Descent methods for Nonnegative Matrix Factorization
Abstract
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.
Cite
@article{arxiv.0801.3199,
title = {Descent methods for Nonnegative Matrix Factorization},
author = {Ngoc-Diep Ho and Paul Van Dooren and Vincent D. Blondel},
journal= {arXiv preprint arXiv:0801.3199},
year = {2009}
}
Comments
47 pages. New convergence proof using damped version of RRI. To appear in Numerical Linear Algebra in Signals, Systems and Control. Accepted. Illustrating Matlab code is included in the source bundle