  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.
