Abstract
A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means (KMPCM) model. The proposed model is an extension of the modified possibilistic c-means (MPCM) algorithm by using kernel methods. Different from MPCM and fuzzy c-means (FCM) model which are based on Euclidean distance, the proposed model is based on kernel-induced distance. Furthermore, with kernel methods the input data can be mapped implicitly into a high-dimensional feature space where the nonlinear pattern now appears linear. It is unnecessary to do calculation in the high-dimensional feature space because the kernel function can do it. Numerical experiments show that KMPCM outperforms FCM and MPCM.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bezdek J C. Pattern Recognition with Fuzzy Objective Function Algorithms [M]. New York: Plenum Press, 1981.
Bezdek J C, Pal M R, Keller J, Krishnapuram R. Fuzzy Models and Algorithms for Pattern Recognition and Image Processing [M]. Massaschusetts: Kluwer Academic, 1999.
Krishnapuram R, Keller J. A possibilistic approach to clustering [J]. IEEE Transactions on Fuzzy Systems, 1993, 1(2): 98–110.
BARNI M, CAPPELLINI V, MECOCCI A. Comments on a possibilistic approach to clustering [J]. IEEE Transactions on Fuzzy Systems, 1996, 4(3): 393–396.
Krishnapuram R, Keller J. The possibilistic cmeans algorithm: insights and recommendations [J]. IEEE Transactions on Fuzzy Systems, 1996, 4(3): 385–393.
Vapnik V N. Statistical Learning Theory [M]. New York: Wiley, 1998.
Girolami M. Mercer kernel based clustering in feature space [J]. IEEE Transactions on Neural Networks, 2002, 13(13): 780–784.
Wu Z D, **e W X. Fuzzy c-means clustering algorithm based on kernel method [C]//The Fifth International Conference on Computational Intelligence and Multimedia Applications, **’an, China. Washington: IEEE Computer Society Press, 2003: 49–54.
Wu X H. A possibilistic c-means clustering algorithm based on kernel methods [C]//2006 International Conference on Communications, Circuits and Systems, Gulin, China. Chengdu: UESTC Press, 2006, 3: 2062–2066.
Aizerman M, Braverman E, Rozonoer L. Theoretical foundations of the potential function method in pattern recognition learning [J]. Automation and Remote Control, 1964, 25: 821–837.
Pal N R, Pal K, Bezdek J C. A new hybrid c-means clustering model [C]//Proceedings of the IEEE International Conference on Fuzzy Systems, Budapest, Hungary. Piscataway: IEEE Press, 2004, 1: 179–184.
PAL N R, PAL K, BEZDEK J C. A possibilistic fuzzy cmeans clustering algorithm [J]. IEEE Transactions on Fuzzy Systems, 2005, 13(4): 517–530.
Anderson E. The iris of gasp peninsula [J]. Bulletin of American Iris Society, 1935, 59(1): 2–5.
TIMM H, BORGELT C, DORING C, KRUSE R. An extension to possibilistic fuzzy cluster analysis [J]. Fuzzy Sets and Systems, 2004, 147(1): 3–16.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the 15th Plan for National Defence Preventive Research Project (Grant No.413030201)
About this article
Cite this article
Wu, Xh., Zhou, Jj. Modified possibilistic clustering model based on kernel methods. J. Shanghai Univ.(Engl. Ed.) 12, 136–140 (2008). https://doi.org/10.1007/s11741-008-0210-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11741-008-0210-2