Fuzzy Co-Clustering   Algorithms   Based on Fuzzy Relational Clustering and TIBA Imputation

Yuchi Kanzawa

doi:10.20965/jaciii.2014.p0182

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JACIII Vol.18 No.2 pp. 182-189

doi: 10.20965/jaciii.2014.p0182

(2014)

Paper:

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Fuzzy Co-Clustering Algorithms Based on Fuzzy Relational Clustering and TIBA Imputation

Yuchi Kanzawa

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

Received:

October 1, 2013

Accepted:

January 13, 2014

Published:

March 20, 2014

Keywords:

fuzzy co-clustering, fuzzy clustering for entropy-regularized fuzzy nonmetric model, entropyregularized relational fuzzy c-means, TIBA

Abstract

In this paper, two types of fuzzy co-clustering algorithms are proposed. First, it is shown that the base of the objective function for the conventional fuzzy co-clustering method is very similar to the base for entropy-regularized fuzzy nonmetric model. Next, it is shown that the non-sense clustering problem in the conventional fuzzy co-clustering algorithms is identical to that in fuzzy nonmetric model algorithms, in the case that all dissimilarities among rows and columns are zero. Based on this discussion, a method is proposed applying entropy-regularized fuzzy nonmetric model after all dissimilarities among rows and columns are set to some values using a TIBA imputation technique. Furthermore, since relational fuzzy cmeans is similar to fuzzy nonmetricmodel, in the sense that both methods are designed for homogeneous relational data, a method is proposed applying entropyregularized relational fuzzy c-means after imputing all dissimilarities among rows and columns with TIBA. Some numerical examples are presented for the proposed methods.

Cite this article as:

Y. Kanzawa, “Fuzzy Co-Clustering Algorithms Based on Fuzzy Relational Clustering and TIBA Imputation,” J. Adv. Comput. Intell. Intell. Inform., Vol.18 No.2, pp. 182-189, 2014.

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References

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[2] S. Miyamoto and K. Umayahara, “Methods in Hard and Fuzzy Clustering,” in: Z.-Q. Liu and S. Miyamoto (Eds.), Soft computing and human-centered machines, Springer-Verlag Tokyo, 2000.
[3] M. Roubens, “Pattern Classification Problems and Fuzzy Sets,” Fuzzy Sets and System, Vol.1, pp. 239-253, 1978.
[4] R. J. Hathaway, J. W. Davenport, and J. C. Bezdek, “Relational Duals of the c-means Clustering Algorithms,” Pattern Recognition, Vol.22, No.2, pp. 205-212, 1989.
[5] Y. Endo, “On Entropy Based Fuzzy NonMetric Model,” Proc. SCIS & ISIS 2010, pp. 406-409, 2010.
[6] M. Filippone, “Dealing with Non-Metric Dissimilarity in Fuzzy Central Clustering Algorithm,” Int. J. Approx. Reasoning, Vol.50, No.2, pp. 363-384, 2009.
[7] C. Oh, K. Honda, and H. Ichihashi, “Fuzzy Clustering for Categorical Multivariate Data,” Proc. IFSA World Congress and 20th NAFIPS Int. Conf., pp. 2154-2159, 2001.
[8] J. W. Davenport and J. C. Bezdek, “Clustering Incomplete Relational Data Using the Non-Euclidean Relational Fuzzy c-means Algorithm,” Pattern Recognition Letters, Vol.23, pp. 151-160, 2002.
[9] M. J. Barber, “Modurality and Community Detection in Bipartite Networks,” Phys. Rev., Vol.E76, 066102, 2007.
[10] A. Davis, B. B. Gardner, and M. R. Gardner, “Deep South,” University of Chicago Press, 1941.
[11] T. K. Landauer and S. T. Dumais, “The latent semantic analysis theory of acquisition, induction and representation of knowledge,” Psychol. Rev., Vol.104, No.2, pp. 211-240, 1997.
[12] G. Ghosh, A. Strehl, and S. Merugu, “A Consensus Framework for Integrating Distributed Clusterings under Limited Knowledge Sharing,” Proc. NSFWorkshop on Next Generation DataMining, pp. 99-108, 2002.
[13] J. C. Bezdek, R. J. Hathaway, and J. M. Huband, “Visual Assessment of Clustering Tendency for Rectangular Dissimilarity Matrices,” IEEE Trans. on Fuzzy Systems, Vol.15, No.5, pp. 890-903, 2007.

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

[1] [1] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenun, New York, 1981.

[2] [2] S. Miyamoto and K. Umayahara, “Methods in Hard and Fuzzy Clustering,” in: Z.-Q. Liu and S. Miyamoto (Eds.), Soft computing and human-centered machines, Springer-Verlag Tokyo, 2000.

[3] [3] M. Roubens, “Pattern Classification Problems and Fuzzy Sets,” Fuzzy Sets and System, Vol.1, pp. 239-253, 1978.

[4] [4] R. J. Hathaway, J. W. Davenport, and J. C. Bezdek, “Relational Duals of the c-means Clustering Algorithms,” Pattern Recognition, Vol.22, No.2, pp. 205-212, 1989.

[5] [5] Y. Endo, “On Entropy Based Fuzzy NonMetric Model,” Proc. SCIS & ISIS 2010, pp. 406-409, 2010.

[6] [6] M. Filippone, “Dealing with Non-Metric Dissimilarity in Fuzzy Central Clustering Algorithm,” Int. J. Approx. Reasoning, Vol.50, No.2, pp. 363-384, 2009.

[7] [7] C. Oh, K. Honda, and H. Ichihashi, “Fuzzy Clustering for Categorical Multivariate Data,” Proc. IFSA World Congress and 20th NAFIPS Int. Conf., pp. 2154-2159, 2001.

[8] [8] J. W. Davenport and J. C. Bezdek, “Clustering Incomplete Relational Data Using the Non-Euclidean Relational Fuzzy c-means Algorithm,” Pattern Recognition Letters, Vol.23, pp. 151-160, 2002.

[9] [9] M. J. Barber, “Modurality and Community Detection in Bipartite Networks,” Phys. Rev., Vol.E76, 066102, 2007.

[10] [10] A. Davis, B. B. Gardner, and M. R. Gardner, “Deep South,” University of Chicago Press, 1941.

[11] [11] T. K. Landauer and S. T. Dumais, “The latent semantic analysis theory of acquisition, induction and representation of knowledge,” Psychol. Rev., Vol.104, No.2, pp. 211-240, 1997.

[12] [12] G. Ghosh, A. Strehl, and S. Merugu, “A Consensus Framework for Integrating Distributed Clusterings under Limited Knowledge Sharing,” Proc. NSFWorkshop on Next Generation DataMining, pp. 99-108, 2002.

[13] [13] J. C. Bezdek, R. J. Hathaway, and J. M. Huband, “Visual Assessment of Clustering Tendency for Rectangular Dissimilarity Matrices,” IEEE Trans. on Fuzzy Systems, Vol.15, No.5, pp. 890-903, 2007.