On Fuzzy c-Means for Data with Tolerance

Ryuichi Murata; Yasunori Endo; Hideyuki Haruyama; Sadaaki Miyamoto

doi:10.20965/jaciii.2006.p0673

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JACIII Vol.10 No.5 pp. 673-681

doi: 10.20965/jaciii.2006.p0673

(2006)

Paper:

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On Fuzzy c-Means for Data with Tolerance

Ryuichi Murata, Yasunori Endo, Hideyuki Haruyama, and Sadaaki Miyamoto

University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan

Received:

January 1, 2006

Accepted:

April 15, 2006

Published:

September 20, 2006

Keywords:

fuzzy c-means, tolerance, optimization problem

Abstract

This paper presents two new clustering algorithms which are based on the entropy regularized fuzzy c-means and can treat data with some errors. First, the tolerance is formulated and introduce into optimization problems of clustering. Next, the problems are solved using Kuhn-Tucker conditions. Last, the algorithms are constructed based on the results of solving the problems.

Cite this article as:

R. Murata, Y. Endo, H. Haruyama, and S. Miyamoto, “On Fuzzy c-Means for Data with Tolerance,” J. Adv. Comput. Intell. Intell. Inform., Vol.10 No.5, pp. 673-681, 2006.

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References

[1] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, New York, 1981.
[2] Y. Endo, “Clustering Algorithm Using Covariance for Fuzzy Data,”In Proc. 1998 International Symposium on Nonlinear Theory and Its Applications, pp. 511-514, 1998.
[3] Y. Endo and K. Horiuchi, “On Clustering Algorithm for Fuzzy Data,” In Proc. 1997 International Symposium on Nonlinear Theory and Its Applications, pp. 381-384, 1997.
[4] R.-P. Li and M. Mukaidono, “A maximum entropy approach to fuzzy clustering,” In Proc. of the 4th IEEE Intern. Conf. on Fuzzy Systems (FUZZ-IEEE/IFES’95), pp. 2227-2232, Japan, March, 1995.
[5] Z.-Q. Liu and S. Miyamoto (eds.), “Soft computing and humancentered machines,” pp. 85-129, Springer-Verlag Tokyo, Japan, 2000.
[6] S. Miyamoto and M. Mukaidono, “Fuzzy c-means as a regularization and maximum entropy approach,” In Proc. of the 7th International Fuzzy Systems Association World Congress (IFES’97), volume II, pp. 86-92, Prague, June, 1997.
[7] N. Wu, “The maximum entropy method,” Springer-Verlag, Berlin, 1997.

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, New York, 1981.

[2] [2] Y. Endo, “Clustering Algorithm Using Covariance for Fuzzy Data,”In Proc. 1998 International Symposium on Nonlinear Theory and Its Applications, pp. 511-514, 1998.

[3] [3] Y. Endo and K. Horiuchi, “On Clustering Algorithm for Fuzzy Data,” In Proc. 1997 International Symposium on Nonlinear Theory and Its Applications, pp. 381-384, 1997.

[4] [4] R.-P. Li and M. Mukaidono, “A maximum entropy approach to fuzzy clustering,” In Proc. of the 4th IEEE Intern. Conf. on Fuzzy Systems (FUZZ-IEEE/IFES’95), pp. 2227-2232, Japan, March, 1995.

[5] [5] Z.-Q. Liu and S. Miyamoto (eds.), “Soft computing and humancentered machines,” pp. 85-129, Springer-Verlag Tokyo, Japan, 2000.

[6] [6] S. Miyamoto and M. Mukaidono, “Fuzzy c-means as a regularization and maximum entropy approach,” In Proc. of the 7th International Fuzzy Systems Association World Congress (IFES’97), volume II, pp. 86-92, Prague, June, 1997.

[7] [7] N. Wu, “The maximum entropy method,” Springer-Verlag, Berlin, 1997.