Abstract
Cluster validity indices have been used to evaluate the quality of fuzzy partitions. In this paper, we propose a new index, which uses concepts of Fuzzy Rough sets to evaluate the average intra-cluster similarity of fuzzy clusters produced by the fuzzy c-means algorithm. Experimental results show that contrasted with several well-known cluster validity indices, the proposed index can yield more desirable cluster number estimation.
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References
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)
Xie, X.L., Beni, G.: A validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell 13(8), 841–847 (1991)
Fukuyama, Y., Sugeno, M.: A new method of choosing the number of clusters for the fuzzy c-mean method. In: 5th Fuzzy Systems Symposium, Japan, pp. 247–250 (1989)
Pal, N.R., Bezdek, J.C.: On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Syst. 13(3), 370–379 (1995)
Kwon, S.H.: Cluster validity index for fuzzy clustering. Electron. Lett 34(22), 2176–2177 (1998)
Kim, D., Lee, K.H., Lee, D.: On cluster validity index for estimation of the optimal number of fuzzy clusters. Pattern Recognition 37(10), 2561–2574 (2004)
Kim, Y., Kim, D., et al.: A cluster validation index for GK cluster analysis based on relative degree of sharing. Information Science 168(1-4), 225–242 (2004)
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Internat. J. General Systems 17(2–3), 191–209 (1990)
Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 203–222. Kluwer, The Netherlands (1992)
Pawlak, Z.: Rough sets. International J. Comp. Inform. Science 11, 341–356 (1982)
Pawlak, Z.: Some Issues on Rough Sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 1–58. Springer, Heidelberg (2004)
Morsi, N.N., Yakout, M.M.: Axiomatics for fuzzy rough set. Fuzzy Sets Syst. 100(1-3), 327–342 (1998)
Mitra, S., Banka, H., Pedrycz, W.: Rough-fuzzy collaborative clustering. IEEE Trans. Syst., Man, Cybern. B, Cybern. 36(4), 795–805 (2006)
Bezdek, J.C., Pal, N.R.: Some New Indexes of Cluster Validity. IEEE Trans. Syst., Man, Cybern. B, Cybern. 28(3), 301–315 (1998)
Lingras, P., Yan, R., West, C.: Comparison of conventional and rough k-means clustering. In: Wang, G., et al. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 130–137. Springer, Heidelberg (2003)
UCI Repository of machine learning databases, http://www.ics.uci.edu/~mlearn/MLRepository.html
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Li, F., Min, F., Liu, Q. (2008). Intra-cluster Similarity Index Based on Fuzzy Rough Sets for Fuzzy C-Means Algorithm. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2008. Lecture Notes in Computer Science(), vol 5009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79721-0_45
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DOI: https://doi.org/10.1007/978-3-540-79721-0_45
Publisher Name: Springer, Berlin, Heidelberg
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