Fast Conical Hull Algorithms for Near-separable Non-negative Matrix Factorization [article]

Abhishek Kumar, Vikas Sindhwani, Prabhanjan Kambadur
2012 arXiv   pre-print
The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. From this geometric perspective, we derive new separable NMF algorithms that are highly scalable and empirically noise
more » ... ust, and have several other favorable properties in relation to existing methods. A parallel implementation of our algorithm demonstrates high scalability on shared- and distributed-memory machines.
arXiv:1210.1190v1 fatcat:pbcp77uzwzf7to364f5rqf25f4