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