First Order Methods for Robust Non-negative Matrix Factorization for Large Scale Noisy Data

Abstract

Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or rows) [1]. In real applications, however, such separability assumption is hard to satisfy. Following [4] and [5], in this paper, we look at the Linear Programming (LP) based reformulation to locate the extreme rays of the convex cone but in a noisy setting. Furthermore, in order to deal with the large scale data, we employ First-Order Methods (FOM) to mitigate the computational complexity of LP, which primarily results from a large number of constraints. We show the performance of the algorithm on real and synthetic data sets.