Gradient Based Fuzzy C-Means Algorithm with a Mercer Kernel

  • Dong-Chul Park
  • Chung Nguyen Tran
  • Sancho Park
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)


In this paper, a clustering algorithm based on Gradient Based Fuzzy C-Means with a Mercer Kernel, called GBFCM (MK), is proposed. The kernel method adopted in this paper implicitly performs nonlinear mapping of the input data into a high-dimensional feature space. The proposed GBFCM(MK) algorithm is capable of dealing with nonlinear separation boundaries among clusters. Experiments on a synthetic data set and several real MPEG data sets show that the proposed algorithm gives better classification accuracies than both the conventional k-means algorithm and the GBFCM.


Feature Space Kernel Method Membership Grade Code Vector Gaussian Kernel Function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bezdek, J.C.: A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms. IEEE Trans. on Pattern Anal. Mach. Int. 2(1), 1–8 (1980)MATHCrossRefGoogle Scholar
  2. 2.
    Park, D.C., Dagher, I.: Gradient Based Fuzzy c-means ( GBFCM ) Algorithm. In: IEEE Int. Conf. on Neural Networks, ICNN 1994, vol. 3, pp. 1626–1631 (1994)Google Scholar
  3. 3.
    Kohonen, T.: The Self-Organizing Map. Proc. IEEE 78, 1464–1480 (1990)CrossRefGoogle Scholar
  4. 4.
    Park, D.C.: Classification of MPEG VBR Video Data Using Gradient-Based FCM with Divergence Measure. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS (LNAI), vol. 3613, pp. 475–483. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Cover, T.M.: Geomeasureal and Statistical Properties of Systems of Linear Inequalities in Pattern Recognition. Electron. Comput. EC-14, 326–334 (1965)MATHGoogle Scholar
  6. 6.
    Girolami, M.: Mercer Kernel-Based Clustering in Feature Space. IEEE Trans. on Neual Networks 13(3), 780–784 (2002)CrossRefGoogle Scholar
  7. 7.
    Chen, J.H., Chen, C.S.: Fuzzy Kernel Perceptron. IEEE Trans. on Neural Networks 13(6), 1364–1373 (2002)CrossRefGoogle Scholar
  8. 8.
    Hartigan, J.: Clustering Algorithms. Wiley, New York (1975)MATHGoogle Scholar
  9. 9.
    Rose, O.: Satistical Properties of MPEG Video Traffic and Their Impact on Traffic Modeling in ATM Systems. In: IEEE Conf. on Local Computer Networks, pp. 397–406 (1995)Google Scholar
  10. 10.
    Liang, Q., Mendel, J.M.: MPEG VBR Video Traffic Modeling and Classification Using Fuzzy Technique. IEEE Trans. on Fuzzy Systems 9(1), 183–193 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dong-Chul Park
    • 1
  • Chung Nguyen Tran
    • 1
  • Sancho Park
    • 2
  1. 1.Dept. of Information EngineeringMyong Ji UniversityKorea
  2. 2.Davan Tech Co.SeongnamKorea

Personalised recommendations