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Volume 13, Issue 2
An Adaptive Nonmonotone Projected Barzilai-Borwein Gradient Method with Active Set Prediction for Nonnegative Matrix Factorization

Jicheng Li, Wenbo Li & Xuenian Liu

DOI: 10.4208/nmtma.OA-2019-0028

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 516-538.

Published online: 2020-03

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  • Abstract

In this paper, we first present an adaptive nonmonotone term to improve the efficiency of nonmonotone line search, and then an active set identification technique is suggested to get more efficient descent direction such that it improves the local convergence behavior of algorithm and decreases the computation cost. By means of the adaptive nonmonotone line search and the active set identification technique, we put forward a global convergent gradient-based method to solve the nonnegative matrix factorization (NMF) based on the alternating nonnegative least squares framework, in which we introduce a modified Barzilai-Borwein (BB) step size. The new modified BB step size and the larger step size strategy are exploited to accelerate convergence. Finally, the results of extensive numerical experiments using both synthetic and image datasets show that our proposed method is efficient in terms of computational speed.

  • Keywords

Active set, projected Barzilai-Borwein method, adaptive nonmonotone line search, modified Barzilai-Borwein step size, larger step size.

  • AMS Subject Headings

15A23, 65F30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wbli35@stu.xjtu.edu.cn (Wenbo Li)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-13-516, author = {Li , JichengLi , Wenbo and Liu , Xuenian}, title = {An Adaptive Nonmonotone Projected Barzilai-Borwein Gradient Method with Active Set Prediction for Nonnegative Matrix Factorization}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {2}, pages = {516--538}, abstract = {

In this paper, we first present an adaptive nonmonotone term to improve the efficiency of nonmonotone line search, and then an active set identification technique is suggested to get more efficient descent direction such that it improves the local convergence behavior of algorithm and decreases the computation cost. By means of the adaptive nonmonotone line search and the active set identification technique, we put forward a global convergent gradient-based method to solve the nonnegative matrix factorization (NMF) based on the alternating nonnegative least squares framework, in which we introduce a modified Barzilai-Borwein (BB) step size. The new modified BB step size and the larger step size strategy are exploited to accelerate convergence. Finally, the results of extensive numerical experiments using both synthetic and image datasets show that our proposed method is efficient in terms of computational speed.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0028}, url = {http://global-sci.org/intro/article_detail/nmtma/15490.html} }
TY - JOUR T1 - An Adaptive Nonmonotone Projected Barzilai-Borwein Gradient Method with Active Set Prediction for Nonnegative Matrix Factorization AU - Li , Jicheng AU - Li , Wenbo AU - Liu , Xuenian JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 516 EP - 538 PY - 2020 DA - 2020/03 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0028 UR - https://global-sci.org/intro/article_detail/nmtma/15490.html KW - Active set, projected Barzilai-Borwein method, adaptive nonmonotone line search, modified Barzilai-Borwein step size, larger step size. AB -

In this paper, we first present an adaptive nonmonotone term to improve the efficiency of nonmonotone line search, and then an active set identification technique is suggested to get more efficient descent direction such that it improves the local convergence behavior of algorithm and decreases the computation cost. By means of the adaptive nonmonotone line search and the active set identification technique, we put forward a global convergent gradient-based method to solve the nonnegative matrix factorization (NMF) based on the alternating nonnegative least squares framework, in which we introduce a modified Barzilai-Borwein (BB) step size. The new modified BB step size and the larger step size strategy are exploited to accelerate convergence. Finally, the results of extensive numerical experiments using both synthetic and image datasets show that our proposed method is efficient in terms of computational speed.

Li , JichengLi , Wenbo and Liu , Xuenian. (2020). An Adaptive Nonmonotone Projected Barzilai-Borwein Gradient Method with Active Set Prediction for Nonnegative Matrix Factorization. Numerical Mathematics: Theory, Methods and Applications. 13 (2). 516-538. doi:10.4208/nmtma.OA-2019-0028
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