Advertisement

Abstract

Possibilistic clustering methods have gained attention in both applied and theoretical research. In this paper, we formulate a general objective function for possibilistic clustering. The objective function can be used as the basis of a mixed clustering approach incorporating both fuzzy memberships and possibilistic typicality values to overcome various problems of previous clustering approaches. We use numerical experiments for a classification task to illustrate the usefulness of the proposal. Beyond a performance comparison with the three most widely used (mixed) possibilistic clustering methods, this also outlines the use of possibilistic clustering for descriptive classification via memberships to a variety of different class clusters. We find that possibilistic clustering using the general objective function outperforms traditional approaches in terms of various performance measures.

Keywords

Possibilistic clustering Membership function Typicality values Classification 

References

  1. 1.
    Alam, P., Booth, D., Lee, K., Thordarson, T.: The use of fuzzy clustering algorithm and self-organizing neural networks for identifying potentially failing banks: an experimental study. Expert Syst. Appl. 18(3), 185–199 (2000)CrossRefGoogle Scholar
  2. 2.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers, Berlin (1981)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bezdek, J.C., Harris, J.D.: Fuzzy partitions and relations; an axiomatic basis for clustering. Fuzzy Sets Syst. 1(2), 111–127 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bradley, A.P.: The use of the area under the roc curve in the evaluation of machine learning algorithms. Pattern Recogn. 30(7), 1145–1159 (1997)CrossRefGoogle Scholar
  5. 5.
    Chuang, K.S., Tzeng, H.L., Chen, S., Wu, J., Chen, T.J.: Fuzzy c-means clustering with spatial information for image segmentation. Comput. Med. Imaging Graph. 30(1), 9–15 (2006)CrossRefGoogle Scholar
  6. 6.
    Döring, C., Lesot, M.J., Kruse, R.: Data analysis with fuzzy clustering methods. Comput. Stat. Data Anal. 51(1), 192–214 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Haberman, S.J.: Generalized residuals for log-linear models. In: Proceedings of the 9th international biometrics conference, pp. 104–122 (1976)Google Scholar
  8. 8.
    Höppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis: Methods For Classification, Data Analysis and Image Recognition. Wiley, Hoboken (1999)zbMATHGoogle Scholar
  9. 9.
    Ji, Z., Xia, Y., Sun, Q., Cao, G.: Interval-valued possibilistic fuzzy c-means clustering algorithm. Fuzzy Sets Syst. 253, 138–156 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kohavi, R.: Scaling up the accuracy of naive-bayes classifiers: a decision-tree hybrid. In: Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, pp. 202–207 (1996)Google Scholar
  11. 11.
    Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1(2), 98–110 (1993)CrossRefGoogle Scholar
  12. 12.
    Marghescu, D., Sarlin, P., Liu, S.: Early-warning analysis for currency crises in emerging markets: a revisit with fuzzy clustering. Intell. Syst. Account. Finance Manage. 17(3–4), 143–165 (2010)CrossRefGoogle Scholar
  13. 13.
    Masulli, F., Schenone, A.: A fuzzy clustering based segmentation system as support to diagnosis in medical imaging. Artif. Intell. Med. 16(2), 129–147 (1999)CrossRefGoogle Scholar
  14. 14.
    Min, J.H., Shim, E.A., Rhee, F.C.H.: An interval type-2 fuzzy pcm algorithm for pattern recognition. In: 2009 IEEE International Conference on Fuzzy Systems, pp. 480–483. IEEE (2009)Google Scholar
  15. 15.
    Pal, N.R., Pal, K., Bezdek, J.C.: A mixed c-means clustering model. In: Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, vol. 1, pp. 11–21. IEEE (1997)Google Scholar
  16. 16.
    Pal, N.R., Pal, K., Keller, J.M., Bezdek, J.C.: A possibilistic fuzzy c-means clustering algorithm. IEEE Trans. Fuzzy Syst. 13(4), 517–530 (2005)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Runkler, T.A., Bezdek, J.C.: Alternating cluster estimation: a new tool for clustering and function approximation. IEEE Trans. Fuzzy Syst. 7(4), 377–393 (1999)CrossRefGoogle Scholar
  18. 18.
    Sarlin, P.: On policymakers’ loss functions and the evaluation of early warning systems. Econ. Lett. 119(1), 1–7 (2013)CrossRefGoogle Scholar
  19. 19.
    Setnes, M.: Supervised fuzzy clustering for rule extraction. IEEE Trans. Fuzzy Syst. 8(4), 416–424 (2000)CrossRefGoogle Scholar
  20. 20.
    Sigillito, V.G., Wing, S.P., Hutton, L.V., Baker, K.B.: Classification of radar returns from the ionosphere using neural networks. Johns Hopkins APL Techn. Dig. 10, 262–266 (1989)Google Scholar
  21. 21.
    Timm, H., Borgelt, C., Döring, C., Kruse, R.: An extension to possibilistic fuzzy cluster analysis. Fuzzy Sets Syst. 147(1), 3–16 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Yeh, I.C., Yang, K.J., Ting, T.M.: Knowledge discovery on rfm model using bernoulli sequence. Expert Syst. Appl. 36(3), 5866–5871 (2009)CrossRefGoogle Scholar
  23. 23.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Social Sciences, Business and EconomicsÅbo Akademi UniversityTurkuFinland
  2. 2.Department of EconomicsHanken School of EconomicsHelsinkiFinland
  3. 3.RiskLab Finland at Arcada University of Applied SciencesHelsinkiFinland

Personalised recommendations