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Volume 41, Issue 5
Efficient Nonnegative Matrix Factorization via Modified Monotone Barzilai-Borwein Method with Adaptive Step Sizes Strategy

Wenbo Li, Jicheng Li & Xuenian Liu

DOI: 10.4208/jcm.2201-m2019-0145

J. Comp. Math., 41 (2023), pp. 866-878.

Published online: 2023-05

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  • Abstract

In this paper, we develop an active set identification technique. By means of the active set technique, we present an active set adaptive monotone projected Barzilai-Borwein method (ASAMPBB) for solving nonnegative matrix factorization (NMF) based on the alternating nonnegative least squares framework, in which the Barzilai-Borwein (BB) step sizes can be adaptively picked to get meaningful convergence rate improvements. To get optimal step size, we take into account of the curvature information. In addition, the larger step size technique is exploited to accelerate convergence of the proposed method. The global convergence of the proposed method is analysed under mild assumption. Finally, the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.

  • Keywords

Adaptive step sizes, Alternating nonnegative least squares, Monotone projected Barzilai-Borwein method, Active set strategy, Larger step size.

  • AMS Subject Headings

15A23, 65F30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wbli57@hotmail.com (Wenbo Li)

jcli@mail.xjtu.edu.cn (Jicheng Li)

lxn901018@163.com (Xuenian Liu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-866, author = {Li , WenboLi , Jicheng and Liu , Xuenian}, title = {Efficient Nonnegative Matrix Factorization via Modified Monotone Barzilai-Borwein Method with Adaptive Step Sizes Strategy}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {5}, pages = {866--878}, abstract = {

In this paper, we develop an active set identification technique. By means of the active set technique, we present an active set adaptive monotone projected Barzilai-Borwein method (ASAMPBB) for solving nonnegative matrix factorization (NMF) based on the alternating nonnegative least squares framework, in which the Barzilai-Borwein (BB) step sizes can be adaptively picked to get meaningful convergence rate improvements. To get optimal step size, we take into account of the curvature information. In addition, the larger step size technique is exploited to accelerate convergence of the proposed method. The global convergence of the proposed method is analysed under mild assumption. Finally, the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2201-m2019-0145}, url = {http://global-sci.org/intro/article_detail/jcm/21677.html} }
TY - JOUR T1 - Efficient Nonnegative Matrix Factorization via Modified Monotone Barzilai-Borwein Method with Adaptive Step Sizes Strategy AU - Li , Wenbo AU - Li , Jicheng AU - Liu , Xuenian JO - Journal of Computational Mathematics VL - 5 SP - 866 EP - 878 PY - 2023 DA - 2023/05 SN - 41 DO - http://doi.org/10.4208/jcm.2201-m2019-0145 UR - https://global-sci.org/intro/article_detail/jcm/21677.html KW - Adaptive step sizes, Alternating nonnegative least squares, Monotone projected Barzilai-Borwein method, Active set strategy, Larger step size. AB -

In this paper, we develop an active set identification technique. By means of the active set technique, we present an active set adaptive monotone projected Barzilai-Borwein method (ASAMPBB) for solving nonnegative matrix factorization (NMF) based on the alternating nonnegative least squares framework, in which the Barzilai-Borwein (BB) step sizes can be adaptively picked to get meaningful convergence rate improvements. To get optimal step size, we take into account of the curvature information. In addition, the larger step size technique is exploited to accelerate convergence of the proposed method. The global convergence of the proposed method is analysed under mild assumption. Finally, the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.

Wenbo Li, Jicheng Li & Xuenian Liu. (2023). Efficient Nonnegative Matrix Factorization via Modified Monotone Barzilai-Borwein Method with Adaptive Step Sizes Strategy. Journal of Computational Mathematics. 41 (5). 866-878. doi:10.4208/jcm.2201-m2019-0145
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