Automatic Relevance Determination in Nonnegative Matrix Factorization

Abstract

This paper addresses the problem of estimating the latent dimensionality in nonnegative matrix fatorization (NMF) via automatic relevance determination (ARD). Uncovering the latent dimensionality is necessary for striking the right balance between data fidelity and overfitting. We propose a Bayesian model for NMF and two algorithms known as ℓ1- and ℓ2-ARD, each assuming different priors on the basis and the coefficients. The proposed algorithms leverage on the recent algorithmic advances in NMF with the β-divergence using majorization-minimization (MM) methods. We show by using auxiliary functions that the cost function decreases monotonically to a local minimum. We demonstrate the efficacy and robustness of our algorithms by performing experiments on the swimmer dataset. 1