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  • 标题:Using underapproximations for sparse nonnegative matrix factorization
  • 本地全文:下载
  • 作者:Nicolas GILLIS ; François GLINEUR
  • 期刊名称:CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
  • 出版年度:2009
  • 卷号:1
  • 出版社:Center for Operations Research and Econometrics (UCL), Louvain
  • 摘要:Nonnegative Matrix Factorization (NMF) has gathered a lot of attention in the last decade and has been successfully applied in numerous applications. It consists in the factorization of a nonnegative matrix by the product of two low-rank nonnegative matrices:. € M ≈VW . In this paper, we attempt to solve NMF problems in a recursive way. In order to do that, we introduce a new variant called Nonnegative Matrix Underapproximation (NMU) by adding the upper bound constraint € VW ≤M. Besides enabling a recursive procedure for NMF, these inequalities make NMU particularly well-suited to achieve a sparse representation, improving the part-based decomposition. Although NMU is NP-hard (which we prove using its equivalence with the maximum edge biclique problem in bipartite graphs), we present two approaches to solve it: a method based on convex reformulations and a method based on Lagrangian relaxation. Finally, we provide some encouraging numerical results for image processing applications.
  • 关键词:nonnegative matrix factorization, underapproximation, maximum edge biclique problem, sparsity, image processing.
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