Descent methods for Nonnegative Matrix Factorization
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Publication:6208172
DOI10.1007/978-94-007-0602-6_13arXiv0801.3199MaRDI QIDQ6208172
Vincent D. Blondel, Ngoc-Diep Ho, Paul Van Dooren
Publication date: 21 January 2008
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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