A PROJECTIVE APPROACH TO NONNEGATIVE MATRIX FACTORIZATION

In data science and machine learning, the method of nonnegative matrix factorization (NMF) is a powerful tool that enjoys great popularity. Depending on the concrete application, there exist several subclasses each of which performs a NMF under certain constraints. Consider a given square matrix A. The symmetric NMF aims for a nonnegative low-rank approximation A approximate to XXT to A, where X is entrywise nonnegative and of given order. Considering a rectangular input matrix A, the general NMF again aims for a nonnegative low-rank approximation to A which is now of the type A approximate to XY for entrywise nonnegative matrices X, Y of given order. In this paper, we introduce a new heuristic method to tackle the exact nonnegative matrix factorization problem (of type A = XY), based on projection approaches to solve a certain feasibility problem.