Non-negative matrix factorization - Archive ouverte HAL Accéder directement au contenu
Chapitre D'ouvrage Année : 2023

Non-negative matrix factorization

David Brie
Nicolas Gillis
  • Fonction : Auteur
  • PersonId : 1094902

Résumé

Solving a source separation problem when the data are explained by a linear mixing of non-negative sources with non-negative mixing coefficients reduces to performing a non-negative factorization (NMF) of the data matrix. This chapter addresses the concept of NMF, discusses some of its geometrical aspects, presents the model indeterminacies, leading to a non-uniqueness of the solution, and summarizes some NMF algorithms. A focus will be made on the conditions ensuring the uniqueness of the NMF solution and on the numerical methods allowing to either calculate the set of admissible (feasible) solutions or to reduce this set by incorporating additional information or constraints on the source signals and the mixing coefficients. The application of NMF to real situations of chemical data processing is illustrated with some examples of spectroscopic data analysis.
Fichier non déposé

Dates et versions

hal-04312655 , version 1 (28-11-2023)

Identifiants

  • HAL Id : hal-04312655 , version 1

Citer

David Brie, Nicolas Gillis, Saïd Moussaoui. Non-negative matrix factorization. Christian Jutten, Leonardo Tomazeli Duarte, Saïd Moussaoui. Source Separation in Physical‐Chemical Sensing, John Wiley & Sons, pp.103-149, 2023, 9781119137221. ⟨hal-04312655⟩
8 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More