Abstract

A novel fuzzy clustering algorithm, called kernel improved possibilistic c-means (KIPCM) algorithm, is presented based on kernel methods. KIPCM is an extension of the improved possibilistic c-means (IPCM) algorithm. Different from IPCM which is applied in Euclidean space, KIPCM can make data clustering in kernel feature space. With kernel methods the input data can be implicitly mapped into a high-dimensional feature space where the nonlinear pattern now appears linear. It is unnecessary to calculate in this high-dimensional feature space because we directly calculate inner products from the input data by kernel function. KIPCM can identify clusters of complex shapes and solve nonlinear separable problems better than IPCM and FCM (fuzzy c-means). Our experiments show that the proposed algorithm compares favorably with FCM and IPCM.

References

  1. 1.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)MATHGoogle Scholar
  2. 2.
    Krishnapuram, R., Keller, J.: A Possibilistic Approach to Clustering. IEEE Trans. Fuzzy Systems 1(2), 98–110 (1993)CrossRefGoogle Scholar
  3. 3.
    Barni, M., Cappellini, V., Mecocci, A.: Comments on A Possibilistic Approach to Clustering. IEEE Trans. Fuzzy Systems 4(3), 393–396 (1996)CrossRefGoogle Scholar
  4. 4.
    Zhang, J.-S., Leung, Y.-W.: Improved possibilistic C-means clustering algorithms. IEEE Trans. Fuzzy Systems 12(2), 209–217 (2004)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Vapnik, V.: Statistical Learning Theory. Wiley, Chichester (1998)MATHGoogle Scholar
  6. 6.
    Girolami, M.: Mercer kernel based clustering in feature space. IEEE Trans. on Neural Networks 13(13), 780–784 (2002)CrossRefGoogle Scholar
  7. 7.
    Aizerman, M., Braverman, E., Rozonoer, L.: Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control 25, 821–837 (1964)MathSciNetGoogle Scholar
  8. 8.
    Pal, N.R., Pal, K., Bezdek, J.C.: A mixed c-means clustering model. Processings of the IEEE Trans. Fuzzy Systems, Spain, 11–21 (1997) Google Scholar
  9. 9.
    Anderson, E.: The Iris of Gasp Peninsula. Bulletin of American Iris Society 59, 2–5 (1935)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiao-Hong Wu
    • 1
    • 2
  • Jian-Jiang Zhou
    • 1
  1. 1.College of Information Science & TechnologyNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.College of Electrical & Information EngineeringJiangsu UniversityZhenjiangChina

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