  A robust algorithm for non-negative matrix factorization (NMF) is presented
in this paper with the purpose of dealing with large-scale data, where the
separability assumption is satisfied. In particular, we modify the Linear
Programming (LP) algorithm of [9] by introducing a reduced set of constraints
for exact NMF. In contrast to the previous approaches, the proposed algorithm
does not require the knowledge of factorization rank (extreme rays [3] or
topics [7]). Furthermore, motivated by a similar problem arising in the context
of metabolic network analysis [13], we consider an entirely different regime
where the number of extreme rays or topics can be much larger than the
dimension of the data vectors. The performance of the algorithm for different
synthetic data sets are provided.
