@article{Xu2024, 
author = {Xiaoping Xu and Jinxuan Liu and Wenbo Li and Yuhan Xu and Fuxiao Li},
title = {Modified nonmonotonic projection Barzilai-Borwein gradient method for nonnegative matrix factorization},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {22067-22090},
keywords = {active set, projected Barzilai-Borwein method, nonmonotonic line search, alternating nonnegative least squares, greater step size},
url = {https://www.sciopen.com/article/10.3934/math.20241073},
doi = {10.3934/math.20241073},
abstract = {In this paper, an active set recognition technique is suggested, and then a modified nonmonotonic line search rule is presented to enhance the efficiency of the nonmonotonic line search rule, in which we introduce a new parameter formula to attempt to control the nonmonotonic degree of the line search, and thus improve the chance of discovering the global minimum. By using a modified linear search and an active set recognition technique, a global convergence gradient solution for nonnegative matrix factorization (NMF) based on an alternating nonnegative least squares framework is proposed. We used a Barzilai-Borwein step size and greater step-size tactics to speed up the convergence. Finally, a large number of numerical experiments were carried out on synthetic and image datasets, and the results showed that our presented method was effective in calculating the speed and solution quality.}
}