A Comparative Study of Temporal Non-Negative Matrix Factorization with Gamma Markov Chains - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

A Comparative Study of Temporal Non-Negative Matrix Factorization with Gamma Markov Chains

Louis Filstroff
  • Fonction : Auteur
  • PersonId : 1272587
  • IdRef : 242769659
Olivier Gouvert
  • Fonction : Auteur
  • PersonId : 1073296
  • IdRef : 237241544
Cédric Févotte
Olivier Cappé

Résumé

Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis of non-negative data. In particular, a lot of effort has been devoted to probabilistic NMF, namely estimation or inference tasks in probabilistic models describing the data, based for example on Pois-son or exponential likelihoods. When dealing with time series data, several works have proposed to model the evolution of the activation coefficients as a non-negative Markov chain, most of the time in relation with the Gamma distribution, giving rise to so-called temporal NMF models. In this paper, we review three Gamma Markov chains of the NMF literature, and show that they all share the same drawback: the absence of a well-defined stationary distribution. We then introduce a fourth process, an overlooked model of the time series literature named BGAR(1), which overcomes this limitation. These four temporal NMF models are then compared in a MAP framework on a prediction task, in the context of the Poisson likelihood.
Fichier principal
Vignette du fichier
submitted.pdf (433.95 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02883800 , version 1 (29-06-2020)
hal-02883800 , version 2 (18-02-2021)
hal-02883800 , version 3 (01-03-2021)

Identifiants

  • HAL Id : hal-02883800 , version 1

Citer

Louis Filstroff, Olivier Gouvert, Cédric Févotte, Olivier Cappé. A Comparative Study of Temporal Non-Negative Matrix Factorization with Gamma Markov Chains. 2020. ⟨hal-02883800v1⟩
222 Consultations
144 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More