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A von Mises–Fisher mixture model for clustering numerical and categorical variables

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  • Xavier Bry

    (Université de Montpellier)

  • Lionel Cucala

    (Université de Montpellier)

Abstract

This work presents a mixture model allowing to cluster variables of different types. All variables being measured on the same n statistical units, we first represent every variable with a unit-norm operator in $${\mathbb {R}}^{n\times n}$$ R n × n endowed with an appropriate inner product. We propose a von Mises–Fisher mixture model on the unit-sphere containing these operators. The parameters of the mixture model are estimated with an EM algorithm, combined with a K-means procedure to obtain a good starting point. The method is tested on simulated data and eventually applied to wine data.

Suggested Citation

  • Xavier Bry & Lionel Cucala, 2022. "A von Mises–Fisher mixture model for clustering numerical and categorical variables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 429-455, June.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:2:d:10.1007_s11634-021-00449-4
    DOI: 10.1007/s11634-021-00449-4
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    References listed on IDEAS

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    1. Hornik, Kurt & Feinerer, Ingo & Kober, Martin & Buchta, Christian, 2012. "Spherical k-Means Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i10).
    2. Grün, Bettina & Leisch, Friedrich, 2008. "FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i04).
    3. Henk Kiers, 1991. "Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 197-212, June.
    4. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    5. Hornik, Kurt & Grün, Bettina, 2014. "movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i10).
    6. Chavent, Marie & Kuentz-Simonet, Vanessa & Liquet, Benoît & Saracco, Jérôme, 2012. "ClustOfVar: An R Package for the Clustering of Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i13).
    7. Celeux, Gilles & Govaert, Gerard, 1992. "A classification EM algorithm for clustering and two stochastic versions," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 315-332, October.
    8. P. Robert & Y. Escoufier, 1976. "A Unifying Tool for Linear Multivariate Statistical Methods: The RV‐Coefficient," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(3), pages 257-265, November.
    9. Kurt Hornik & Bettina Grün, 2014. "On maximum likelihood estimation of the concentration parameter of von Mises–Fisher distributions," Computational Statistics, Springer, vol. 29(5), pages 945-957, October.
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