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...

We study the problem of constructing explicit families matrices which cannot be expressed as a product few sparse matrices. In addition to being natural mathematical question on its own, this appears in various incarnations computer science; most significant context lower bounds for algebraic circuits compute linear transformations, matrix rigidity and data structure bounds. first show, every c...