EFFICIENT NONNEGATIVE MATRIX FACTORIZATION VIA MODIFIED MONOTONE BARZILAI-BORWEIN METHOD WITH ADAPTIVE STEP SIZES STRATEGY  

作　　者：Wenbo Li Jicheng Li Xuenian Liu 

机构地区：[1]Department of Applied Mathematics,Xi’an University of Technology,Xi’an 710054,China [2]College of Mathematics and Statistics,Xi’an Jiaotong University,Xi’an 710049,China

出　　处：《Journal of Computational Mathematics》2023年第5期866-878,共13页计算数学（英文）

基　　金：the support from the National Natural Science Foundation of China(Nos.12171384,12201492,61976176);the National Science Foundation of Shaanxi(No.2021JM-323).

摘　　要：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.

关 键 词：Adaptive step sizes Alternating nonnegative least squares Monotone projected Barzilai-Borwein method Active set strategy Larger step size 

分 类 号：O24[理学—计算数学]