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Robust principal component analysis: A factorization-based approach with linear complexity
Peng, Chong1; Chen, Yongyong2; Kang, Zhao3; Chen, Chenglizhao1; Cheng, Qiang4,5
2020-03-01
Source PublicationInformation Sciences
ISSN0020-0255
Volume513Pages:581-599
Abstract

Low-rankness has been widely observed in real world data and there is often a need to recover low-rank matrices in many machine learning and data mining problems. Robust principal component analysis (RPCA) has been used for such problems by separating the data into a low-rank and a sparse part. The convex approach to RPCA has been well studied due to its elegant properties in theory and many extensions have been developed. However, the state-of-the-art algorithms for the convex approach and their extensions are usually expensive in complexity due to the need for solving singular value decomposition (SVD) of large matrices. In this paper, we propose a novel RPCA model based on matrix tri-factorization, which only needs the computation of SVDs for very small matrices. Thus, this approach reduces the complexity of RPCA to be linear and makes it fully scalable. It also overcomes the drawback of the state-of-the-art scalable approach such as AltProj, which requires the precise knowledge of the true rank of the low-rank component. As a result, our method is about 4 times faster than AltProj. Our method can be used as a light-weight, scalable tool for RPCA in the absence of the precise value of the true rank.

KeywordFactorization Linear Complexity Robust Principal Component Analysis
DOI10.1016/j.ins.2019.09.074
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaComputer Science
WOS SubjectComputer Science, Information Systems
WOS IDWOS:000512221800034
Scopus ID2-s2.0-85075527639
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Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorChen, Chenglizhao
Affiliation1.College of Computer Science and Technology, Qingdao University, China
2.Department of Computer and Information Science, University of Macau, China
3.School of Computer Science and Engineering, University of Electronic Science and Technology of China, China
4.Department of Computer Science, University of Kentucky, United States
5.Institute of Biomedical Informatics, University of Kentucky, United States
Recommended Citation
GB/T 7714
Peng, Chong,Chen, Yongyong,Kang, Zhao,et al. Robust principal component analysis: A factorization-based approach with linear complexity[J]. Information Sciences, 2020, 513, 581-599.
APA Peng, Chong., Chen, Yongyong., Kang, Zhao., Chen, Chenglizhao., & Cheng, Qiang (2020). Robust principal component analysis: A factorization-based approach with linear complexity. Information Sciences, 513, 581-599.
MLA Peng, Chong,et al."Robust principal component analysis: A factorization-based approach with linear complexity".Information Sciences 513(2020):581-599.
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