An Adaptive Correction Approach for Tensor Completion
文献类型：期刊论文
| 作者 | Bai, Minru1; Zhang, Xiongjun1; Ni, Guyan2; Cui, Chunfeng3 |
| 刊名 | SIAM JOURNAL ON IMAGING SCIENCES
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000385277200017 |
| 出版者 | SIAM PUBLICATIONS |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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