NMF method aim to factorize a non-negative observation matrix X as the product X =G.F between two non-negative matrices G and F, respectively the matrix of contributions and profiles. Although these approaches are studied with great interest by the scientific community, they often suffer from a lack of robustness with regard to data and initial conditions and can present multiple solutions. The work of this chapter aims to examine the different approaches of NMF, thus introducing the constraint of sparsity in order to avoid local minima. The NMF can be informed by introducing desired constraints on the matrix F (resp G) such as the sum of 1 of each of its lines. Applications on images made it possible to test the interest of many algorithms in terms of precision and speed.
Blind source separation with optimal transport non-negative matrix factorization
