Nonnegative Low Rank Matrix Completion by Riemannian Optimalization Methods  

作　　者：Guang-Jing Song Michael K.Ng 

机构地区：[1]School of Mathematics and Information Sciences,Weifang University,Weifang,Shandong 261061,China [2]Department of Mathematics,The University of Hong Kong,Hong Kong,China

出　　处：《Annals of Applied Mathematics》2023年第2期181-205,共25页应用数学年刊（英文版）

基　　金：supported in part by the National Natural Science Foundation of China under Grant No.12171369;Key NSF of Shandong Province under Grant No.ZR2020KA008;supported in part by HKRGC GRF 12300519,17201020 and 17300021,HKRGC CRF C1013-21GF and C7004-21GF;Joint NSFC and RGC N-HKU769/21。

摘　　要：In this paper,we study Riemannian optimization methods for the problem of nonnegative matrix completion that is to recover a nonnegative low rank matrix from its partial observed entries.With the underlying matrix incohence conditions,we show that when the number m of observed entries are sampled independently and uniformly without replacement,the inexact Riemannian gradient descent method can recover the underlying n_(1)-by-n_(2)nonnegative matrix of rank r provided that m is of O(r^(2)slog^(2)s),where s=max{n_(1),n_(2)}.Numerical examples are given to illustrate that the nonnegativity property would be useful in the matrix recovery.In particular,we demonstrate the number of samples required to recover the underlying low rank matrix with using the nonnegativity property is smaller than that without using the property.

关 键 词：MANIFOLDS tangent spaces nonnegative matrices low rank 

分 类 号：O18[理学—数学]