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A Self-tuning Possibilistic c-Means Clustering Algorithm

  • László Szilágyi
  • Szidónia Lefkovits
  • Zsolt Levente Kucsván
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11144)

Abstract

Most c-means clustering models have serious difficulties when facing clusters of different sizes and severely outlier data. The possibilistic c-means (PCM) algorithm can handle both problems to some extent. However, its recommended initialization using a terminal partition produced by the probabilistic fuzzy c-means does not work when severe outliers are present. This paper proposes a possibilistic c-means clustering model that uses only three parameters independently of the number of clusters, which is able to more robustly handle the above mentioned obstacles. Numerical evaluation involving synthetic and standard test data sets prove the advantages of the proposed clustering model.

Keywords

Fuzzy c-means clustering Possibilistic c-means clustering Cluster size sensitivity Outlier data 

References

  1. 1.
    Anderson, E.: The Irises of the Gaspe Peninsula. Bull. Am. Iris Soc. 59, 2–5 (1935)Google Scholar
  2. 2.
    Barni, M., Capellini, V., Mecocci, A.: Comments on a possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 4, 393–396 (1996)CrossRefGoogle Scholar
  3. 3.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)CrossRefGoogle Scholar
  4. 4.
    Dave, R.N.: Characterization and detection of noise in clustering. Patt. Recogn. Lett. 12, 657–664 (1991)CrossRefGoogle Scholar
  5. 5.
    Komazaki, Y., Miyamoto, S.: Variables for controlling cluster sizes on fuzzy c-means. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., Megías, D. (eds.) MDAI 2013. LNCS (LNAI), vol. 8234, pp. 192–203. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-41550-0_17CrossRefGoogle Scholar
  6. 6.
    Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1, 98–110 (1993)CrossRefGoogle Scholar
  7. 7.
    Krishnapuram, R., Keller, J.M.: The possibilistic \(c\)-means clustering algorithm: insights and recommendation. IEEE Trans. Fuzzy Syst. 4, 385–393 (1996)CrossRefGoogle Scholar
  8. 8.
    Leski, J.M.: Fuzzy \(c\)-ordered-means clustering. Fuzzy Sets Syst. 286, 114–133 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Miyamoto, S., Kurosawa, N.: Controlling cluster volume sizes in fuzzy \(c\)-means clustering. In: SCIS and ISIS, Yokohama, Japan, pp. 1–4 (2004)Google Scholar
  10. 10.
    Pedrycz, W.: Conditional fuzzy \(c\)-means. Patt. Recogn. Lett. 17, 625–631 (1996)CrossRefGoogle Scholar
  11. 11.
    Szilágyi, L., Szilágyi, S.M.: A possibilistic c-means clustering model with cluster size estimation. In: Mendoza, M., Velastín, S. (eds.) CIARP 2017. LNCS, vol. 10657, pp. 661–668. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-75193-1_79CrossRefGoogle Scholar
  12. 12.
    Xie, X.L., Beni, G.A.: Validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell. 3, 841–846 (1991)CrossRefGoogle Scholar
  13. 13.
    Yang, M.S.: On a class of fuzzy classification maximum likelihood procedures. Fuzzy Sets Syst. 57, 365–375 (1993)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • László Szilágyi
    • 1
    • 2
  • Szidónia Lefkovits
    • 3
  • Zsolt Levente Kucsván
    • 1
  1. 1.Computational Intelligence Research GroupSapientia - Hungarian Science University of TransylvaniaTîrgu MureşRomania
  2. 2.Department of Control Engineering and Information TechnologyBudapest University of Technology and EconomicsBudapestHungary
  3. 3.Department of InformaticsPetru Maior UniversityTîrgu MureşRomania

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