In Western countries where food supply is satisfactory, consumers organize their diets around a large combination of foods. It is the purpose of this paper to examine how recent nonnegative matrix fac- torization (NMF) techniques can be applied to food consumption data in order 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 coe cients, we call consumption systems, in a small number. As the NMF approach may encourage sparsity of the data representation produced, the resulting consumption systems 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, in order to recover food consumption patterns easily usable for nutritionists. Extraction of food consumption systems by non-negative matrix factorization (NMF) for the assessment of food choices.

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