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

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