Sparse Separable Nonnegative Matrix Factorization

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 source separation problems, such multispectral image unmixing. introduce an algorithm solve SSNMF, based on successive projection (SNPA, effective for NMF), exact least squares solver. that, noiseless settings under mild assumptions, our recovers true underlying sources. This illustrated by experiments synthetic data sets unmixing image.