Fe b 20 08 Descent methods for Nonnegative Matrix

In this paper, we present several descent methods that can be applied to nonnegative matrix factorization and we analyze a recently developed fast block coordinate method. We also give a comparison of these different methods and show that the new block coordinate method has better properties in terms of approximation error and complexity. By interpreting this method as a rank-one approximation of the residue matrix, we also extend it to the nonnegative tensor factorization and introduce some variants of the method by imposing some additional controllable constraints such as: sparsity, discreteness and smoothness.