Fast Nonnegative Matrix Factorization and Completion Using Nesterov Iterations

In this paper, we aim to extend Nonnegative Matrix Factorization with Nesterov iterations (Ne-NMF)—well-suited to large-scale problems—to the situation when some entries are missing in the observed matrix. In particular, we investigate the Weighted and Expectation-Maximization strategies which both provide a way to process missing data. We derive their associated extensions named W-NeNMF and EM-W-NeNMF, respectively. The proposed approaches are then tested on simulated nonnegative low-rank matrix completion problems where the EM-W-NeNMF is shown to outperform state-of-the-art methods and the W-NeNMF technique.