Abstract
Five papers have appeared in the last three years that propose different fuzzy generalizations of Rand’s classical comparison index for crisp clustering algorithms. We review the five generalizations, compare their complexities, and then give two numerical examples to compare their performance. Our extension (for the pairwise agreements) is O(n), while the other four generalizations are O(n2).
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Bezdek, J.C., Keller, J.M., Krishnapuram, R., Pal, N.R.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer, Norwell (1999)
Jain, A., Dubes, R.: Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs (1988)
Theodoridis, S., Koutroumbas, K.: Pattern Recognition, 4th edn. Academic Press, NY (2006)
Hoppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis. Wiley and Sons, Chichester (1999)
Rand, W.M.: Objective criteria for the evaluation of clustering methods. JASA 66(336), 846–850 (1971)
Hubert, L.J., Arabie, P.: Comparing partitions. J. Classification 2, 193–218 (1985)
Sneath, P.H.A., Sokal, R.R.: Numerical Taxonomy - The Principles and Practice of Numerical Classification. W. H. Freeman, San Francisco (1973)
Sokal, R.R., Michener, C.D.: A Statistical Method for Evaluating Systematic Relationships. The University of Kansas Scientific Bulletin 38, 1409–1438 (1958)
Duan, F., Zhang, H.: Correcting the loss of cell-cycle synchrony in clustering analysis of microarray data using weights. Bioinformatics 20(11), 1766–1771 (2004)
Thalamuthu, A., Mukhopadhyay, I., Zheng, X., Tseng, G.: Evaluation and comparison of gene clustering methods in microarray analysis. Bioinformatics 22(19), 2405–2412 (2006)
Wong, D.S.V., Wong, F.K., Wood, G.R.: A multi-stage approach to clustering and imputation of gene expression profiles. Bioinformatics 23(8), 998–1005 (2007)
Yu, Z., Wong, H.S., Wang, H.: Graph-based consensus clustering for class discovery from gene expression data. Bioinformatics 23(21), 2888–2896 (2007)
Campello, R.J.G.B.: A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Patt. Recog. Letters 28, 833–841 (2007)
Frigui, H., Hwang, C., Rhee, F.: Clustering and aggregation of relational data with applications to image database categorization. Pattern Recognition (40), 3053–3068 (2007)
Brower, R.K.: Extending the Rand, adjusted Rand, and Jaccard indices to fuzzy partitions. J. Intell. Inf. Systems 32, 213–235 (2009)
Hullermeier, E., Rifqi, M.: A fuzzy variant of the Rand index for comparing clustering structures. In: Proc. IFSA, Lisbon, Portugal, pp. 1–6 (2009)
Anderson, D., Bezdek, J.C., Keller, J.M., Popescu, M.: Comparing soft partitions. IEEE Trans. Fuzzy Systems (2010) (in review)
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Anderson, D.T., Bezdek, J.C., Keller, J.M., Popescu, M. (2010). A Comparison of Five Fuzzy Rand Indices. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_46
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DOI: https://doi.org/10.1007/978-3-642-14055-6_46
Publisher Name: Springer, Berlin, Heidelberg
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