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Pattern Recognition and Image Analysis

, Volume 28, Issue 1, pp 1–10 | Cite as

A Probabilistic Model of Fuzzy Clustering Ensemble

  • V. B. Berikov
Mathematical Method in Pattern Recognition
  • 54 Downloads

Abstract

A probabilistic model of clustering ensemble based on a collection of fuzzy clustering algorithms and a weighted co-association matrix is proposed. An expression for the upper bound of the misclassification probability of an arbitrary pair of objects is obtained depending on the characteristics of the ensemble. This expression is used to determine the optimal weights of the algorithms.

Keywords

fuzzy cluster analysis collective decision-making misclassification probability 

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References

  1. 1.
    A. K. Jain, “Data clustering: 50 years beyond kmeans,” Pattern Recogn. Lett. 31 (8), 651–666 (2010).CrossRefGoogle Scholar
  2. 2.
    F. Hoppner, F. Klawonn, R. Kruse, and T. Runkler, Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition (Wiley, 1999).zbMATHGoogle Scholar
  3. 3.
    J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms (Kluwer Acad. Publ., Norwell, MA, 1981).CrossRefzbMATHGoogle Scholar
  4. 4.
    L. Fu and E. Medico, “FLAME: a novel fuzzy clustering method for the analysis of DNA microarray data,” BMC Bioinf. 8 (3) (2007).Google Scholar
  5. 5.
    J. Yao, M. Dash, S. T. Tan, and H. Liu, “Entropybased fuzzy clustering and fuzzy modeling,” Fuzzy Sets Syst. 113, 381–388 (2000).CrossRefzbMATHGoogle Scholar
  6. 6.
    M. Gimiami, “Mercer kernel based clustering in feature space,” IEEE Trans. Neural Networks 3 (3), 780–784 (2002).Google Scholar
  7. 7.
    J. Ghosh and A. Acharya, “Cluster ensembles,” Wiley Interdiscipl. Rev.: Data Mining Knowledge Discovery 1 (4), 305–315 (2011).Google Scholar
  8. 8.
    S. Vega-Pons and J. Ruiz-Shulcloper, “A survey of clustering ensemble algorithms,” Int. J. Pattern Recogn. Artif. Intellig. 25 (3), 337–372 (2011).MathSciNetCrossRefGoogle Scholar
  9. 9.
    Yu. I. Zhuravlev and V. V. Nikiforov, “Algorithms for recognition based on calculation of evaluations,” Kibernetika 3, 1–11 (1971).Google Scholar
  10. 10.
    V. V. Ryazanov, “On the synthesis of classifying algorithms in finite sets of classification algorithms (taxonomy),” USSR Comput. Math. Math. Phys. 22 (2), 186–198 (1982).CrossRefzbMATHGoogle Scholar
  11. 11.
    L. Breiman, “Random forests,” Mach. Learn. 45 (1), 5–32 (2001).CrossRefzbMATHGoogle Scholar
  12. 12.
    L. Kuncheva, Combining Pattern Classifiers. Methods and Algorithms (Wiley, NJ, 2004).CrossRefzbMATHGoogle Scholar
  13. 13.
    R. Schapire, Y. Freund, P. Bartlett, and W. Lee, “Boosting the margin: a new explanation for the effectiveness of voting methods,” Ann. Stat. 26 (5), 1651–1686 (1998).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    A. Topchy, M. Law, A. Jain, and A. Fred, “Analysis of consensus partition in cluster ensemble,” in Proc. 4th IEEE Int. Conf. on Data Mining (ICDM’04) (Brighton, 2004), pp. 225–232.CrossRefGoogle Scholar
  15. 15.
    A. Fred and A. Jain, “Combining multiple clusterings using evidence accumulation,” IEEE Trans. Pattern Anal. Mach. Intellig. 27, 835–850 (2005).CrossRefGoogle Scholar
  16. 16.
    R. Avogadri and G. Valentini, “Ensemble clustering with a fuzzy approach,” Stud. Comput. Intellig. 126, 49–69 (2008).Google Scholar
  17. 17.
    X. Sevillano, F. Alias, and J. Socoro, “Positional and confidence voting-based consensus functions for fuzzy cluster ensembles,” Fuzzy Sets Syst. 193, 1–32 (2012).MathSciNetCrossRefGoogle Scholar
  18. 18.
    P. Su, C. Shang, and Q. Shen, “Link-based pairwise similarity matrix approach for fuzzy c-means clustering ensemble,” in IEEE Int. Conf. on Fuzzy Systems (FUZZIEEE) (Beijing, 2014), pp. 1538–1544.Google Scholar
  19. 19.
    S. Kullback and R. A. Leibler, “On information and sufficiency,” Ann. Math. Stat. 22 (1), 79–86 (1951).MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    T. Kailath, “The divergence and Bhattacharyya distance measures in signal selection,” IEEE Trans. Commun. 15 (1), 52–60 (1967).CrossRefGoogle Scholar
  21. 21.
    V. Berikov, “Cluster ensemble with averaged co-association matrix maximizing the expected margin,” in Proc. 9th Int. Conf. on Discrete Optimization and Operations Research and Scientific School (DOOR 2016) (Vladivostok, Sept. 19–23, 2016), No. CEUR-WS.org/Vol-1623, pp. 489–500. http://ceur-ws.org/Vol- 1623/papercpr1.pdfGoogle Scholar
  22. 22.
    G. Casella and R. L. Berger, Statistical Inference (Thomson Learning, 2002).zbMATHGoogle Scholar
  23. 23.
    S. S. Wilks, Mathematical Statistics (Wiley, New York, 1962).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsSiberian Branch, Russian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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