Nonnegative matrix factorization using projected gradient algorithms with sparseness constraints

Recently projected gradient (PG) approaches have found many applications in solving the minimization problems underlying nonnegative matrix factorization (NMF). NMF is a linear representation of data that could lead to sparse result of natural images. To improve the parts-based representation of data some sparseness constraints have been proposed. In this paper the efficiency and execution time of five different PG algorithms and the basic multiplicative algorithm for NMF are compared. The factorization is done for an existing and proposed sparse NMF and the results are compared for all these PG methods. To compare the algorithms the resulted factorizations are used for a hand-written digit classifier.