Power-Regularized Fuzzy Clustering for Spherical Data

Yuchi Kanzawa

doi:10.20965/jaciii.2018.p0163

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JACIII Vol.22 No.2 pp. 163-171

doi: 10.20965/jaciii.2018.p0163

(2018)

Paper:

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Power-Regularized Fuzzy Clustering for Spherical Data

Yuchi Kanzawa

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

Received:

June 30, 2017

Accepted:

November 2, 2017

Published:

March 20, 2018

Keywords:

fuzzy clustering, spherical data, power-regularization

Abstract

In this paper, a power-regularization-based fuzzy clustering method is proposed for spherical data. Power regularization has not been previously applied to fuzzy clustering for spherical data. The proposed method is transformed to the conventional fuzzy clustering method, entropy-regularized fuzzy clustering for spherical data (eFCS), for a specified fuzzification parameter value. Numerical experiments on two artificial datasets reveal the properties of the proposed method. Furthermore, numerical experiments on four real datasets indicate that this method is more accurate than the conventional fuzzy clustering methods: standard fuzzy clustering for spherical data (sFCS) and eFCS.

Cite this article as:

Y. Kanzawa, “Power-Regularized Fuzzy Clustering for Spherical Data,” J. Adv. Comput. Intell. Intell. Inform., Vol.22 No.2, pp. 163-171, 2018.

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References

[1] J. B. MacQueen, “Some Methods of Classification and Analysis of Multivariate Observations,” Proc. 5th Berkeley Symposium on Math. Stat. and Prob., pp. 281-297, 1967.
[2] J. Bezdek, ”Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, 1981.
[3] 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.
[4] S. Miyamoto and K. Umayahara, “Fuzzy Clustering by Quadratic Regularization,” Proc. 1998 IEEE Int. Conf. Fuzzy Syst., pp. 1394-1399, 1998.
[5] Y. Kanzawa, “Generalization of Quadratic Regularized and Standard Fuzzy c-Means Clustering with respect to Regularization of Hard c-Means,” LNCS, Vol.8234, pp. 152-165, 2013.
[6] Y. Kanzawa, “Power-Regularized Fuzzy c-Means Clustering with a Fuzzification Parameter Less than One,” J. Adv. Comput. Intell. Intell. Inform., Vol.20, No.4, pp. 561-570, 2016.
[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,” Springer, 2008.
[9] 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.
[10] L. Hubert and P. Arabie, “Comparing Partitions,” Journal of Classification, Vol.2, pp. 193-218, 1985.
[11] 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.
[12] Y. Kanzawa, “Entropy-regularized Fuzzy Clustering for non-Euclidean Relational Data and for Indefinite Kernel Data,” J. Adv. Comput. Intell. Intell. Inform., Vol.16, No.7, pp. 784-792, 2012.
[13] Y. Kanzawa, “Relational Fuzzy c-means and Kernel Fuzzy c-means Using an Object-wise beta-spread Transformation,” J. Adv. Comput. Intell. Intell. Inform., Vol.17, No.4, pp. 511-519, 2013.
[14] Y. Kanzawa, “Relational Fuzzy c-lines Clustering Derived from Kernelization of Fuzzy c-lines,” J. Adv. Comput. Intell. Intell. Inform., Vol.18, No.2, pp. 175-181, 2014.
[15] 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.
[16] K. Honda, S. Oshio, and A. Notsu, “FCM-type Fuzzy Co-clustering by K-L information regularization,” Proc. of 2014 IEEE Int. Conf. on Fuzzy Systems, pp. 2505-2510, 2014.
[17] K. Honda, S. Oshio, and A. Notsu, “Item Membership Fuzzification in Fuzzy Co-clustering Based on Multinomial Mixture Concept,” Proc. of 2014 IEEE Int. Conf. on Granular Computing, pp. 94-99, 2014.
[18] 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.
[19] Y. Kanzawa, “On Possibilistic Clustering Methods Based on Shannon/Tsallis-Entropy for Spherical Data and Categorical Multivariate Data,” LNCS, Vol.9321, pp. 125-138, 2015.
[20] Y. Kanzawa, “Bezdek-type Fuzzified Co-Clustering Algorithm,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.6, pp. 852-860, 2015.

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. 5th Berkeley Symposium on Math. Stat. and Prob., pp. 281-297, 1967.

[2] [2] J. Bezdek, ”Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, 1981.

[3] [3] 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.

[4] [4] S. Miyamoto and K. Umayahara, “Fuzzy Clustering by Quadratic Regularization,” Proc. 1998 IEEE Int. Conf. Fuzzy Syst., pp. 1394-1399, 1998.

[5] [5] Y. Kanzawa, “Generalization of Quadratic Regularized and Standard Fuzzy c-Means Clustering with respect to Regularization of Hard c-Means,” LNCS, Vol.8234, pp. 152-165, 2013.

[6] [6] Y. Kanzawa, “Power-Regularized Fuzzy c-Means Clustering with a Fuzzification Parameter Less than One,” J. Adv. Comput. Intell. Intell. Inform., Vol.20, No.4, pp. 561-570, 2016.

[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,” Springer, 2008.

[9] [9] 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.

[10] [10] L. Hubert and P. Arabie, “Comparing Partitions,” Journal of Classification, Vol.2, pp. 193-218, 1985.

[11] [11] 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.

[12] [12] Y. Kanzawa, “Entropy-regularized Fuzzy Clustering for non-Euclidean Relational Data and for Indefinite Kernel Data,” J. Adv. Comput. Intell. Intell. Inform., Vol.16, No.7, pp. 784-792, 2012.

[13] [13] Y. Kanzawa, “Relational Fuzzy c-means and Kernel Fuzzy c-means Using an Object-wise beta-spread Transformation,” J. Adv. Comput. Intell. Intell. Inform., Vol.17, No.4, pp. 511-519, 2013.

[14] [14] Y. Kanzawa, “Relational Fuzzy c-lines Clustering Derived from Kernelization of Fuzzy c-lines,” J. Adv. Comput. Intell. Intell. Inform., Vol.18, No.2, pp. 175-181, 2014.

[15] [15] 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.

[16] [16] K. Honda, S. Oshio, and A. Notsu, “FCM-type Fuzzy Co-clustering by K-L information regularization,” Proc. of 2014 IEEE Int. Conf. on Fuzzy Systems, pp. 2505-2510, 2014.

[17] [17] K. Honda, S. Oshio, and A. Notsu, “Item Membership Fuzzification in Fuzzy Co-clustering Based on Multinomial Mixture Concept,” Proc. of 2014 IEEE Int. Conf. on Granular Computing, pp. 94-99, 2014.

[18] [18] 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.

[19] [19] Y. Kanzawa, “On Possibilistic Clustering Methods Based on Shannon/Tsallis-Entropy for Spherical Data and Categorical Multivariate Data,” LNCS, Vol.9321, pp. 125-138, 2015.

[20] [20] Y. Kanzawa, “Bezdek-type Fuzzified Co-Clustering Algorithm,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.6, pp. 852-860, 2015.