Projected Gradient Methods for Nonnegative Matrix Factorization

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 proj...

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Bibliographic Details
Published in:Neural computation 2007-10, Vol.19 (10), p.2756-2779
Main Author: Lin, Chih-Jen
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Biological and medical sciences
Codes
Computer science
control theory
systems
Exact sciences and technology
Fundamental and applied biological sciences. Psychology
General aspects
Image Interpretation, Computer-Assisted - methods
Learning and adaptive systems
Least-Squares Analysis
Mathematical analysis
Mathematics
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Matrix
Miscellaneous
Models, Theoretical
Optimization algorithms
Pattern Recognition, Automated - methods
Sciences and techniques of general use
Sequences, series, summability
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Summary: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.
ISSN:0899-7667
1530-888X
DOI:10.1162/neco.2007.19.10.2756