# A majorization-minimization algorithm for nonnegative binary matrix factorization

arXiv: https://arxiv.org/abs/2204.09741 · HTML: https://mlsanity.com/paper/2204.09741/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 20 Apr 2022.

## Builds on (most cited first, 6 of 6)

- [Probabilistic Latent Semantic Analysis](https://mlsanity.com/paper/1301.6705/) (2013)
- [Infinite Edge Partition Models for Overlapping Community Detection and Link Prediction](https://mlsanity.com/paper/1501.06218/) (2015)
- [Dimensionality Reduction for Binary Data through the Projection of Natural Parameters](https://mlsanity.com/paper/1510.06112/) (2015)
- [Providing reliability in Recommender Systems through Bernoulli Matrix Factorization](https://mlsanity.com/paper/2006.03481/) (2020)
- [Bayesian Mean-parameterized Nonnegative Binary Matrix Factorization](https://mlsanity.com/paper/1812.06866/) (2018)
- [L'evy NMF for robust nonnegative source separation](https://mlsanity.com/paper/1608.01844/) (2016)

## Built on by (most cited first, 1 of 1)

- [A Majorization-Minimization Gauss-Newton Method for 1-Bit Matrix Completion](https://mlsanity.com/paper/2304.13940/) (2023)

## Abstract (arXiv)

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.