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Folded-concave penalization approaches to tensor completion
Cao WF(曹文飞); Wang Y(王尧); Yang, Can; Chang, Xiangyu; Han Z(韩志); Xu ZB(徐宗本)
Department机器人学研究室
Source PublicationNeurocomputing
ISSN0925-2312
2015
Volume152Pages:261-273
Indexed BySCI ; EI
EI Accession number20150400440904
WOS IDWOS:000349572600027
Contribution Rank3
Funding OrganizationNational 973 Project of China under Grant number 2013 CB329404 and Natural Science Foundation of China under Grantnumbers 61273020and61303168.
KeywordTensor Completion Nuclear Norm Folded-concave Penalization Local Linear Approximation Sparse Learning
Abstract

The existing studies involving matrix or tensor completion problems are commonly under the nuclear norm penalization framework due to the computational efficiency of the resulting convex optimization problem. Folded-concave penalization methods have demonstrated surprising developments in sparse learning problems due to their nice practical and theoretical properties. To share the same light of folded-concave penalization methods, we propose a new tensor completion model via folded-concave penalty for estimating missing values in tensor data. Two typical folded-concave penalties, the minmax concave plus (MCP) penalty and the smoothly clipped absolute deviation (SCAD) penalty, are employed in the new model. To solve the resulting nonconvex optimization problem, we develop a local linear approximation augmented Lagrange multiplier (LLA-ALM) algorithm which combines a two-step LLA strategy to search a local optimum of the proposed model efficiently. Finally, we provide numerical experiments with phase transitions, synthetic data sets, real image and video data sets to exhibit the superiority of the proposed model over the nuclear norm penalization method in terms of the accuracy and robustness.

Language英语
WOS HeadingsScience & Technology ; Technology
WOS SubjectComputer Science, Artificial Intelligence
WOS KeywordVariable Selection ; Oracle Properties ; Regularization ; Algorithms ; Matrices ; Lasso ; Model
WOS Research AreaComputer Science
Citation statistics
Document Type期刊论文
Identifierhttp://ir.sia.cn/handle/173321/15660
Collection机器人学研究室
Corresponding AuthorWang Y(王尧)
Affiliation1.School of Mathematics and Statistics, Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi'an Jiaotong University, Xi'an, China
2.Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong
3.Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, China
Recommended Citation
GB/T 7714
Cao WF,Wang Y,Yang, Can,et al. Folded-concave penalization approaches to tensor completion[J]. Neurocomputing,2015,152:261-273.
APA Cao WF,Wang Y,Yang, Can,Chang, Xiangyu,Han Z,&Xu ZB.(2015).Folded-concave penalization approaches to tensor completion.Neurocomputing,152,261-273.
MLA Cao WF,et al."Folded-concave penalization approaches to tensor completion".Neurocomputing 152(2015):261-273.
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