de.mpg.escidoc.pubman.appbase.FacesBean
English
 
Help Guide Disclaimer Contact us Login
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Fast Projection-based Methods for the Least Squares Nonnegative Matrix Approximation Problem

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons76142

Sra,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)
There are no public fulltexts available
Supplementary Material (public)
There is no public supplementary material available
Citation

Kim, D., Sra, S., & Dhillon, I. (2008). Fast Projection-based Methods for the Least Squares Nonnegative Matrix Approximation Problem. Statistical Analysis and Data Mining, 1(1), 38-51. doi:10.1002/sam.104.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CA5F-1
Abstract
Nonnegative matrix approximation (NNMA) is a popular matrix decomposition technique that has proven to be useful across a diverse variety of fields with applications ranging from document analysis and image processing to bioinformatics and signal processing. Over the years, several algorithms for NNMA have been proposed, e.g. Lee and Seungamp;lsquo;s multiplicative updates, alternating least squares (ALS), and gradient descent-based procedures. However, most of these procedures suffer from either slow convergence, numerical instability, or at worst, serious theoretical drawbacks. In this paper, we develop a new and improved algorithmic framework for the least-squares NNMA problem, which is not only theoretically well-founded, but also overcomes many deficiencies of other methods. Our framework readily admits powerful optimization techniques and as concrete realizations we present implementations based on the Newton, BFGS and conjugate gradient methods. Our algorithms provide numerical resu lts supe rior to both Lee and Seungamp;lsquo;s method as well as to the alternating least squares heuristic, which was reported to work well in some situations but has no theoretical guarantees[1]. Our approach extends naturally to include regularization and box-constraints without sacrificing convergence guarantees. We present experimental results on both synthetic and real-world datasets that demonstrate the superiority of our methods, both in terms of better approximations as well as computational efficiency.