Advertisement

Hybrid Fuzzy Clustering Using LP Norms

  • Tomasz Przybyła
  • Janusz Jeżewski
  • Krzysztof Horoba
  • Dawid Roj
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6591)

Abstract

The fuzzy clustering methods are useful in the data mining applications. This paper describes a new fuzzy clustering method in which each cluster prototype is calculated as a value that minimizes introducted generalized cost function. The generalized cost function utilizes the L p norm. The fuzzy meridian is a special case of cluster prototype for p = 2 as well as the fuzzy meridian for p = 1. A method for the norm selection is proposed. An example illustrating the performance of the proposed method is given.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kaufman, L., Rousseeuw, P.: Finding Groups in Data. Wiley–Interscience, Chichester (1990)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)CrossRefzbMATHGoogle Scholar
  3. 3.
    Hathaway, R.J., Bezdek, J.C., Hu, Y.: Genalized Fuzzy c-Means Clustering Strategies Using L p Norm Distances. IEEE Trans. on Fuzzy Sys. 8, 576–582 (2000)CrossRefGoogle Scholar
  4. 4.
    Krishnapuram, R., Keller, J.M.: A Possibilistic Approach to Clustering. IEEE Trans. on Fuzzy Sys. 1, 98–110 (1993)CrossRefGoogle Scholar
  5. 5.
    Krishnapuram, R., Keller, J.M.: The Possibilistic C–Means Algorithm: Insights and Recomendations. IEEE Trans on Fuzzy Sys. 4, 385–396 (1996)CrossRefGoogle Scholar
  6. 6.
    Kersten, P.R.: Fuzzy Order Statistics and Their Application to Fuzzy Clustering. IEEE Trans. on Fuzzy Sys. 7, 708–712 (1999)CrossRefGoogle Scholar
  7. 7.
    Huber, P.: Robust statistics. Wiley, New York (1981)CrossRefzbMATHGoogle Scholar
  8. 8.
    Dave, R.N., Krishnapuram, R.: Robust Clustering Methods: A Unified View. IEEE Trans. on Fuzzy System 5, 270–293 (1997)CrossRefGoogle Scholar
  9. 9.
    Chatzis, S., Varvarigou, T.: Robust Fuzzy Clustering Using Mixtures of Student’s–t Distributions. Pattern Recognition Letters 29, 1901–1905 (2008)CrossRefGoogle Scholar
  10. 10.
    Frigui, H., Krishnapuram, R.: A Robust Competitive Clustering Algorithm With Applications in Computer Vision. IEEE Trans. Pattern Analysis and Machine Intelligence 21, 450–465 (1999)CrossRefGoogle Scholar
  11. 11.
    Sun, J., Kaban, A., Garibaldi, J.M.: Robust mixture clustering using Pearson type VII distribution. Pattern Recognition Letters 31, 2447–2454Google Scholar
  12. 12.
    Arce, G.R., Kalluri, S.: Fast Algorithm For Weighted Myriad Computation by Fixed Point Search. IEEE Trans. on Signal Proc. 48, 159–171 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Przybyła, T.: Fuzzy c–Myriad Clustering Method. System Modeling Control, 249–254 (2005)Google Scholar
  14. 14.
    Aysal, T.C., Barner, K.E.: Meridian Filtering for Robust Signal Processing. IEEE Trans. on Signal Proc. 55, 3949–3962 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Parzen, E.: On Estimation Of A Probability Density Function And Mode. Ann. Math. Stat. 33, 1065–1076 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Przybyła, T., Jeżewski, J., Horoba, K.: The Adaptive Fuzzy Meridian and Its Application to Fuzzy Clustering. In: Advances in Intelligent and Soft Computing, vol. 57, pp. 247–256. Springer, Heidelberg (2009)Google Scholar
  17. 17.
    Arce, G.R., Kalluri, S.: Robust Frequency–Selective Filtering Using Weighted Myriad Filters admitting Real–Valued Weights. IEEE Trans. on Signal Proc. 49, 2721–2733 (2001)CrossRefGoogle Scholar
  18. 18.
    Pedrycz, W.: Konwledge–Based Clustering. Wiley–Interscience, Chichester (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tomasz Przybyła
    • 1
  • Janusz Jeżewski
    • 2
  • Krzysztof Horoba
    • 2
  • Dawid Roj
    • 2
  1. 1.Institute of ElectronicsSilesian University of TechnologyGliwicePoland
  2. 2.Biomedical Signal Processing DepartmentInstitute of Medical Technology and EquipmentZabrzePoland

Personalised recommendations