Negative Binomial Matrix Factorization

Olivier Gouvert (1) , Thomas Oberlin (1) , Cédric Févotte (1, 2)

1 IRIT-SC - Signal et Communications
2 CNRS - Centre National de la Recherche Scientifique

We introduce negative binomial matrix factoriza-tion (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson factorization (PF) perturbed by a multiplicative term which models exposure. This term brings a degree of freedom for controlling the dispersion, making NBMF more robust to outliers. We describe a majorization-minimization (MM) algorithm for a maximum likelihood estimation of the parameters. We provide results on a recommendation task and demonstrate the ability of NBMF to efficiently exploit raw data.

Mots clés: Non-negative matrix factorization; Poisson factorization; Majorization-minimization; Over-dispersion; Collaborative filtering

Domaines: Apprentissage [cs.LG]; Machine Learning [stat.ML]

Olivier Gouvert, Thomas Oberlin, Cédric Févotte. Negative Binomial Matrix Factorization. IEEE Signal Processing Letters, 2020, 27, ⟨10.1109/LSP.2020.2991613⟩. ⟨hal-02871905⟩