A Possibilistic c-means Clustering Model with Cluster Size Estimation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10657)

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 two parameters independently of the number of clusters, which is able to correctly 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 sensitivity 

References

  1. 1.
    Anderson, E.: The irises of the Gaspe Peninsula. Bull. Am. Iris Soc. 59, 2–5 (1935)Google Scholar
  2. 2.
    Asuncion, A., Newman, D.J.: UCI Machine Learning Repository. http://archive.ics.uci.edu/ml/datasets.html
  3. 3.
    Barni, M., Capellini, V., Mecocci, A.: Comments on a possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 4, 393–396 (1996)CrossRefGoogle Scholar
  4. 4.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)CrossRefMATHGoogle Scholar
  5. 5.
    Dave, R.N.: Characterization and detection of noise in clustering. Pattern Recogn. Lett. 12, 657–664 (1991)CrossRefGoogle Scholar
  6. 6.
    Dunn, J.C.: A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters. Cybern. Syst. 3(3), 32–57 (1973)MathSciNetMATHGoogle Scholar
  7. 7.
    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_17 CrossRefGoogle Scholar
  8. 8.
    Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1, 98–110 (1993)CrossRefGoogle Scholar
  9. 9.
    Leski, J.M.: Fuzzy \(c\)-ordered-means clustering. Fuzzy Sets Syst. 286, 114–133 (2016)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Lin, P.L., Huang, P.W., Kuo, C.H., Lai, Y.H.: A size-insensitive integrity-based fuzzy \(c\)-means method for data clustering. Pattern Recogn. 47(5), 2024–2056 (2014)CrossRefGoogle Scholar
  11. 11.
    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
  12. 12.
    Pal, N.R., Pal, K., Bezdek, J.C.: A mixed \(c\)-means clustering model. In: Proceedings of IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 11–21 (1997)Google Scholar
  13. 13.
    Pal, N.R., Pal, K., Keller, J.M., Bezdek, J.C.: A possibilistic fuzzy \(c\)-means clustering algorithm. IEEE Trans. Fuzzy Syst. 13, 517–530 (2005)CrossRefGoogle Scholar
  14. 14.
    Szilágyi, L.: Fuzzy-possibilistic product partition: a novel robust approach to c-means clustering. In: Torra, V., Narakawa, Y., Yin, J., Long, J. (eds.) MDAI 2011. LNCS (LNAI), vol. 6820, pp. 150–161. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22589-5_15 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computational Intelligence Research GroupSapientia - Hungarian Science University of TransylvaniaTîrgu MureşRomania
  2. 2.Department of InformaticsPetru Maior UniversityTîrgu MureşRomania

Personalised recommendations