%0 Journal Article
%T Descent methods for Nonnegative Matrix Factorization
%A Ngoc-Diep Ho
%A Paul Van Dooren
%A Vincent D. Blondel
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0801.3199v3