2011 • Other
Descent methods for nonnegative matrix factorization
Authors:
Ho, Ngoc Diep,
Van Dooren, Paul,
Blondel, Vincent
Published in:
Numerical Linear Algebra in Signals, Systems and Control
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.