Kernelized Fuzzy C-Means Method and Gaussian Mixture Model in Unsupervised Cascade Clustering

  • Joanna Czajkowska
  • Monika Bugdol
  • Ewa Pietka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7339)


Fuzzy C-Means (FCM) clustering and Gaussian Mixture Model (GMM) are two popular tools for data processing. In this study the unsupervised algorithm combining FCM clustering in the Kernel Space (KFCM) and GMM is presented. First, a ”kernel trick” is applied to the FCM algorithm. Then, the number of clusters is chosen automatically in the kernel space. On the basis of obtained starting parameters, i.e. number of mixture components, mean vector, covariance matrices and mixing proportion coefficients, the final GMM parameters are estimated. For this estimation the Expectation Maximization (EM) algorithm is used. The presented methodology - combination of KFCM and GMM methods named unsupervised cascade clustering - constitutes the basic step in Ewing’s sarcoma segmentation. On this basis the voxels intensity values describing segmented tumour and surrounded healthy tissue are defined and fuzzy connectedness analysis is performed. The obtained mixture parameters estimation results are compared with the results obtained using two different methods described in literature.


Cascade Clustering Gaussian Mixture Model Fuzzy C-Means Kernel Space 


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  1. 1.
    Buraczewski, J.: Radiodiagnostyka zmian nowotworowych. Państwowy Zakład Wydawnictw Lekarskich, Warszawa (1987)Google Scholar
  2. 2.
    Davies, A.M., Sundaram, M., James, S.L.J.: Imaging of Bone Tumors and Tumor-Like Lesions, Techniques and Applications, Medical Radiology, Diagnostic Imaging. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Pruszynski, B.: Radiologia, Diagnostyka obrazowa, Rtg, TK, USG, MR i medycyna nuklearna. Wydawnictwo Lekarskie PZWL, Warszawa (2005)Google Scholar
  4. 4.
    Stoba, C., Czauderna, P.: Guzy kości u dzieci. Diagnostyka i leczenie. Wydawnictwo Folium, Lublin (1997)Google Scholar
  5. 5.
    Czajkowska, J.: Parametryzacja i trójwymiarowa segmentacja guzow kości w seriach rezonansu magnetycznego. Politechnika Ślźska, Gliwice (2011)Google Scholar
  6. 6.
    Helimed Diagnostic Imaging, Katowice (2004-2010)Google Scholar
  7. 7.
    Kawa, J., Pietka, E.: Kernelized Fuzzy C-Means Method in Fast Segmentation of Demyelination Plaques in Multiple Sclerosis. In: Proceedings of the 29th Annual International Conference of the IEEE EMBS (August 2007)Google Scholar
  8. 8.
    Heo, G., Gader, P.: An Extension of Global Fuzzy C-Means Using Kernel Methods. In: IEEE International Conference on Fuzzy Systems (July 2010)Google Scholar
  9. 9.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers (1981)Google Scholar
  10. 10.
    Chuang, K.S., Tzeng, H.L., Chen, S., Wu, J., Chen, T.J.: Fuzzy C-Means Clustering with Spatial Information for Image Segmentation. In: Computerized Medical Imaging and Graphics, vol. 30, pp. 9–15. Elsevier (2006)Google Scholar
  11. 11.
    Wieclawek, W., Rudzki, M., Czajkowska, J.: Live-Wire Approach with FCM Clustering and Adaptive Filtering for Edge Detection in Medical Images. In: XIăInternational PhD Workshop, OWD 2009, Conference Archives PTETiS, Wisşa, vol. 26, pp. 475–478 (2009)Google Scholar
  12. 12.
    Gustafson, D.E., Kessel, W.C.: Fuzzy Clustering with a Fuzzy Covariance Matrix. In: Proceedings of Conference on Decision Control, pp. 761–766. IEEE (1979)Google Scholar
  13. 13.
    Hathaway, R.J., Huband, J.M., Bezdek, J.C.: Kernelized Fuzzy C-Means Method in Fast Segmentation of Demyelination Plaques in Multiple Sclerosis. In: Proceedings of International Conference on Fuzzy Systems. IEEE (August 2005)Google Scholar
  14. 14.
    Chou, C.H., Su, M.C., Lai, E.: A New Cluster Validity Measure and Its Application to Image Compression. Pattern Analysis and Applications 7(2), 205–220 (2004)Google Scholar
  15. 15.
    Milligan, G.W., Cooper, M.C.: An Examination of Procedures for Determining the Number of Clusters in Data Set. Psychometrika 50(2), 159–179 (1985)CrossRefGoogle Scholar
  16. 16.
    Pal, N.R., Bezdek, J.C.: On Cluster Validity for the Fuzzy C-Means Model. IEEE Transactions on Fuzzy Systems 3(3), 370–379 (1995)CrossRefGoogle Scholar
  17. 17.
    Figueiredo, M., Jain, A.K.: Unsupervised Learning of Finite Mixture Models. IEEE Transaction on Pattern Analysis and Machine Intelligence 24(3), 381–396 (2002)CrossRefGoogle Scholar
  18. 18.
    McLachlan, G., Peel, D.: Finite Mixture Model. Wiley Series in Probability and Statistics (2000)Google Scholar
  19. 19.
    Honda, K., Ichihashi, H.: Regularized Linear Fuzzy Clustering and Probabilistic PCA Mixture Models. IEEE Transaction on Fuzzy Systems 13(4), 508–516 (2005)CrossRefGoogle Scholar
  20. 20.
    Mekhalfa, F., Nacereddine, N., Goumeidane, A.B.: Unsupervised Algorithm for Radiographic Image Segmentation Based on the Gaussian Mixture Model. In: The International Conference on Computer as a Tool, EUROCON (September 2007)Google Scholar
  21. 21.
    Chandramouli, R., Srikantam, V.K.: Optimum Probability Model Selection Using Akaike’s Information Criterion for Low Power Applications. In: IEEE International Symposium on Circuits and Systems (May 2000)Google Scholar
  22. 22.
    Wagenaar, D.A.: FSMEM for MoG, Term Project for CS/CNS/EE 156b: Learning Systems, Class by P. Perona and M. Welling, Caltech (June 2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Joanna Czajkowska
    • 1
  • Monika Bugdol
    • 1
  • Ewa Pietka
    • 1
  1. 1.Faculty of Biomedical EngineeringSilesian University of TechnologyGliwicePoland

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