Minimum-Volume Nonnegative Matrix Completion

Low-rank matrix approximation is a standard, yet powerful, embedding technique that can be used to tackle a broad range of problems, including the recovery of missing data. In this paper, we focus on the performance of nonnegative matrix factorization (NMF) with minimum-volume (MinVol) regularization on the task of nonnegative data imputation. The particular choice of the MinVol regularization is justified by its interesting identifiability property and by its link with the nuclear norm. We show experimentally that MinVol NMF is a relevant model for nonnegative data recovery, especially when the recovery of a unique embedding is desired. Additionally, we introduce a new version of MinVol NMF that exhibits some promising results.