The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank-one factors needed to …. In this paper, we introduce and study a related quantity, called the restricted nonnegative rank. We show that computing …. This in turn sheds new light on the nonnegative rank problem, and in particular allows us to provide new improved lower …

. Finally, we discuss the use of these heuristics to gain insight on the behavior of the nonnegative rank, i.e., the minimum … factorization rank such that an exact NMF exists. In particular, we disprove a conjecture on the nonnegative rank of a Kronecker … extension complexity of regular n-gons and (ii) the nonnegative rank of a submatrix of the slack matrix of the correlation …