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Descent methods for Nonnegative Matrix Factorization

Authors
  • Ho, Ngoc-Diep
  • Van Dooren, Paul
  • Blondel, Vincent D.
Type
Preprint
Publication Date
Aug 24, 2009
Submission Date
Jan 21, 2008
Identifiers
arXiv ID: 0801.3199
Source
arXiv
License
Yellow
External links

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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