GeCiM: A Novel Generalized Approach to C-Means Clustering

  • László Szilágyi
  • David Iclănzan
  • Sándor M. Szilágyi
  • Dan Dumitrescu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5197)

Abstract

All three conventional c-means clustering algorithms have their advantages and disadvantages. This paper presents a novel generalized approach to c-means clustering: the objective function is considered to be a mixture of the FCM, PCM, and HCM objective functions. The optimal solution is obtained via evolutionary computation. Our main goal is to reveal the properties of such mixtures and to formulate some rules that yield accurate partitions.

Keywords

fuzzy c-means clustering possibilistic c-means clustering hard c-means clustering evolutionary computation 

References

  1. 1.
    Anderson, E.: The IRISes of the Gaspe peninsula. Bull. Amer. IRIS Soc. 59, 2–5 (1935)Google Scholar
  2. 2.
    Baraldi, A., Blonda, P.: A survey of fuzzy clustering algorithms for pattern recognition - Part I. IEEE Trans. Syst. Man Cybern. Part B. 29, 778–785 (1999)CrossRefGoogle Scholar
  3. 3.
    Barni, M., Capellini, V., Mecocci, A.: Comments on a possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 4, 393–396 (1996)CrossRefGoogle Scholar
  4. 4.
    Belacel, N., Hansen, P., Mladenovic, N.: Fuzzy J-means: a new heuristic for fuzzy clustering. Patt. Recogn. 35, 2193–2200 (2002)CrossRefMATHGoogle Scholar
  5. 5.
    Benyó, B.: Analysis of temporal patterns of physiological parameters. In: Kamruzzaman, J., Begg, R.K., Sarker, R.A. (eds.) Artificial neural networks in finance, health and manufacturing: potential and challenges, pp. 285–317. Idea Group Publishing, Hershey (2006)Google Scholar
  6. 6.
    Bezdek, J.C.: Pattern recognition with fuzzy objective function algorithms. Plenum, New York (1981)CrossRefMATHGoogle Scholar
  7. 7.
    Cartwright, H.: An introduction to evolutionary computation and evolutionary algorithms. In: Johnston, R., Mingos, D.M.P. (eds.) Applications of evolutionary computation in chemistry. Structure and Bonding, vol. 110, pp. 1–32. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Dasgupta, D., Michalewicz, Z. (eds.): Evolutionary algorithms in engineering applications. Springer, New York (2001)Google Scholar
  9. 9.
    Dennis Jr., J.E., Woods, D.J.: Optimization on Microcomputers: The Nelder-Mead Simplex Algorithm. In: Wouk, A. (ed.) New Computing Environments: Microcomputers in Large-Scale Computing, Soc. Ind. Appl. Math., Philadelphia, PA, pp. 116–122 (1987)Google Scholar
  10. 10.
    Fan, J.L., Zhen, W.Z., Xie, W.X.: Suppressed fuzzy c-means clustering algorithm. Patt. Recogn. Lett. 24, 1607–1612 (2003)CrossRefMATHGoogle Scholar
  11. 11.
    Goldberg, D.E.: Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading (1989)MATHGoogle Scholar
  12. 12.
    Hathaway, R.J., Bezdek, J.C.: Optimization of clustering by reformulation. IEEE Trans. Fuzzy Syst. 3, 241–245 (1995)CrossRefGoogle Scholar
  13. 13.
    Holland, J.H.: Adaptation in natural artificial systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  14. 14.
    Karayiannis, N.B., Bezdek, J.C., Pal, N.R., Hathaway, R.J., Pai, P.I.: Repairs to GLVQ: a new family of competitive learning scheme. IEEE Trans. Neural Networks 7, 1062–1071 (1996)CrossRefGoogle Scholar
  15. 15.
    Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1, 98–110 (1993)CrossRefGoogle Scholar
  16. 16.
    Lagarias, J., Reeds, J., Wright, M., Wright, P.: Convergence properties of the Nelder-Mead simplex algorithm in low dimensions. SIAM J. Optim. 9, 112–147 (1998)CrossRefMATHGoogle Scholar
  17. 17.
    Pal, N.R., Bezdek, J.C., Tsao, E.C.K.: Generalized clustering networks and Kohonen’s self-organizing scheme. IEEE Trans. Neural Networks 4, 549–557 (1993)CrossRefGoogle Scholar
  18. 18.
    Yu, J.: General c-means clustering model. IEEE Trans. Patt. Recogn. Mach. Intell. 27, 1197–1211 (2005)CrossRefGoogle Scholar
  19. 19.
    Zadeh, L.A.: Fuzzy sets. Inform. Contr. 8, 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • László Szilágyi
    • 1
    • 2
  • David Iclănzan
    • 1
    • 3
  • Sándor M. Szilágyi
    • 1
  • Dan Dumitrescu
    • 3
  1. 1.SapientiaHungarian Science University of Transylvania, Faculty of Technical and Human ScienceTârgu-MureşRomania
  2. 2.Department of Control Engineering and Information TechnologyBudapest University of Technology and EconomicsBudapestHungary
  3. 3.Faculty of Mathematics and Computer ScienceBabeş-Bolyai University of Cluj-NapocaRomania

Personalised recommendations