A Maximizing Model of Spherical Bezdek-Type Fuzzy Multi-Medoids Clustering

Yuchi Kanzawa

doi:10.20965/jaciii.2015.p0738

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JACIII Vol.19 No.6 pp. 738-746

doi: 10.20965/jaciii.2015.p0738

(2015)

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A Maximizing Model of Spherical Bezdek-Type Fuzzy Multi-Medoids Clustering

Yuchi Kanzawa

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

Received:

April 27, 2015

Accepted:

July 28, 2015

Published:

November 20, 2015

Keywords:

spherical clustering, multi-medoids, kernelization, spectral clustering

Abstract

This paper proposes three modifications for the maximizing model of spherical Bezdek-type fuzzy c-means clustering (msbFCM). First, we use multi-medoids instead of centroids (msbFMMdd), which is similar to modifying fuzzy c-means to fuzzy multi-medoids. Second, we kernelize msbFMMdd (K-msbFMMdd). msbFMMdd can only be applied to objects in the first quadrant of the unit hypersphere, whereas its kernelized form can be applied to a wider class of objects. The third modification is a spectral clustering approach to K-msbFMMdd using a certain assumption. This approach improves the local convergence problem in the original algorithm. Numerical examples demonstrate that the proposed methods can produce good results for clusters with nonlinear borders when an adequate parameter value is selected.

Cite this article as:

Y. Kanzawa, “A Maximizing Model of Spherical Bezdek-Type Fuzzy Multi-Medoids Clustering,” J. Adv. Comput. Intell. Intell. Inform., Vol.19 No.6, pp. 738-746, 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] J. Mei and L. Chen, “Fuzzy relational clustering around medoids: A unified view,” Fuzzy Sets and Systems, Vol.183, No.1, pp. 44-56, 2011.
[5] R. Krishnapuram, A. Joshi, O. Nasraoui, and L. Yi, “Low-complexity fuzzy relational clustering algorithms for web mining,” IEEE Trans. Fuzzy Syst. Vol.9, No.4, pp. 595-607, 2001.
[6] M. Windham, “Numerical classification of proximity data with assignment measures,” J. of Classification Vol.2, No.1, pp. 157-172, 1985.
[7] I. S. Dhillon and D. S. Modha, “Concept Decompositions for Large Sparse Text Data Using Clustering,” Machine Learning, Vol.42, pp. 143-175, 2001.
[8] S. Miyamoto, H. Ichihashi, and K. Honda, “Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with Applications,” Vol.229, Springer, 2008.
[9] Y. Kanzawa, “A maximizing model of Bezdek-like spherical fuzzy c-means clustering,” Proc. IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE), pp. 2482-2488, 2014.
[10] 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.
[11] R. Krishnapuram and J. M. Keller, “A Possibilistic Approach to Clustering,” IEEE Trans. on Fuzzy Systems, Vol.1, pp. 98-110, 1993.
[12] C. Oh, K. Honda, and H. Ichihashi, “Fuzzy Clustering for Categorical Multivariate Data”, Proc. IFSA World Congress and 20^th NAFIPS Int. Conf., pp. 2154-2159, 2001.

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] J. Mei and L. Chen, “Fuzzy relational clustering around medoids: A unified view,” Fuzzy Sets and Systems, Vol.183, No.1, pp. 44-56, 2011.

[5] [5] R. Krishnapuram, A. Joshi, O. Nasraoui, and L. Yi, “Low-complexity fuzzy relational clustering algorithms for web mining,” IEEE Trans. Fuzzy Syst. Vol.9, No.4, pp. 595-607, 2001.

[6] [6] M. Windham, “Numerical classification of proximity data with assignment measures,” J. of Classification Vol.2, No.1, pp. 157-172, 1985.

[7] [7] I. S. Dhillon and D. S. Modha, “Concept Decompositions for Large Sparse Text Data Using Clustering,” Machine Learning, Vol.42, pp. 143-175, 2001.

[8] [8] S. Miyamoto, H. Ichihashi, and K. Honda, “Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with Applications,” Vol.229, Springer, 2008.

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

[10] [10] 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.

[11] [11] R. Krishnapuram and J. M. Keller, “A Possibilistic Approach to Clustering,” IEEE Trans. on Fuzzy Systems, Vol.1, pp. 98-110, 1993.

[12] [12] C. Oh, K. Honda, and H. Ichihashi, “Fuzzy Clustering for Categorical Multivariate Data”, Proc. IFSA World Congress and 20^th NAFIPS Int. Conf., pp. 2154-2159, 2001.