We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns first NMF factor are equal to input matrix, while second sparse. call this sparse separable (SSNMF), which we prove be NP-complete, as opposed can solved in polynomial time. The main motivation consider model is handle underdetermined blind ...

Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation, and hyperspectral unmixing. Given MM rank rr, NMF looks WW rr columns HH rows that M ≈ WHM≈WH. NP-hard to solve in general. However, it can be computed efficiently under the separability assumption which requires basis v...

Nonnegative matrix factorization NMF is a popular tool for analyzing the latent structure of nonnegative data. For a positive pairwise similarity matrix, symmetric NMF SNMF and weighted NMF WNMF can be used to cluster the data. However, both of them are not very efficient for the ill-structured pairwise similarity matrix. In this paper, a novel model, called relationship matrix nonnegative deco...

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n×m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d ×m matrix H. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are also rational. We answer this question negat...

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n×m matrix M into a product of a nonnegative n× d matrix W and a nonnegative d ×m matrix H . A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are also rational. We answer this question negat...