JACIII Vol.19 No.5 pp. 624-631
doi: 10.20965/jaciii.2015.p0624


Fuzzy c-Means with Quadratic Penalty-Vector Regularization Using Kullback-Leibler Information for Uncertain Data

Naohiko Kinoshita*, Yasunori Endo**, and Yukihiro Hamasuna***

*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

***Department of Informatics, Kindai University
3-4-1 Kowakae, Higashiosaka, Osaka 577-8502, Japan

January 31, 2015
June 16, 2015
September 20, 2015
clustering, fuzzy c-means, EM algorithm, uncertainty, K-L information

Clustering, a highly useful unsupervised classification, has been applied in many fields. When, for example, we use clustering to classify a set of objects, it generally ignores any uncertainty included in objects. This is because uncertainty is difficult to deal with and model. It is desirable, however, to handle individual objects as is so that we may classify objects more precisely. In this paper, we propose new clustering algorithms that handle objects having uncertainty by introducing penalty vectors. We show the theoretical relationship between our proposal and conventional algorithms verifying the effectiveness of our proposed algorithms through numerical examples.

  1. [1] S. Miyamoto, “Introduction to Cluster Analysis,” Morikita-Shuppan, Tokyo, 1999. (in Japanese)
  2. [2] J. MacQueen, “Some methods for classification and analysis of multivariate observations,” Proc. of the 5th Berkeley Symp. on Mathematical Statistics and Probability, Vol.1, pp. 281-297, 1967.
  3. [3] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, New York, 1981.
  4. [4] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, pp. 338-353, 1965.
  5. [5] A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm,” J. of the Royal Statistical Society Series B (Methodological), Vol.39, No.1, pp. 1-38, 1977.
  6. [6] R. Murata, Y. Endo, H. Haruyama, and S. Miyamoto, “On Fuzzy c-Means for Data with Tolerance,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII) Vol.10, No.5, pp. 673-681, 2006.
  7. [7] O. Takata and S. Miyamoto, “Fuzzy Clustering of Data with Interval Uncertainties,” Japan Society for Fuzzy Theory and Systems, Vol.12, No.5, pp. 686-695, 2000. (in Japanese)
  8. [8] R. J. Hathaway, “Fuzzy c-Means Clustering of Incomplete Data,” IEEE Trans. on Systems, Man, and Cybernetics - Part B: Cybernetics, Vol.31, No.5, pp. 735-744, 2001.
  9. [9] Y. Endo, Y. Hasegawa, Y. Hamasuna, and Y. Kanzawa, “Fuzzy c-Means Clustering for Uncertain Data Using Quadratic Penalty-Vector Regularization,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.15, No.1, pp. 76-82, 2011.
  10. [10] K. Miyagishi, H. Ichihashi, and K. Honda, “Fuzzy c-Means Clustering with Regularization by K-L Information,” Japan Society for Fuzzy Theory and Systems, Vol.13, No.4, pp. 64-75, 2001. (in Japanese)
  11. [11] L. Hubert and P. Arabie, “Comparing Partitions,” J. of Classification, Vol.2, Issue 1, pp. 193-218, 1985.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, IE9,10,11, Opera.

Last updated on Apr. 20, 2018