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Journal of Computer Science and Technology

, Volume 21, Issue 1, pp 137–140 | Cite as

Novel Cluster Validity Index for FCM Algorithm

  • Jian YuEmail author
  • Cui-Xia Li
Article

Abstract

How to determine an appropriate number of clusters is very important when implementing a specific clustering algorithm, like c-means, fuzzy c-means (FCM). In the literature, most cluster validity indices are originated from partition or geometrical property of the data set. In this paper, the authors developed a novel cluster validity index for FCM, based on the optimality test of FCM. Unlike the previous cluster validity indices, this novel cluster validity index is inherent in FCM itself. Comparison experiments show that the stability index can be used as cluster validity index for the fuzzy c-means.

Keywords

cluster validity optimality test FCM 

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References

  1. 1.
    Pal N R, Bezdek J C. On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Systems, June, 1995, 3(3): 370–379.CrossRefGoogle Scholar
  2. 2.
    Bezdek J C. Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum Press, 1981.Google Scholar
  3. 3.
    Bezdek J C. Cluster validity with fuzzy sets. J. Cybernt., 1974, 3(3): 58–72.MathSciNetGoogle Scholar
  4. 4.
    Windham M P. Cluster validity for the fuzzy c-means clustering algorithm. IEEE Trans. PAMI, July 1982, PAMI-4(4): 357–363.Google Scholar
  5. 5.
    Windham M P. Cluster validity for fuzzy clustering algorithms. Fuzzy Sets Systems, 1981, 5: 177–185.CrossRefzbMATHGoogle Scholar
  6. 6.
    Backer E, Jain A K. A Cluster performance measure based on fuzzy set decomposition. IEEE Trans. PAMI, Jan. 1981, PAMI–3(1).Google Scholar
  7. 7.
    Xie X L, Beni G. A validity measure for fuzzy clustering. IEEE Trans. PAMI, Aug. 1991, 13(8): 841–847.Google Scholar
  8. 8.
    Gunderson R. Applications of fuzzy ISODATA algorithms to startracker printing systems. In Proc. 7th Triannual World IFAC Congr., 1978, pp.1319–1323.Google Scholar
  9. 9.
    Bezdek J C. A physical interpretation of Fuzzy ISODATA. IEEE Trans. SMC, 1976, SMC-6: 387–390.MathSciNetGoogle Scholar
  10. 10.
    Halkidi M, Batistakis Y, Vazirgiannis M. Cluster algorithms and validity measures. In Proc. 13th Int. Conf. Scientific and Statistical Database Management, 2001, pp.3–22.Google Scholar
  11. 11.
    Yu Jian, Cheng Qiansheng. The upper bound of the optimal number of clusters in fuzzy clustering. Science in China, Series F, 2001, 44(2): 119–125.Google Scholar
  12. 12.
    Fukuyanma Y, Sugeno M. A new method of choosing the number of clusters for the fuzzy c-means method. In Proc. 5th Fuzzy Syst. Symp., 1989, pp.247–250. (in Japanese)Google Scholar
  13. 13.
    Wei W, Mendel J M. Optimality tests for the fuzzy c-means algorithm. Pattern Recognition, 1994, 27(11): 1567–1573.CrossRefGoogle Scholar
  14. 14.
    Yu Jian, Huang Houkuan, Tian Shengfeng. An efficient optimality test for the fuzzy c-means algorithm. In Proc. the 2002 IEEE Int. Conf. Fuzzy Systems, 2002, 1: 98–103.Google Scholar
  15. 15.
    Bezdek J C, Hathaway R J, Sabin M J et al. Convergence theory for fuzzy c-means: Counter-examples and repairs. IEEE Trans. Syst. Man, Cybern., Sept./Oct. 1987, SMC17: 873–877.Google Scholar
  16. 16.
    Yu Jian. On the fuzziness index of the FCM algorithms. Chinese Journal of Computers, Aug. 2003, 26(8): 968–973.Google Scholar
  17. 17.
    Anderson E. The IRISes of the Gaspe Peninsula. Bull. Amer. IRIS Soc., 1935, 59: 2–5.Google Scholar
  18. 18.
    Yu Jian, Cheng Qiansheng, Huang Houkuan. Analysis of the weighting exponent in the FCM. IEEE Trans. Systems, Man and Cybernetics—Part B: Cybernetics, Feb. 2004, 34(1): 634–639.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Institute of Computer ScienceBeijing Jiaotong UniversityBeijingP.R. China

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