Robust low-rank tensor factorization by cyclic weighted median  

作　　者：MENG DeYu ZHANG Biao XU ZongBen ZHANG Lei GAO ChenQiang 

机构地区：[1]Institute for Information and System Sciences and Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi'an Jiaotong University [2]Department of Computing, Hong Kong Polytechnic University [3]Chongqing Key Laboratory of Signal and Information Processing, Chongqing University of Posts and Telecommunications

出　　处：《Science China(Information Sciences)》2015年第5期141-151,共11页中国科学（信息科学）（英文版）

基　　金：supported by the National Basic Research Program of China(Grant No.2013CB329404);the National Natural Science Fundation of China(Grant Nos.61373114,11131006,61075054&61102131)

摘　　要：Low-rank tensor factorization （LRTF） provides a useful mathematical tool to reveal and analyze multi-factor structures underlying data in a wide range of practical applications. One challenging issue in LRTF is how to recover a low-rank higher-order representation of the given high dimensional data in the presence of outliers and missing entries, i.e., the so-called robust LRTF problem. The Ll-norm LRTF is a popular strategy for robust LRTF due to its intrinsic robustness to heavy-tailed noises and outliers. However, few Ll-norm LRTF algorithms have been developed due to its non-convexity and non-smoothness, as well as the high order structure of data. In this paper we propose a novel cyclic weighted median （CWM） method to solve the Ll-norm LRTF problem. The main idea is to recursively optimize each coordinate involved in the Ll-norm LRTF problem with all the others fixed. Each of these single-scalar-parameter sub-problems is convex and can be easily solved by weighted median filter, and thus an effective algorithm can be readily constructed to tackle the original complex problem. Our extensive experiments on synthetic data and real face data demonstrate that the proposed method performs more robust than previous methods in the presence of outliers and/or missing entries.Low-rank tensor factorization （LRTF） provides a useful mathematical tool to reveal and analyze multi-factor structures underlying data in a wide range of practical applications. One challenging issue in LRTF is how to recover a low-rank higher-order representation of the given high dimensional data in the presence of outliers and missing entries, i.e., the so-called robust LRTF problem. The Ll-norm LRTF is a popular strategy for robust LRTF due to its intrinsic robustness to heavy-tailed noises and outliers. However, few Ll-norm LRTF algorithms have been developed due to its non-convexity and non-smoothness, as well as the high order structure of data. In this paper we propose a novel cyclic weighted median （CWM） method to solve the Ll-norm LRTF problem. The main idea is to recursively optimize each coordinate involved in the Ll-norm LRTF problem with all the others fixed. Each of these single-scalar-parameter sub-problems is convex and can be easily solved by weighted median filter, and thus an effective algorithm can be readily constructed to tackle the original complex problem. Our extensive experiments on synthetic data and real face data demonstrate that the proposed method performs more robust than previous methods in the presence of outliers and/or missing entries.

关 键 词：tensor factorization low-rank weighted median filter tensorface 

分 类 号：O183.2[理学—数学]