Projected Gradient Methods for Nonnegative Matrix Factorization

by: Chih-Jen Lin

Neural Comp., Vol. 19, No. 10. (1 October 2007), pp. 2756-2779.

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摘要

Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided.

@article{citeulike:2903283, abstract = {Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided.}, author = {Lin, Chih-Jen }, citeulike-article-id = {2903283}, journal = {Neural Comp.}, keywords = {factorization, matrix, non-negative, software}, month = {October}, number = {10}, pages = {2756--2779}, posted-at = {2008-06-18 00:21:56}, priority = {2}, title = {Projected Gradient Methods for Nonnegative Matrix Factorization}, url = {http://neco.mitpress.org/cgi/content/abstract/19/10/2756}, volume = {19}, year = {2007} }

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TY - JOUR ID - citeulike:2903283 L3 - citeulike-article-id:2903283 N2 - Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided. IS - 10 JF - Neural Comp. EP - 2779 TI - Projected Gradient Methods for Nonnegative Matrix Factorization VL - 19 SP - 2756 KW - factorization KW - matrix KW - non-negative KW - software AU - Lin, Chih-Jen PY - 2007/10/01/ UR - http://neco.mitpress.org/cgi/content/abstract/19/10/2756 ER -

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