Accelerated Matrix Recovery via Random Projection Based on Inexact Augmented Lagrange Multiplier Method

In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier （IALM） method. Additionally, a rand...

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Bibliographic Details
Published inTransactions of Tianjin University Vol. 19; no. 4; pp. 293 - 299
Main Author 王萍 张楚涵 蔡思佳 李林昊
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2013
School of Sciences, Tianjin University, Tianjin 300072, China
Subjects
Engineering
Humanities and Social Sciences
Mechanical Engineering
multidisciplinary
Science
主成分分析
凸优化问题
加速技术
恢复模式
拉格朗日乘子法
拉格朗日乘数法
矩阵
随机投影
matrix recovery
robust principal component analysis
matrix completion
inexact augmented Lagrange multiplier method
outlier pursuit
random projection
Online AccessGet full text
ISSN1006-4982
1995-8196
DOI10.1007/s12209-013-2135-0

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Summary:In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier （IALM） method. Additionally, a random projection accelerated technique （IALM＋RP） was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis （PCA） problem, IALM＋RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit （OP） problem, IALM＋RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.
Bibliography:In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier （IALM） method. Additionally, a random projection accelerated technique （IALM＋RP） was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis （PCA） problem, IALM＋RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit （OP） problem, IALM＋RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.
12-1248/T
matrix recovery; random projection; robust principal component analysis; matrix completion; outlier pursuit; inexact augmented Lagrange multiplier method
Wang Ping, Zhang Chuhan, Cai Sijia, Li Linhao（School of Sciences, Tianjin University, Tianjin 300072, China）
ISSN:1006-4982
1995-8196
DOI:10.1007/s12209-013-2135-0