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Beyond Fuzzy, Possibilistic and Rough: An Investigation of Belief Functions in Clustering

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Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

In evidential clustering, uncertainty about the assignment of objects to clusters is represented by Dempster-Shafer mass functions. The resulting clustering structure, called a credal partition, is shown to be more general than hard, fuzzy, possibility and rough partitions, which are recovered as special cases. Different algorithms to generate a credal partition are reviewed. We also describe different ways in which a credal partition, such as produced by the EVCLUS or ECM algorithms, can be summarized into any of the simpler clustering structures.

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Acknowledgments

This research was supported by the Labex MS2T, which was funded by the French Government, through the program “Investments for the future” by the National Agency for Research (reference ANR-11-IDEX-0004-02).

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Authors and Affiliations

  1. Heudiasyc, Sorbonne Universités, Université de Technologie de Compiègne, CNRS, UMR 7253, Paris, France

    Thierry Denœux

  2. Faculty of Management Sciences, Chiang Mai Rajabhat University, Chiang Mai, Thailand

    Orakanya Kanjanatarakul

Authors
  1. Thierry Denœux
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  2. Orakanya Kanjanatarakul
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Corresponding author

Correspondence to Thierry Denœux .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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Denœux, T., Kanjanatarakul, O. (2017). Beyond Fuzzy, Possibilistic and Rough: An Investigation of Belief Functions in Clustering. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_20

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42971-7

  • Online ISBN: 978-3-319-42972-4

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