Given a nonnegative matrix factorization, , and factorization rank, exact (exact NMF) decomposes as the product of two matrices, with columns, such . A central research topic in literature is conditions under which decomposition unique/identifiable up to trivial ambiguities. In this paper, we focus on partial identifiability, that is, uniqueness subset columns We start our investigations data‐b...

Given a nonnegative matrix M , the orthogonal nonnegative matrix factorization (ONMF) problem consists in finding a nonnegative matrix U and an orthogonal nonnegative matrix V such that the product UV is as close as possible to M . The importance of ONMF comes from its tight connection with data clustering. In this paper, we propose a new ONMF method, called ONP-MF, and we show that it performs...

By a nonnegative matrix we mean a matrix whose entries are nonnegative real numbers. By positive matrix we mean a matrix all of whose entries are strictly positive real numbers. These notes give the core elements of the Perron-Frobenius theory of nonnegative matrices. This splits into three parts: (1) the primitive case (due to Perron) (2) the irreducible case (due to Frobenius) (3) the general...

The exact nonnegative matrix factorization (exact NMF) problem is the following: given an m-by-n nonnegative matrix X and a factorization rank r, find, if possible, an m-by-r nonnegative matrix W and an r-by-n nonnegative matrix H such that X = WH . In this paper, we propose two heuristics for exact NMF, one inspired from simulated annealing and the other from the greedy randomized adaptive sea...