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Multivariate fuzzy k-modes algorithm

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Abstract

In the fuzzy k-modes clustering, there is just one membership degree of interest by class for each individual which cannot be sufficient to model ambiguity of data precisely. It is known that the essence of a multivariate thinking allows to expose the inherent structure and meaning revealed within a set of variables classified. In this paper, a multivariate approach for membership degrees is presented to better handle ambiguous data that share properties of different clusters. This method is compared with other fuzzy k-modes methods of the literature based on a multivariate internal index that is also proposed in this paper. Synthetic and real categorical data sets are considered in this study.

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Acknowledgments

The authors would like to thank Brazilian agencies CNPq (National Council for Scientific and Technological Development) and CAPES (Coordination for the Improvement of Higher Education Personnel) for financial support.

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Authors and Affiliations

  1. Faculdade de Estudos Sociais, Universidade Federal do Amazonas (UFAM), Av. Gen. Rodrigo Octávio Jordão Ramos 3000, Campus Universitário, Coroado I, AM, 69077-000, Brazil

    Diêgo B. M. Maciel

  2. Departamento de Estatística, CCEN, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n-Cidade Universitária, Recife, PE, CEP 50740-540, Brazil

    Getulio J. A. Amaral

  3. Centro de Informática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n-Cidade Universitária, Recife, PE, CEP 50740-540, Brazil

    Renata M. C. R. de Souza

  4. Centro de Informática, Universidade Federal de Pernambuco, Av. Jornalista Anibal Fernandes, s/n-Cidade Universitária, Recife, PE, CEP 50740-540, Brazil

    Bruno A. Pimentel

Authors
  1. Diêgo B. M. Maciel
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  2. Getulio J. A. Amaral
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  3. Renata M. C. R. de Souza
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  4. Bruno A. Pimentel
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Corresponding author

Correspondence to Renata M. C. R. de Souza.

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Maciel, D.B.M., Amaral, G.J.A., de Souza, R.M.C.R. et al. Multivariate fuzzy k-modes algorithm. Pattern Anal Applic 20, 59–71 (2017). https://doi.org/10.1007/s10044-015-0465-3

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  • DOI: https://doi.org/10.1007/s10044-015-0465-3

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