A Majorization-Minimization Algorithm for Nonnegative Binary Matrix Factorization

This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli param...

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Veröffentlicht in:IEEE signal processing letters Jg. 29; S. 1526 - 1530
Hauptverfasser: Magron, Paul, Fevotte, Cedric
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.01.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Schlagworte:
Algorithms
Bayesian analysis
Binary data
Biological system modeling
Computational modeling
Computer Science
Data models
Estimation
Factorization
Information Retrieval
Logistics
majorization-minimization
Mathematical models
mean-parametrized Bernoulli model
nonnegative matrix factorization
Optimization
Parameters
Performance enhancement
Principal component analysis
Statistical inference
Upper bound
binary data
mean-parametrized Bernoulli model
majorization-minimization
nonnegative matrix factorization
ISSN:1070-9908, 1558-2361
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Zusammenfassung:This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an additional Beta prior on one of the factors to further improve the model's expressive power. While similar models have been proposed in the literature, they only exploit the Beta prior as a proxy to ensure a valid Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform or uninformative prior. Besides, estimation in these models has focused on costly Bayesian inference. In this paper, we propose a simple yet very efficient majorization-minimization algorithm for maximum a posteriori estimation. Our approach leverages the Beta prior whose parameters can be tuned to improve performance in matrix completion tasks. Experiments conducted on three public binary datasets show that our approach offers an excellent trade-off between prediction performance, computational complexity, and interpretability.
Bibliographie:ObjectType-Article-1
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2022.3187368