Fast Conical Hull Algorithms for Near-separable Non-negative Matrix Factorization
This work addresses the problem of scalable and robust NMF for researchers and practitioners in machine learning and data analysis, but it is incremental as it builds on existing separable NMF methods.
The paper tackled the separable non-negative matrix factorization (NMF) problem by reformulating it as finding extreme rays of a conical hull, resulting in new algorithms that are highly scalable and empirically noise robust, with a parallel implementation showing high scalability on shared- and distributed-memory machines.
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 robust, 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.