Descent methods for nonnegative matrix factorization

Ho, Ngoc Diep;Van Dooren, Paul;Blondel, Vincent
(2011) Numerical Linear Algebra in Signals, Systems and Control — ISBN: [978-94-007-0602-6], 251-293, published

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  • Ho, Ngoc DiepUCLouvain
    Author
  • Van Dooren, PaulUCLouvain
    Author
  • Blondel, Vincentorcid-logoUCLouvain
    Author
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.
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Ho, N. D., Van Dooren, P., & Blondel, V. (2011). Descent methods for nonnegative matrix factorization. In Van Dooren Paul et al (ed.), Numerical Linear Algebra in Signals, Systems and Control (pp. 251-293). Springer Verlag. https://doi.org/10.1007/978-94-007-0602-6_13