Bayesian mean-parameterized nonnegative binary matrix factorization - Signal et Communications Accéder directement au contenu
Article Dans Une Revue Data Mining and Knowledge Discovery Année : 2020

Bayesian mean-parameterized nonnegative binary matrix factorization

Alberto Lumbreras
Louis Filstroff
  • Fonction : Auteur
  • PersonId : 1272587
  • IdRef : 242769659

Résumé

Binary data matrices can represent many types of data such as social networks, votes, or gene expression. In some cases, the analysis of binary matrices can be tackled with nonneg-ative matrix factorization (NMF), where the observed data matrix is approximated by the product of two smaller nonnegative matrices. In this context, probabilistic NMF assumes a generative model where the data is usually Bernoulli-distributed. Often, a link function is used to map the factorization to the [0, 1] range, ensuring a valid Bernoulli mean parameter. However, link functions have the potential disadvantage to lead to uninterpretable models. Mean-parameterized NMF, on the contrary, overcomes this problem. We propose a unified framework for Bayesian mean-parameterized nonnegative binary matrix factorization models (NBMF). We analyze three models which correspond to three possible constraints that respect the mean-parameterization without the need for link functions. Furthermore, we derive a novel collapsed Gibbs sampler and a collapsed variational algorithm to infer the posterior distribution of the factors. Next, we extend the proposed models to a nonpara-metric setting where the number of used latent dimensions is automatically driven by the observed data. We analyze the performance of our NBMF methods in multiple datasets for different tasks such as dictionary learning and prediction of missing data. Experiments show that our methods provide similar or superior results than the state of the art, while automatically detecting the number of relevant components.
Fichier principal
Vignette du fichier
arxiv-1812.06866.pdf (5.65 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02933102 , version 1 (08-09-2020)

Identifiants

Citer

Alberto Lumbreras, Louis Filstroff, Cédric Févotte. Bayesian mean-parameterized nonnegative binary matrix factorization. Data Mining and Knowledge Discovery, 2020, ⟨10.1007/s10618-020-00712-w⟩. ⟨hal-02933102⟩
100 Consultations
94 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More