for k-means clustering, Ann. Probabil. 10 (1982) 919-926.

Google Scholar

[13] J. Yu, General c-means clustering model, IEEE Trans. Pattern Anal. Mach. Intell. 27 (2005) 1197-1211.

DOI: 10.1109/tpami.2005.160

Google Scholar

[14] W.M. Rand, Objective criteria for the evaluation of clustering methods, J. Am. Statistical Assoc. 66 (1971) 846-850.

Google Scholar

[15] E. Anderson, The Irises of the gaspe peninsula, Bull. Am. IRIS Soc. 59 (1935) 2-5.

Google Scholar

[16] J.C. Bezdek, J.M. Keller, R. Krishnapuram, L.I. Kuncheva, N.R. Pal, Will the Iris data please stand up? IEEE Trans. Fuzzy Syst. 7 (1999) 368-369.

DOI: 10.1109/91.771092

Google Scholar

[17] K. Pal, N.R. Pal, J.M. Keller, J.C. Bezdek, Relational mountain (density) clustering method and web log analysis, Int. J. Intell. Syst. 20 (2005) 375-392.

DOI: 10.1002/int.20071

Google Scholar

[18] C.M. Hwang, M.S. Yang, W.L. Hung, M.G. Lee, A similarity measure of intuitionistic fuzzy sets based on Sugeno integral with its application to pattern recognition, Inf. Sci. 189 (2012) 93-109.

DOI: 10.1016/j.ins.2011.11.029

Google Scholar

[19] M.S. Yang, H.M. Shih, Cluster analysis based on fuzzy relations, Fuzzy Sets Syst. 120 (2001) 197-212.

DOI: 10.1016/s0165-0114(99)00146-3

Google Scholar