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 - <p style="text-align: justify;">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.</p>