Regular Articles

FastNMF: highly efficient monotonic fixed-point nonnegative matrix factorization algorithm with good applicability

[+] Author Affiliations
Le Li

Tsinghua University, Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Beijing 100084, China

Yu-Jin Zhang

Tsinghua University, Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Beijing 100084, China

J. Electron. Imaging. 18(3), 033004 (August 10, 2009). doi:10.1117/1.3184771
History: Received January 09, 2009; Revised May 14, 2009; Accepted June 02, 2009; Published August 10, 2009
Text Size: A A A

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.

Figures in this Article
© 2009 SPIE and IS&T

Topics

Algorithms ; Matrices

Citation

Le Li and Yu-Jin Zhang
"FastNMF: highly efficient monotonic fixed-point nonnegative matrix factorization algorithm with good applicability", J. Electron. Imaging. 18(3), 033004 (August 10, 2009). ; http://dx.doi.org/10.1117/1.3184771


Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging & repositioning the boxes below.

Related Book Chapters

Topic Collections

PubMed Articles
Advertisement
  • Don't have an account?
  • Subscribe to the SPIE Digital Library
  • Create a FREE account to sign up for Digital Library content alerts and gain access to institutional subscriptions remotely.
Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).
Access This Proceeding
Sign in or Create a personal account to Buy this article ($15 for members, $18 for non-members).
Access This Chapter

Access to SPIE eBooks is limited to subscribing institutions and is not available as part of a personal subscription. Print or electronic versions of individual SPIE books may be purchased via SPIE.org.