  In this paper, we present several descent methods that can be applied to
nonnegative matrix factorization and we analyze a recently developped fast
block coordinate method called Rank-one Residue Iteration (RRI). 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
prove that it \emph{converges} and 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.
