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Journal of Electronic Imaging

FastNMF: highly efficient monotonic fixed-point nonnegative matrix factorization algorithm with good applicability
Author(s): Le Li; Yu-Jin Zhang
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Paper Abstract

Nonnegative matrix factorization (NMF) is a recently developed method for dimensionality reduction, feature extraction, and data mining, etc. Currently, no NMF algorithm holds both satisfactory efficiency for applications and enough ease of use. To improve the applicability of NMF, we propose a new monotonic, fixed-point algorithm called FastNMF by implementing least-squares error-based nonnegative factorization essentially according to the basic properties of parabola functions. The minimization problem corresponding to an operation in FastNMF can be analytically solved just by this operation, which is far beyond all existing algorithms' power, and therefore FastNMF holds much higher efficiency, which is validated by a set of experimental results. For the simplicity of design philosophy, FastNMF is still one of the NMF algorithms that are the easiest to use and the most comprehensible. In addition, theoretical analysis and experimental results also show that FastNMF tends to converge to better solutions than the popular multiplicative update-based algorithms as far as approximation accuracy is concerned.

Paper Details

Date Published: 1 July 2009
PDF: 12 pages
J. Electron. Imaging. 18(3) 033004 doi: 10.1117/1.3184771
Published in: Journal of Electronic Imaging Volume 18, Issue 3
Show Author Affiliations
Le Li, Tsinghua Univ. (China)
Yu-Jin Zhang, Tsinghua Univ. (China)


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