Extraction of Food Consumption Systems by Nonnegative Matrix Factorization (NMF) for the Assessment of Food Choices

Authors

  • Mélanie Zetlaoui,

    Corresponding author
    1. Institut de la Recherche Agronomique (INRA), Métarisk, 16 rue Claude Bernard, 75231 Paris cedex 05, France
      email: melanie.zetlaoui@agroparistech.fr
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  • Max Feinberg,

    1. Institut de la Recherche Agronomique (INRA), Métarisk, 16 rue Claude Bernard, 75231 Paris cedex 05, France
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  • Philippe Verger,

    1. Institut de la Recherche Agronomique (INRA), Métarisk, 16 rue Claude Bernard, 75231 Paris cedex 05, France
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  • Stephan Clémençon

    Corresponding author
    1. LTCI UMR Telecom ParisTech/CNRS No. 5141, 46 rue Barrault, 75634 Paris cedex 13, France
      email: stephan.clemencon@telecom-paristech.fr
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email:melanie.zetlaoui@agroparistech.fr

email:stephan.clemencon@telecom-paristech.fr

Abstract

Summary In Western countries where food supply is satisfactory, consumers organize their diets around a large combination of foods. It is the purpose of this article to examine how recent nonnegative matrix factorization (NMF) techniques can be applied to food consumption data to understand these combinations. Such data are nonnegative by nature and of high dimension. The NMF model provides a representation of consumption data through latent vectors with nonnegative coefficients, that we call consumption systems (CS), in a small number. As the NMF approach may encourage sparsity of the data representation produced, the resulting CS are easily interpretable. Beyond the illustration of its properties we provide through a simple simulation result, the NMF method is applied to data issued from a French consumption survey. The numerical results thus obtained are displayed and thoroughly discussed. A clustering based on the k-means method is also achieved in the resulting latent consumption space, to recover food consumption patterns easily usable for nutritionists.

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