Split gradient method for nonnegative matrix factorization

This article deals with an extension of the split gradient method (SGM) applied to the optimization of any divergence between two data fields, under positivity and flux conservation constraints. SGM is guaranteed to converge for convex cost functions. A SGM-based algorithm is also derived to solve the nonnegative matrix factorization (NMF) problem. It is shown that the multiplicative algorithms that are usually used for NMF, under positivity constraints, are particular cases of SGM. Finally, to validate the algorithm, we propose an example of application to hyperspectral data unmixing.