An efficient nonmonotone projected Barzilai–Borwein method for nonnegative matrix factorization with extrapolation

ABSTRACT

In this paper, we present an efficient method for nonnegative matrix factorization (NMF) based on the alternating nonnegative least-squares framework. To solve the nonnegativity constrained least-squares problems efficiently, we propose an extrapolated quadratic regularization projected Barzilai–Borwein (EQRPBB) method utilizing the extrapolation technique and a modified nonmonotone line search. The efficiency of the proposed method is demonstrated through experiments on synthetic and image datasets. We observe that our method significantly outperform existing ones in terms of computational speed.

Keywords:

• Nonnegative matrix factorization
• alternating nonnegative least squares
• projected Barzilai–Borwein method
• nonmonotone line search
• extrapolation

2010 AMS Subject Classifications:

• 65F30
• 15A23

Acknowledgments

The authors would like to express their thanks to the editors and reviewers for their valuable comments on the paper, which have greatly improved its presentation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The code is available at https://sites.google.com/site/nmfsolvers/.

2 The code is available at http://homepages.umflint.edu/∼lxhan/software.html.

3 The code is available at https://github.com/huangyakui2006/QRPBB-method-for-NMF.

4 ORL image database and Yale image database in MATLAB format are available at http://www.cad.zju.edu.cn/home/dengcai/Data/TextData.html.

Additional information

Funding

This work was supported by the Natural Science Foundation of China [grant no. 11671318].