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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.

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  • 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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