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.
Similar content being viewed by others
References
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.
Bezdek J C. Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum Press, 1981.
Bezdek J C. Cluster validity with fuzzy sets. J. Cybernt., 1974, 3(3): 58–72.
Windham M P. Cluster validity for the fuzzy c-means clustering algorithm. IEEE Trans. PAMI, July 1982, PAMI-4(4): 357–363.
Windham M P. Cluster validity for fuzzy clustering algorithms. Fuzzy Sets Systems, 1981, 5: 177–185.
Backer E, Jain A K. A Cluster performance measure based on fuzzy set decomposition. IEEE Trans. PAMI, Jan. 1981, PAMI–3(1).
Xie X L, Beni G. A validity measure for fuzzy clustering. IEEE Trans. PAMI, Aug. 1991, 13(8): 841–847.
Gunderson R. Applications of fuzzy ISODATA algorithms to startracker printing systems. In Proc. 7th Triannual World IFAC Congr., 1978, pp.1319–1323.
Bezdek J C. A physical interpretation of Fuzzy ISODATA. IEEE Trans. SMC, 1976, SMC-6: 387–390.
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.
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.
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)
Wei W, Mendel J M. Optimality tests for the fuzzy c-means algorithm. Pattern Recognition, 1994, 27(11): 1567–1573.
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.
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.
Yu Jian. On the fuzziness index of the FCM algorithms. Chinese Journal of Computers, Aug. 2003, 26(8): 968–973.
Anderson E. The IRISes of the Gaspe Peninsula. Bull. Amer. IRIS Soc., 1935, 59: 2–5.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China under Grant No. 60303014.
Rights and permissions
About this article
Cite this article
Yu, J., Li, CX. Novel Cluster Validity Index for FCM Algorithm. J Comput Sci Technol 21, 137–140 (2006). https://doi.org/10.1007/s11390-006-0137-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11390-006-0137-2