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Parameter Selections of Fuzzy C-Means Based on Robust Analysis

Authors: Kuo-Lung Wu


The weighting exponent m is called the fuzzifier that can have influence on the clustering performance of fuzzy c-means (FCM) and mÎ[1.5,2.5] is suggested by Pal and Bezdek [13]. In this paper, we will discuss the robust properties of FCM and show that the parameter m will have influence on the robustness of FCM. According to our analysis, we find that a large m value will make FCM more robust to noise and outliers. However, if m is larger than the theoretical upper bound proposed by Yu et al. [14], the sample mean will become the unique optimizer. Here, we suggest to implement the FCM algorithm with mÎ[1.5,4] under the restriction when m is smaller than the theoretical upper bound.

Keywords: Fuzzy c-means, robust, fuzzifier.

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[1] J.C. Bezdek, Pattern Reccognition with Fuzzy Objective Function Algorithm, Plenum Press, 1981.
[2] M.S. Yang, "A survey of fuzzy clustering," Math. Comput. Modelling, vol.18, pp. 1-16, 1993.
[3] J. Yu, "General c-means clustering model," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, pp. 1197-1211, 2005.
[4] K.L. Wu and M.S. Yang, "Alternative c-means clustering algorithms," Pattern Recognition, vol. 35, pp.2267-2278, 2002.
[5] J. Leski, "Towards a robust fuzzy clustering," Fuzzy Sets and Systems, vol. 137, pp.215-233, 2003.
[6] H. Frigui and R. Krishnapuram, "A robust competitive clustering algorithm with applications in computer vision," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, 450-465, 1999.
[7] J. Yu and M.S. Yang, "Optimality test for generalized FCM and its application to parameter selection," IEEE Trans. Fuzzy Systems, vol. 13, pp. 164-176, 2005.
[8] D. Özdemir and L. Akarun, "A fuzzy algorithm for color quantization of images," Pattern Recognition, vol. 35, pp.1785-1791, 2002.
[9] D. Özdemir and L. Akarun, "Fuzzy algorithms for combined quantization and dithering," IEEE Trans. Image Processing, vol. 10, pp. 923-931, 2001.
[10] R. Krishnapuram and J.M. Keller, "A possibilistic approach to clustering," IEEE Trans. Fuzzy Systems, vol. 1, pp. 98-110, 1993.
[11] M.S. Yang and K.L. Wu, "Unsupervised possibilistic clustering," Pattern Recognition, vol. 39, pp. 5-21, 2006.
[12] J.C. Bezdek, "Cluster validity with fuzzy sets," J. Cybernet., vol. 3, pp. 58-73, 1974.
[13] N. R. Pal and J. C. Bezdek, "On cluster validity for fuzzy c-means model," IEEE Trans. Fuzzy Systems, vol. 1, pp. 370-379, 1995.
[14] J. Yu, Q. Cheng and H. Huang, "Analysis of the weighting exponent in the FCM," IEEE Trans. Systems, Man, Cybern., Part B, vol. 34, pp. 634-639, 2004.
[15] E. Anderson, "The Irises of the gaspe peninsula," Bull. Am. IRIS Soc. 59, pp. 2-5, 1935.
[16] J.C. Bezdek, J.M. Keller, R. Krishnapuram, L.I. Kuncheva, N.R. Pal, "Will the Iris data please stand up?," IEEE Trans. Fuzzy Syst. Vol. 7, pp. 368-369, 1999.
[17] P.J. Huber, Robust Statistics, Wiley, 1981.