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Extraction of Food Consumption Systems by Nonnegative Matrix Factorization (NMF) for the Assessment of Food Choices
Author(s) -
Zetlaoui Mélanie,
Feinberg Max,
Verger Philippe,
Clémençon Stephan
Publication year - 2011
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2011.01588.x
Subject(s) - non negative matrix factorization , dimension (graph theory) , consumption (sociology) , cluster analysis , representation (politics) , computer science , food consumption , nonnegative matrix , usable , matrix decomposition , data mining , mathematics , artificial intelligence , combinatorics , economics , symmetric matrix , social science , eigenvalues and eigenvectors , physics , quantum mechanics , sociology , politics , agricultural economics , political science , world wide web , law
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.