Bezdek-Type Fuzzified Co-Clustering Algorithm
Shibaura Institute of Technology
3-7-5 Toyosu, Koto, Tokyo 135-8548, Japan
In this study, two co-clustering algorithms based on Bezdek-type fuzzification of fuzzy clustering are proposed for categorical multivariate data. The two proposed algorithms are motivated by the fact that there are only two fuzzy co-clustering methods currently available – entropy regularization and quadratic regularization – whereas there are three fuzzy clustering methods for vectorial data: entropy regularization, quadratic regularization, and Bezdek-type fuzzification. The first proposed algorithm forms the basis of the second algorithm. The first algorithm is a variant of a spherical clustering method, with the kernelization of a maximizing model of Bezdek-type fuzzy clustering with multi-medoids. By interpreting the first algorithm in this way, the second algorithm, a spectral clustering approach, is obtained. Numerical examples demonstrate that the proposed algorithms can produce satisfactory results when suitable parameter values are selected.
-  J. B. MacQueen, “Some Methods of Classification and Analysis of Multivariate Observations,” Proc. 5th Berkeley Symp. on Math. Stat. and Prob., pp. 281-297, 1967.
-  J. Dunn, “A Fuzzy Relative of the Isodata Process and Its Use in Detecting Compact, Well-Separated Clusters,” J. of Cybernetics, Vol.3, No.3, pp. 32-57, 1973.
-  J. Bezdek, “Pattern recognition with fuzzy objective function algorithms,” Kluwer Academic Publishers, 1981.
-  S. Miyamoto and M. Mukaidono, “Fuzzy c-Means as a Regularization and Maximum Entropy Approach,” Proc. 7th Int. Fuzzy Systems Association World Congress (IFSA’97), Vol.2, pp. 86-92, 1997.
-  S. Miyamoto and K. Umayahara, “Fuzzy clustering by quadratic regularization,” Proc. 1998 IEEE Int. Conf. Fuzzy Syst., pp. 1394-1399, 1998. bibitemeFCCM-honda C. Oh, K. Honda, and H. Ichihashi, “Fuzzy clustering for categorical multivariate Data,” Proc. of IFSA World Congress and 20th NAFIPS Int. Conf., pp. 2154-2159, 2001.
-  K. Kummamuru, A. Dhawaie, and R. Krishnapuram, “Fuzzy co-clustering of document and keywords,” Proc. of FUZZ-IEEE 2003, pp. 772-777, 2003.
-  Y. Kanzawa and Y. Endo, “On FNM-based and RFCM-based Fuzzy Co-Clustering Algorithms,” Proc. of WCCI2012, 2012.
-  Y. Kanzawa, “A maximizing model of spherical Bezdek-type possibilistic c-means and fuzzy multi-medoids clustering,” Proc. of IEEE GrC2014, pp. 121-126, 2014.
-  Y. Kanzawa, “A maximizing model of Bezdek-like spherical fuzzy c-means clustering,” Proc. of FUZZ-IEEE 2014, pp. 2482-2488, 2014.
-  M. J. Barber, “Modurality and Community Detection in Bipartite Networks,” Phys. Rev., E76, 066102, 2007.
-  A. Davis, B. B. Gardner, and M. R. Gardner, “Deep South,” University of Chicago Press, 1941.
-  A. Banerjee, I. S. Dhillon, J. Ghosh, and S. Sra, “Clustering on the Unit Hypersphere using von Mises-Fisher Distributions,” J. of Machine Learning Research, Vol.6, pp. 1345-1382, 2005.
-  G. Ghosh, A. Strehl, and S. Merugu, “A Consensus framework for integrating distributed clusterings under limited knowledge sharing,” Proc. of NSF Workshop on Next Generation Data Mining, pp. 99-108, 2002.