First results on uniqueness of sparse non-negative matrix factorization

Sparse non-negative matrix factorization (sNMF) allows for the decomposition of a given data set into a mixing matrix and a feature data set, which are both non-negative and fulfill certain sparsity conditions. In this paper it is shown that the employed projection step proposed by Hoyer has a unique solution, and that it indeed finds this solution. Then indeterminacies of the sNMF model are identified and first uniqueness results are presented, both theoretically and experimentally.