Noise Rejection in MMMs-Induced Fuzzy Co-Clustering

Katsuhiro Honda; Nami Yamamoto; Seiki Ubukata; Akira Notsu

doi:10.20965/jaciii.2017.p1144

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JACIII Vol.21 No.7 pp. 1144-1151

doi: 10.20965/jaciii.2017.p1144

(2017)

Paper:

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Noise Rejection in MMMs-Induced Fuzzy Co-Clustering

Katsuhiro Honda, Nami Yamamoto, Seiki Ubukata, and Akira Notsu

Osaka Prefecture University
1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan

Received:

January 10, 2017

Accepted:

July 5, 2017

Published:

November 20, 2017

Keywords:

fuzzy clustering, co-clustering, noise rejection

Abstract

Noise rejection is an important issue in practical application of FCM-type fuzzy clustering, and noise clustering achieves robust estimation of cluster prototypes with an additional noise cluster for dumping noise objects into it. Noise objects having larger distances from all clusters are designed to be assigned to the noise cluster, which is located in an equal (fixed) distance from all objects. Fuzzy co-clustering is an extended version of FCM-type clustering for handling cooccurrence information among objects and items, where the goal of analysis is to extract pair-wise clusters of familiar objects and items. This paper proposes a novel noise rejection model for fuzzy co-clustering induced by multinomial mixture models (MMMs), where a noise cluster is defined with homogeneous item memberships for drawing noise objects having dissimilar cooccurrence features from all general clusters. The noise rejection scheme can be also utilized in selecting the optimal cluster number through a sequential implementation with different cluster numbers.

Cite this article as:

K. Honda, N. Yamamoto, S. Ubukata, and A. Notsu, “Noise Rejection in MMMs-Induced Fuzzy Co-Clustering,” J. Adv. Comput. Intell. Intell. Inform., Vol.21 No.7, pp. 1144-1151, 2017.

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References

[1] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, 1981.
[2] S. Miyamoto, H. Ichihashi, and K. Honda, “Algorithms for Fuzzy Clustering,” Springer, 2008.
[3] J. B. MacQueen, “Some methods of classification and analysis of multivariate observations,” Proc. of 5th Berkeley Sympo. on Math. Stat. and Prob., pp. 281-297, 1967.
[4] R. N. Davé, “Characterization and detection of noise in clustering,” Pattern Recognition Letters, Vol.12, No.11, pp. 657-664, 1991.
[5] R. N. Davé and R. Krishnapuram, “Robust clustering methods: a unified view,” IEEE Trans. on Fuzzy Systems, Vol.5, pp. 270-293, 1997.
[6] C.-H. Oh, K. Honda, and H. Ichihashi, “Fuzzy clustering for categorical multivariate data,” Proc. of Joint 9th IFSA World Congress and 20th NAFIPS Int. Conf., pp. 2154-2159, 2001.
[7] K. Honda, S. Oshio, and A. Notsu, “Fuzzy co-clustering induced by multinomial mixture models,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.6, pp. 717-726, 2015.
[8] L. Rigouste, O. Cappé, and F. Yvon, “Inference and evaluation of the multinomial mixture model for text clustering,” Information Processing and Management, Vol.43, No.5, pp. 1260-1280, 2007.
[9] K. Honda, A. Notsu, and H. Ichihashi, “Fuzzy PCA-guided robust k-means clustering,” IEEE Trans. on Fuzzy Systems, Vol.18, No.1, pp. 67-79, 2010.
[10] R. Krishnapuram and J. M. Keller, “A possibilistic approach to clustering,” IEEE Trans. on Fuzzy Systems, Vol.1, pp. 98-110, 1993.
[11] S. Miyamoto and M. Mukaidono, “Fuzzy c-Means as a regularization and maximum entropy approach,” Proc. of the 7th Int. Fuzzy Systems Association World Congress, Vol.2, pp. 86-92, 1997.
[12] G. Salton and C. Buckley, “Term-weighting approaches in automatic text retrieval,” Information Processing and Management, Vol.24, Issue 5, pp. 513-523, 1988.
[13] W. Wang and Y. Zhang, “On fuzzy cluster validity indices,” Fuzzy Sets and Systems, Vol.158, pp. 2095-2117, 2007.
[14] K. Honda, M. Muranishi, A. Notsu, and H. Ichihashi, “FCM-type cluster validation in fuzzy co-clustering and collaborative filtering applicability,” Int. J. of Computer Science and Network Security,” Vol.13, No.1, pp. 24-29, 2013.
[15] H. Frigui and O. Nasraoui, “Simultaneous categorization of text documents and identification of cluster dependent keywords,” Proc. 2002 IEEE Int. Conf. Fuzzy Systems, Vol.2, pp. 1108-1113, 2002.
[16] K. Kummamuru, A. Dhawale, and R. Krishnapuram, “Fuzzy co-clustering of documents and keywords,” Proc. 2003 IEEE Int. Conf. Fuzzy Systems, Vol.2, pp. 772-777, 2003.

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,” Plenum Press, 1981.

[2] [2] S. Miyamoto, H. Ichihashi, and K. Honda, “Algorithms for Fuzzy Clustering,” Springer, 2008.

[3] [3] J. B. MacQueen, “Some methods of classification and analysis of multivariate observations,” Proc. of 5th Berkeley Sympo. on Math. Stat. and Prob., pp. 281-297, 1967.

[4] [4] R. N. Davé, “Characterization and detection of noise in clustering,” Pattern Recognition Letters, Vol.12, No.11, pp. 657-664, 1991.

[5] [5] R. N. Davé and R. Krishnapuram, “Robust clustering methods: a unified view,” IEEE Trans. on Fuzzy Systems, Vol.5, pp. 270-293, 1997.

[6] [6] C.-H. Oh, K. Honda, and H. Ichihashi, “Fuzzy clustering for categorical multivariate data,” Proc. of Joint 9th IFSA World Congress and 20th NAFIPS Int. Conf., pp. 2154-2159, 2001.

[7] [7] K. Honda, S. Oshio, and A. Notsu, “Fuzzy co-clustering induced by multinomial mixture models,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.6, pp. 717-726, 2015.

[8] [8] L. Rigouste, O. Cappé, and F. Yvon, “Inference and evaluation of the multinomial mixture model for text clustering,” Information Processing and Management, Vol.43, No.5, pp. 1260-1280, 2007.

[9] [9] K. Honda, A. Notsu, and H. Ichihashi, “Fuzzy PCA-guided robust k-means clustering,” IEEE Trans. on Fuzzy Systems, Vol.18, No.1, pp. 67-79, 2010.

[10] [10] R. Krishnapuram and J. M. Keller, “A possibilistic approach to clustering,” IEEE Trans. on Fuzzy Systems, Vol.1, pp. 98-110, 1993.

[11] [11] S. Miyamoto and M. Mukaidono, “Fuzzy c-Means as a regularization and maximum entropy approach,” Proc. of the 7th Int. Fuzzy Systems Association World Congress, Vol.2, pp. 86-92, 1997.

[12] [12] G. Salton and C. Buckley, “Term-weighting approaches in automatic text retrieval,” Information Processing and Management, Vol.24, Issue 5, pp. 513-523, 1988.

[13] [13] W. Wang and Y. Zhang, “On fuzzy cluster validity indices,” Fuzzy Sets and Systems, Vol.158, pp. 2095-2117, 2007.

[14] [14] K. Honda, M. Muranishi, A. Notsu, and H. Ichihashi, “FCM-type cluster validation in fuzzy co-clustering and collaborative filtering applicability,” Int. J. of Computer Science and Network Security,” Vol.13, No.1, pp. 24-29, 2013.

[15] [15] H. Frigui and O. Nasraoui, “Simultaneous categorization of text documents and identification of cluster dependent keywords,” Proc. 2002 IEEE Int. Conf. Fuzzy Systems, Vol.2, pp. 1108-1113, 2002.

[16] [16] K. Kummamuru, A. Dhawale, and R. Krishnapuram, “Fuzzy co-clustering of documents and keywords,” Proc. 2003 IEEE Int. Conf. Fuzzy Systems, Vol.2, pp. 772-777, 2003.