Convex nonnegative matrix factorization with missing data

Abstract

Convex nonnegative matrix factorization (CNMF) is a variant of nonnegative matrix factorization (NMF) in which the components are a convex combination of atoms of a known dictionary. In this contribution, we propose to extend CNMF to the case where the data matrix and the dictionary have missing entries. After a formulation of the problem in this context of missing data, we propose a majorization-minimization algorithm for the solving of the optimization problem incurred. Experimental results with synthetic data and audio spectrograms highlight an improvement of the performance of reconstruction with respect to standard NMF. The performance gap is particularly significant when the task of reconstruction becomes arduous, e.g. when the ratio of missing data is high, the noise is steep, or the complexity of data is high.