Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 846483, 11 pages
Research Article

A Symmetric Rank-One Quasi-Newton Method for Nonnegative Matrix Factorization

1School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 611731, China
2School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China

Received 10 October 2013; Accepted 5 November 2013; Published 22 January 2014

Academic Editors: I. K. Argyros and S. Zhang

Copyright © 2014 Shu-Zhen Lai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


As is well known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing, signal processing, and so forth. In this paper, an algorithm on nonnegative matrix approximation is proposed. This method is mainly based on a relaxed active set and the quasi-Newton type algorithm, by using the symmetric rank-one and negative curvature direction technologies to approximate the Hessian matrix. The method improves some recent results. In addition, some numerical experiments are presented in the synthetic data, imaging processing, and text clustering. By comparing with the other six nonnegative matrix approximation methods, this method is more robust in almost all cases.