Robust low-rank data matrix approximations  

作　　者：FENG XingDong HE XuMing 

机构地区：[1]School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China [2]Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai 200433, China [3]Department of Statistics, University of Michigan, Ann Arbor, MI 48109, USA

出　　处：《Science China Mathematics》2017年第2期189-200,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 11571218);the State Key Program in the Major Research Plan of National Natural Science Foundation of China (Grant No. 91546202);Program for Changjiang Scholars and Innovative Research Team in Shanghai University of Finance and Economics (Grant No. IRT13077);Program for Innovative Research Team of Shanghai University of Finance and Economics

摘　　要：We review some recent approaches to robust approximations of low-rank data matrices.We consider the problem of estimating a low-rank mean matrix when the data matrix is subject to measurement errors as well as gross outliers in some of its entries.The purpose of the paper is to make various algorithms accessible with an understanding of their abilities and limitations to perform robust low-rank matrix approximations in both low and high dimensional problems.We review some recent approaches to robust approximations of low-rank data matrices. We consider the problem of estimating a low-rank mean matrix when the data matrix is subject to measurement errors as well as gross outliers in some of its entries. The purpose of the paper is to make various algorithms accessible with an understanding of their abilities and limitations to perform robust low-rank matrix approximations in both low and high dimensional problems.

关 键 词：dimension reduction low-rank M-ESTIMATOR regression robust estimator singular value decom-position 

分 类 号：O151.21[理学—数学] TP13[理学—基础数学]