An Adaptive Nonmonotone Projected Barzilai-Borwein Gradient Method with Active Set Prediction for Nonnegative Matrix Factorization

An Adaptive Nonmonotone Projected Barzilai-Borwein Gradient Method with Active Set Prediction for Nonnegative Matrix Factorization

Year:    2020

Author:    Xuenian Liu, Jicheng Li, Wenbo Li, Xuenian Liu

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2019-0028

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 516–538

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

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

Author Details

Xuenian Liu

Jicheng Li

Wenbo Li

Xuenian Liu

  1. A new nonmonotone spectral projected gradient algorithm for box-constrained optimization problems in m×n real matrix space with application in image clustering

    Li, Ting | Wan, Zhong | Guo, Jie

    Journal of Computational and Applied Mathematics, Vol. 438 (2024), Iss. P.115563

    https://doi.org/10.1016/j.cam.2023.115563 [Citations: 2]
  2. Efficient algorithms of box-constrained Nonnegative Matrix Factorization and its applications in image clustering

    Guo, Jie | Li, Ting | Wan, Zhong | Li, Jiaoyan | Xiao, Yamei

    Applied Numerical Mathematics, Vol. (2024), Iss.

    https://doi.org/10.1016/j.apnum.2024.10.015 [Citations: 0]
  3. An alternating nonmonotone projected Barzilai–Borwein algorithm of nonnegative factorization of big matrices

    Li, Ting | Tang, Jiayi | Wan, Zhong

    Data Mining and Knowledge Discovery, Vol. 35 (2021), Iss. 5 P.1972

    https://doi.org/10.1007/s10618-021-00773-5 [Citations: 6]