Descent methods for Nonnegative Matrix Factorization
For researchers working on nonnegative matrix and tensor factorization, this work offers an improved method with theoretical guarantees, though it is incremental in nature.
The paper presents and analyzes descent methods for nonnegative matrix factorization, showing that a new block coordinate method (RRI) achieves better approximation error and complexity. It proves convergence and extends the method to nonnegative tensor factorization with additional constraints.
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.