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Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization
Hu, Yao1; Zhang, Debing1; Ye, Jieping2,3; Li, Xuelong4; He, Xiaofei1
2013-09-01
Source PublicationIEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume35Issue:9Pages:2117-2130
AbstractRecovering a large matrix from a small subset of its entries is a challenging problem arising in many real applications, such as image inpainting and recommender systems. Many existing approaches formulate this problem as a general low-rank matrix approximation problem. Since the rank operator is nonconvex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation. One major limitation of the existing approaches based on nuclear norm minimization is that all the singular values are simultaneously minimized, and thus the rank may not be well approximated in practice. In this paper, we propose to achieve a better approximation to the rank of matrix by truncated nuclear norm, which is given by the nuclear norm subtracted by the sum of the largest few singular values. In addition, we develop a novel matrix completion algorithm by minimizing the Truncated Nuclear Norm. We further develop three efficient iterative procedures, TNNR-ADMM, TNNR-APGL, and TNNR-ADMMAP, to solve the optimization problem. TNNR-ADMM utilizes the alternating direction method of multipliers (ADMM), while TNNR-AGPL applies the accelerated proximal gradient line search method (APGL) for the final optimization. For TNNR-ADMMAP, we make use of an adaptive penalty according to a novel update rule for ADMM to achieve a faster convergence rate. Our empirical study shows encouraging results of the proposed algorithms in comparison to the state-of-the-art matrix completion algorithms on both synthetic and real visual datasets.
SubtypeArticle
KeywordMatrix Completion Nuclear Norm Minimization Alternating Direction Method Of Multipliers Accelerated Proximal Gradient Method
WOS HeadingsScience & Technology ; Technology
DOI10.1109/TPAMI.2012.271
Indexed BySCI ; EI
WOS KeywordALTERNATING DIRECTION METHOD ; LOW-RANK ; THRESHOLDING ALGORITHM ; MINIMIZATION ; ENTRIES
Language英语
WOS Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Artificial Intelligence ; Engineering, Electrical & Electronic
WOS IDWOS:000322029000006
Citation statistics
Cited Times:224[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.opt.ac.cn/handle/181661/23452
Collection光学影像学习与分析中心
Affiliation1.Zhejiang Univ, Coll Comp Sci, State Key Lab CAD&CG, Hangzhou 310058, Zhejiang, Peoples R China
2.Arizona State Univ, Dept Comp Sci & Engn, Tempe, AZ 85287 USA
3.Arizona State Univ, Ctr Evolutionary Med & Informat, Biodesign Inst, Tempe, AZ 85287 USA
4.Chinese Acad Sci, Xian Inst Opt & Precis Mech, State Key Lab Transicent Opt & Photon, Ctr Opt IMagery Anal & Learning OPTIMAL, Xian 710119, Shaanxi, Peoples R China
Recommended Citation
GB/T 7714
Hu, Yao,Zhang, Debing,Ye, Jieping,et al. Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization[J]. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,2013,35(9):2117-2130.
APA Hu, Yao,Zhang, Debing,Ye, Jieping,Li, Xuelong,&He, Xiaofei.(2013).Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization.IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,35(9),2117-2130.
MLA Hu, Yao,et al."Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization".IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 35.9(2013):2117-2130.
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