An Adaptive Correction Approach for Tensor Completion

doi:10.1137/15M1048008

	An Adaptive Correction Approach for Tensor Completion
	Bai, Minru 1; Zhang, Xiongjun 1; Ni, Guyan 2; Cui, Chunfeng 3
刊名	SIAM JOURNAL ON IMAGING SCIENCES
	2016
卷号	9 期号:3 页码:1298-1323
关键词	adaptive correction approach error bound tensor completion square deal 3-block ADMM
ISSN号	1936-4954
DOI	10.1137/15M1048008
英文摘要	In this paper, we study the tensor completion problem on recovery of the multilinear data under limited sampling. A popular convex relaxation of this problem is to minimize the nuclear norm of the more square matrix produced by matricizing a tensor. However, it may fail to produce a highly accurate solution under low sample ratio. In order to get a recovery with high accuracy, we propose an adaptive correction approach for tensor completion. First, a corrected model for matrix completion with bound constraint is proposed and its error bound is established. Then, we extend it to tensor completion with bound constraint and propose a corrected model for tensor completion. The adaptive correction approach consists of solving a series of corrected models with an initial estimator where the initial estimator used for the next step is computed from the value of the current solution. Moreover, the error bound of the corrected model for tensor completion is also established. A convergent 3-block alternating direction method of multipliers (ADMM) is applied to solve the dual problem of the corrected model. Numerical experiments on both random data and real world data validate the efficiency of our proposed correction approach.
资助项目	National Science Foundation of China[11571098] ; Hunan Provincial National Science Foundation of China[14JJ2053] ; Innovation Platform Open Funds of Hunan Provincial Higher Education Institutions of China[14K018]
WOS研究方向	Computer Science ; Mathematics ; Imaging Science & Photographic Technology
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000385277200017
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/23744]
专题	中国科学院数学与系统科学研究院
通讯作者	Bai, Minru
作者单位	1.Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China 2.Natl Univ Def Technol, Coll Sci, Changsha 410073, Hunan, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Bai, Minru,Zhang, Xiongjun,Ni, Guyan,et al. An Adaptive Correction Approach for Tensor Completion[J]. SIAM JOURNAL ON IMAGING SCIENCES,2016,9(3):1298-1323.
APA	Bai, Minru,Zhang, Xiongjun,Ni, Guyan,&Cui, Chunfeng.(2016).An Adaptive Correction Approach for Tensor Completion.SIAM JOURNAL ON IMAGING SCIENCES,9(3),1298-1323.
MLA	Bai, Minru,et al."An Adaptive Correction Approach for Tensor Completion".SIAM JOURNAL ON IMAGING SCIENCES 9.3(2016):1298-1323.