期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2010
卷号：2010
期号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix
with the product of two low-rank nonnegative matrices and has been shown to be particularly
useful in many applications, e.g., in text mining, image processing, computational biology, etc. In
this paper, we explain how algorithms for NMF can be embedded into the framework of multi-
level methods in order to accelerate their convergence. This technique can be applied in situations
where data admit a good approximate representation in a lower dimensional space through linear
transformations preserving nonnegativity. A simple multilevel strategy is described and is experi-
mentally shown to speed up significantly three popular NMF algorithms (alternating nonnegative
least squares, multiplicative updates and hierarchical alternating least squares) on several standard
image datasets.
Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix
with the product of two low-rank nonnegative matrices and has been shown to be particularly
useful in many applications, e.g., in text mining, image processing, computational biology, etc. In
this paper, we explain how algorithms for NMF can be embedded into the framework of multi-
level methods in order to accelerate their convergence. This technique can be applied in situations
where data admit a good approximate representation in a lower dimensional space through linear
transformations preserving nonnegativity. A simple multilevel strategy is described and is experi-
mentally shown to speed up significantly three popular NMF algorithms (alternating nonnegative
least squares, multiplicative updates and hierarchical alternating least squares) on several standard
image datasets.
