single-jc.php

JACIII Vol.12 No.5 pp. 454-460
doi: 10.20965/jaciii.2008.p0454
(2008)

Paper:

Formulation of Fuzzy c-Means Clustering Using Calculus of Variations and Twofold Membership Clusters

Sadaaki Miyamoto*

*Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba
Ibaraki 305-8573, Japan

Received:
October 10, 2007
Accepted:
February 15, 2008
Published:
September 20, 2008
Keywords:
fuzzy c-means clustering, calculus of variations, twofold memberships
Abstract
A membership matrix of fuzzy c-means clustering is associated with corresponding fuzzy classification rules as membership functions defined on the whole data space. We directly derive such functions in fuzzy c-means and possibilistic clustering using the calculus of variations, generalizing ordinary fuzzy c-means and deriving new twofold membership clustering using this framework.
Cite this article as:
S. Miyamoto, “Formulation of Fuzzy c-Means Clustering Using Calculus of Variations and Twofold Membership Clusters,” J. Adv. Comput. Intell. Intell. Inform., Vol.12 No.5, pp. 454-460, 2008.
Data files:
References
  1. [1]
    S. Miyamoto, “Introduction to Cluster Analysis: Theory and Applications of Fuzzy Clustering,” Morikita-Shuppan, Tokyo, 1999 (in Japanese).
    I. M. Gelfand and S. V. Fomin, “Calculus of Variations,” tr. and ed. R. A. Silverman, Prentice-Hall, Englewood Cliffs, N. J. 1963.
    R. Krishnapuram and J. M. Keller, “A possibilistic approach to clustering,” IEEE Trans. on Fuzzy Syst, Vol.1, No.2, pp. 98-110, 1993.
    J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum, New York, 1981. J. C. Dunn, “A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters,” J. of Cybernetics, Vol.3, pp. 32-57, 1974.
    S. Miyamoto and M. Mukaidono, “Fuzzy c-means as a regularization and maximum entropy approach,” Proc. of the 7th Int. Fuzzy Systems Association World Congress (IFSA'97), June 25-30, 1997, Prague, Czech, Vol.II, pp. 86-92, 1997.
    R. N. Davé and R. Krishnapuram, “Robust clustering methods: a unified view,” IEEE Trans. Fuzzy Syst, Vol.5, No.2, pp. 270-293, 1997.
    J. C. Bezdek, J. Keller, R. Krishnapuram, and N. R. Pal, “Fuzzy Models and Algorithms for Pattern Recognition and Image Processing,” Kluwer, Boston, 1999.
    N. K. Pal, J. C. Bezdek, and E .C.-K. Tsao, “Generalized clustering networks and Kohonen's self-organizing scheme,” IEEE Trans. on Neural Networks, Vol.4, No.4, pp. 549-557, 1993.
    J. M. Keller, M. R. Gray, and J. A. Givens, Jr., “A fuzzy k - nearest neighbor algorithm,” IEEE Trans., on Syst., Man, and Cybern, Vol.15, pp. 580-585, 1985.
    R. N. Dave, “Characterization and detection of noise in clustering,” Pattern Recognition Letters, Vol.12, pp. 657-664, 1991.
    R. J. Hathaway and J. C. Bezdek, “Switching regression models and fuzzy clustering,” IEEE Trans. on Fuzzy Systems, Vol.1, No.3, pp. 195-204, 1993.
    F. Höppner, F. Klawonn, R. Kruse, and T. Runkler, “Fuzzy Cluster Analysis,” Wiley, Chichester, 1999.
    T. Kohonen, “Self-Organizing Maps,” 2nd Ed., Springer, Berlin, 1997.
    K. T. Atanassov, “Intuitionistic fuzzy sets, Fuzzy Sets and Systems,” Vol.20, pp. 87-96, 1986.
    Z. Pawlak, “Rough sets,” Int. Journal of Computer and Information Sciences, Vol.11, pp.341-356, 1982.
    Z. Pawlak, “Rough Sets,” Kluwer Academic Publishers, Dordrecht, 1991.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Dec. 06, 2024