On Objective-Based Rough Clustering with Fuzzy-Set Representation

Naohiko Kinoshita; Yasunori Endo; Ken Onishi

doi:10.20965/jaciii.2015.p0632

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JACIII Vol.19 No.5 pp. 632-638

doi: 10.20965/jaciii.2015.p0632

(2015)

Paper:

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On Objective-Based Rough Clustering with Fuzzy-Set Representation

Naohiko Kinoshita^, Yasunori Endo^, and Ken Onishi^

^*Graduate School of Systems and Information Engineering, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

^**Faculty of Engineering, Information and Systems, University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573 Japan

^***Toyota Motor Corporation
1 Toyota-Cho, Toyota, Aichi 471-8571, Japan

Received:

January 31, 2015

Accepted:

June 16, 2015

Published:

September 20, 2015

Keywords:

clustering, rough clustering, optimization, fuzzy set

Abstract

The rough clustering algorithm we proposed based on the optimization of objective function (RCM) has a problem because conventional rough clustering algorithm results do not ensure that solutions are optimal. To solve this problem, we propose rough clustering algorithms based on optimization of an objective function with fuzzy-set representation. This yields more flexible results than RCM. We verify algorithm effectiveness through numerical examples.

Cite this article as:

N. Kinoshita, Y. Endo, and K. Onishi, “On Objective-Based Rough Clustering with Fuzzy-Set Representation,” J. Adv. Comput. Intell. Intell. Inform., Vol.19 No.5, pp. 632-638, 2015.

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References

[1] S. Miyamoto, “Introduction to Cluster Analysis,” Morikita-Shuppan, Tokyo, 1999. (in Japanese)
[2] P. Lingras and G. Peters, “Rough clustering,” WIREs Data Mining and Knowledge Discovery, Vol.1, Issue 1, pp. 64-72, 2011.
[3] Z. Pawlak, “Rough Sets,” Int. J. of Computer and Information Sciences, Vol.11, No.5, pp. 341-356, 1982.
[4] P. Lingrs and C. West, “Interval Set Clustering of Web Users with Rough K-Means,” J. of Intelligent Information Systems, Vol.23, No.1, pp. 5-16, 2004.
[5] P. Maji and S. K. Pal, “Rough Set based Generalized Fuzzy C-Means Algorithm and Quantitative Indices,” IEEE Trans. on Systems, Man, and Cybernetics – Part B: Cybernetics, Vol.37, No.6, pp. 1529-1540, 2007.
[6] G. Peters, “Outliers in Rough k-Means Clustering,” Proc. PReMI 2005, LNCS 3776, pp. 702-707, 2005.
[7] S. Mitra, H. Banka, and W. Pedrycz, “Rough-Fuzzy Collaborative Clustering,” IEEE Trans. on Systems, Man, and Cybernetics - Part B: Cybernetics, Vol.36, No.4, pp. 795-805, 2006.
[8] S. Mitra, “An evolutionary rough partitive clustering,” Pattern Recognition Letters, Vol.25, No.12, pp. 1439-1449, 2004.
[9] S. Mitra and B. Barman, “Rough-Fuzzy Clustering: An Application to Medical Imagery,” Proc. RKST 2008, LNAI 5009, pp. 300-307, 2008.
[10] S. Hirano and S. Tsumoto, “An Indiscernibility-Based Clustering Method with Iterative Refinement of Equivalence Relations – Rough Clustering –,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.7, No.2, pp. 169-177, 2003.
[11] Y. Endo, A. Heki, and Y. Hamasuna, “Non Metric Model Based on Rough Set Representation,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.17, No.4, pp. 540-551, 2013.
[12] Y. Endo and N. Kinoshita, “On Objective-Based Rough c-Means Clustering,” Int. J. of Intelligent Systems, Vol.28, Issue 9, pp. 907-925, 2013.
[13] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, pp. 338-353, 1965.
[14] J. MacQueen, “Some methods for classification and analysis of multivariate observations,” Proc. of the 5^th Berkeley Symp. on Mathematical Statistics and Probability, Vol.1, pp. 281-297, 1967.
[15] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, New York, 1981.

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

[1] [1] S. Miyamoto, “Introduction to Cluster Analysis,” Morikita-Shuppan, Tokyo, 1999. (in Japanese)

[2] [2] P. Lingras and G. Peters, “Rough clustering,” WIREs Data Mining and Knowledge Discovery, Vol.1, Issue 1, pp. 64-72, 2011.

[3] [3] Z. Pawlak, “Rough Sets,” Int. J. of Computer and Information Sciences, Vol.11, No.5, pp. 341-356, 1982.

[4] [4] P. Lingrs and C. West, “Interval Set Clustering of Web Users with Rough K-Means,” J. of Intelligent Information Systems, Vol.23, No.1, pp. 5-16, 2004.

[5] [5] P. Maji and S. K. Pal, “Rough Set based Generalized Fuzzy C-Means Algorithm and Quantitative Indices,” IEEE Trans. on Systems, Man, and Cybernetics – Part B: Cybernetics, Vol.37, No.6, pp. 1529-1540, 2007.

[6] [6] G. Peters, “Outliers in Rough k-Means Clustering,” Proc. PReMI 2005, LNCS 3776, pp. 702-707, 2005.

[7] [7] S. Mitra, H. Banka, and W. Pedrycz, “Rough-Fuzzy Collaborative Clustering,” IEEE Trans. on Systems, Man, and Cybernetics - Part B: Cybernetics, Vol.36, No.4, pp. 795-805, 2006.

[8] [8] S. Mitra, “An evolutionary rough partitive clustering,” Pattern Recognition Letters, Vol.25, No.12, pp. 1439-1449, 2004.

[9] [9] S. Mitra and B. Barman, “Rough-Fuzzy Clustering: An Application to Medical Imagery,” Proc. RKST 2008, LNAI 5009, pp. 300-307, 2008.

[10] [10] S. Hirano and S. Tsumoto, “An Indiscernibility-Based Clustering Method with Iterative Refinement of Equivalence Relations – Rough Clustering –,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.7, No.2, pp. 169-177, 2003.

[11] [11] Y. Endo, A. Heki, and Y. Hamasuna, “Non Metric Model Based on Rough Set Representation,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.17, No.4, pp. 540-551, 2013.

[12] [12] Y. Endo and N. Kinoshita, “On Objective-Based Rough c-Means Clustering,” Int. J. of Intelligent Systems, Vol.28, Issue 9, pp. 907-925, 2013.

[13] [13] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, pp. 338-353, 1965.

[14] [14] J. MacQueen, “Some methods for classification and analysis of multivariate observations,” Proc. of the 5^th Berkeley Symp. on Mathematical Statistics and Probability, Vol.1, pp. 281-297, 1967.

[15] [15] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, New York, 1981.

On Objective-Based Rough Clustering with Fuzzy-Set Representation

Naohiko Kinoshita*, Yasunori Endo**, and Ken Onishi***

Naohiko Kinoshita^, Yasunori Endo^, and Ken Onishi^