Bezdek-Type Fuzzified Co-Clustering Algorithm

Yuchi Kanzawa

doi:10.20965/jaciii.2015.p0852

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JACIII Vol.19 No.6 pp. 852-860

doi: 10.20965/jaciii.2015.p0852

(2015)

Paper:

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Bezdek-Type Fuzzified Co-Clustering Algorithm

Yuchi Kanzawa

Shibaura Institute of Technology
3-7-5 Toyosu, Koto, Tokyo 135-8548, Japan

Received:

May 20, 2015

Accepted:

August 20, 2015

Published:

November 20, 2015

Keywords:

fuzzy co-clustering, Bezdek-type fuzzification, spectral clustering

Abstract

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.

Cite this article as:

Y. Kanzawa, “Bezdek-Type Fuzzified Co-Clustering Algorithm,” J. Adv. Comput. Intell. Intell. Inform., Vol.19 No.6, pp. 852-860, 2015.

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References

[1] J. B. MacQueen, “Some Methods of Classification and Analysis of Multivariate Observations,” Proc. 5^th Berkeley Symp. on Math. Stat. and Prob., pp. 281-297, 1967.
[2] 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.
[3] J. Bezdek, “Pattern recognition with fuzzy objective function algorithms,” Kluwer Academic Publishers, 1981.
[4] S. Miyamoto and M. Mukaidono, “Fuzzy c-Means as a Regularization and Maximum Entropy Approach,” Proc. 7^th Int. Fuzzy Systems Association World Congress (IFSA’97), Vol.2, pp. 86-92, 1997.
[5] 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 20^th NAFIPS Int. Conf., pp. 2154-2159, 2001.
[6] K. Kummamuru, A. Dhawaie, and R. Krishnapuram, “Fuzzy co-clustering of document and keywords,” Proc. of FUZZ-IEEE 2003, pp. 772-777, 2003.
[7] Y. Kanzawa and Y. Endo, “On FNM-based and RFCM-based Fuzzy Co-Clustering Algorithms,” Proc. of WCCI2012, 2012.
[8] 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.
[9] Y. Kanzawa, “A maximizing model of Bezdek-like spherical fuzzy c-means clustering,” Proc. of FUZZ-IEEE 2014, pp. 2482-2488, 2014.
[10] M. J. Barber, “Modurality and Community Detection in Bipartite Networks,” Phys. Rev., E76, 066102, 2007.
[11] A. Davis, B. B. Gardner, and M. R. Gardner, “Deep South,” University of Chicago Press, 1941.
[12] 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.
[13] 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.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] J. B. MacQueen, “Some Methods of Classification and Analysis of Multivariate Observations,” Proc. 5^th Berkeley Symp. on Math. Stat. and Prob., pp. 281-297, 1967.

[2] [2] 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.

[3] [3] J. Bezdek, “Pattern recognition with fuzzy objective function algorithms,” Kluwer Academic Publishers, 1981.

[4] [4] S. Miyamoto and M. Mukaidono, “Fuzzy c-Means as a Regularization and Maximum Entropy Approach,” Proc. 7^th Int. Fuzzy Systems Association World Congress (IFSA’97), Vol.2, pp. 86-92, 1997.

[5] [5] 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 20^th NAFIPS Int. Conf., pp. 2154-2159, 2001.

[6] [6] K. Kummamuru, A. Dhawaie, and R. Krishnapuram, “Fuzzy co-clustering of document and keywords,” Proc. of FUZZ-IEEE 2003, pp. 772-777, 2003.

[7] [7] Y. Kanzawa and Y. Endo, “On FNM-based and RFCM-based Fuzzy Co-Clustering Algorithms,” Proc. of WCCI2012, 2012.

[8] [8] 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.

[9] [9] Y. Kanzawa, “A maximizing model of Bezdek-like spherical fuzzy c-means clustering,” Proc. of FUZZ-IEEE 2014, pp. 2482-2488, 2014.

[10] [10] M. J. Barber, “Modurality and Community Detection in Bipartite Networks,” Phys. Rev., E76, 066102, 2007.

[11] [11] A. Davis, B. B. Gardner, and M. R. Gardner, “Deep South,” University of Chicago Press, 1941.

[12] [12] 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.

[13] [13] 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.