JACIII Vol.13 No.4 pp. 421-428
doi: 10.20965/jaciii.2009.p0421


On Tolerant Fuzzy c -Means Clustering

Yukihiro Hamasuna*, Yasunori Endo**, and Sadaaki Miyamoto**

*Doctoral Program in Risk Engineering, University of Tsukuba

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

November 22, 2008
March 10, 2009
July 20, 2009
fuzzy c -means clustering, uncertainty, tolerance, fuzzy classification function, optimization
This paper presents a new type of clustering algorithms by using a tolerance vector called tolerant fuzzy c -means clustering (TFCM). In the proposed algorithms, the new concept of tolerance vector plays very important role. In the original concept of tolerance, a tolerance vector attributes to each data. This concept is developed to handle data flexibly, that is, a tolerance vector attributes not only to each data but also each cluster. Using the new concept, we can consider the influence of clusters to each data by the tolerance. First, the new concept of tolerance is introduced into optimization problems based on conventional fuzzy c -means clustering (FCM). Second, the optimization problems with tolerance are solved by using Karush-Kuhn-Tucker conditions. Third, new clustering algorithms are constructed based on the explicit optimal solutions of the optimization problems. Finally, the effectiveness of the proposed algorithms is verified through numerical examples by fuzzy classification function.
Cite this article as:
Y. Hamasuna, Y. Endo, and S. Miyamoto, “On Tolerant Fuzzy c -Means Clustering,” J. Adv. Comput. Intell. Intell. Inform., Vol.13 No.4, pp. 421-428, 2009.
Data files:
  1. [1] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, New York, 1981.
  2. [2] 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 (IFSA'97), June 25-30, 1997, Prague, Czech, Vol.2, pp. 86-92, 1997.
  3. [3] W. K. Ngai, B. Kao, C. K. Chui, R. Cheng, M. Chau, and K. Y. Yip, “Efficient Clustering of Uncertain Data,” Proc. of the Sixth Int. Conf. on Data Mining (ICDM'06), December 18-22, 2006, Hong Kong, China, pp. 436-445, 2006.
  4. [4] O. Takata and S. Miyamoto, “Fuzzy Clustering of Data with Interval Uncertainties,” Journal of Japan Society for Fuzzy Theory and Systems, Vol.12, No.5, pp. 686-695, 2000 (in Japanese).
  5. [5] Y. Endo, R. Murata, H. Haruyama, and S. Miyamoto, “Fuzzy c -Means for Data with Tolerance,” Proc. of Int. Symposium on Nonlinear Theory and Its Applications, pp. 345-348, 2005.
  6. [6] R. Murata, Y. Endo, H. Haruyama, and S. Miyamoto, “On Fuzzy c -Means for data with Tolerance,” Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.5, pp. 673-681, 2006.
  7. [7] Y. Hasegawa, Y. Endo, Y. Hamasuna, and S. Miyamoto, “Fuzzy c -Means for Data with Tolerance Defined as Hyper-rectangles,” Modeling Decisions for Artificial Intelligence (MDAI2007), pp. 237-248. Springer, Heidelberg 2007.
  8. [8] Y. Hamasuna, Y. Endo, S. Miyamoto, and Y. Hasegawa, “On Hard Clustering for Data with Tolerance,” Journal of Japan Society for Fuzzy Theory and Intelligent Informatics, Vol.20, No.3, pp. 388-398, 2008 (in Japanese).
  9. [9] Y. Endo, Y. Hasegawa, Y. Hamasuna, and S. Miyamoto, “Fuzzy c -Means for Data with Rectangular Maximum Tolerance Range,” Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.12, No.5, pp. 461-466, 2007.
  10. [10] Y. Hamasuna, Y. Endo, and M. Yamashiro, “On Tolerant Entropy Regularized Fuzzy c -Means,” IEEE Int. Conf. on Granular Computing (GrC2008), Aug 26-28, 2008, Hangzhou, China, pp. 244-247, 2008.
  11. [11] Y. Hamasuna, Y. Endo, and S. Miyamoto, “On Tolerant Fuzzy c -Means,” Joint 4th Int. Conf. on Soft Computing and Intelligent Systems and 9th Int. Symposium on advanced Intelligent Systems (SCIS&ISIS2008), Sep 17-21, 2008, Nagoya, Japan, pp. 574-577, 2008.
  12. [12] UCI Machine Learning Repository Content Summary
  13. [13] S. Miyamoto, H. Ichihashi, and K. Honda, “Algorithms for Fuzzy Clustering,” Springer, Heidelberg, 2008.
  14. [14] K. Jajuga, “L1-norm based fuzzy clustering,” Fuzzy Sets and Systems, Vol.39, pp. 43-50, 1991.
  15. [15] S. Miyamoto and Y. Agusta, “An Efficient Algorithm for l1 Fuzzy c -Means and Its Termination,” Control and Cybernetics, Vol.24, No.4, pp. 421-436, 1995.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Jun. 19, 2024