On the equivalence between low-rank matrix completion and tensor rank

被引：1
|
作者：
Derksen, Harm [1 ]
机构：
[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
来源：
LINEAR & MULTILINEAR ALGEBRA | 2018年 / 66卷 / 04期
关键词：
Matrix completion; tensor rank; complexity; rank minimization; APPROXIMATION; MINIMIZATION;
D O I：
10.1080/03081087.2017.1315044
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The rank minimization problem (RMP) asks to find a matrix of lowest rank inside a linear variety of the space of nxm matrices. The low-rank matrix completion (LRMC) problem asks to complete a partially filled matrix such that the resulting matrix has smallest possible rank. The tensor rank problem asks to determine the rank of a tensor. We show that these three problems are equivalent: each one of the problems can be reduced to the other two.
引用
收藏
页码：645 / 667
页数：23
相关论文
共 50 条
  • [1] PARALLEL MATRIX FACTORIZATION FOR LOW-RANK TENSOR COMPLETION
    Xu, Yangyang
    Hao, Ruru
    Yin, Wotao
    Su, Zhixun
    INVERSE PROBLEMS AND IMAGING, 2015, 9 (02) : 601 - 624
  • [2] Robust Low-Rank and Sparse Tensor Decomposition for Low-Rank Tensor Completion
    Shi, Yuqing
    Du, Shiqiang
    Wang, Weilan
    PROCEEDINGS OF THE 33RD CHINESE CONTROL AND DECISION CONFERENCE (CCDC 2021), 2021, : 7138 - 7143
  • [3] Low-Rank Tensor Completion by Approximating the Tensor Average Rank
    Wang, Zhanliang
    Dong, Junyu
    Liu, Xinguo
    Zeng, Xueying
    2021 IEEE/CVF INTERNATIONAL CONFERENCE ON COMPUTER VISION (ICCV 2021), 2021, : 4592 - 4600
  • [4] Low-Rank Matrix Completion
    Chi, Yuejie
    IEEE SIGNAL PROCESSING MAGAZINE, 2018, 35 (05) : 178 - 181
  • [5] Tensor Factorization for Low-Rank Tensor Completion
    Zhou, Pan
    Lu, Canyi
    Lin, Zhouchen
    Zhang, Chao
    IEEE TRANSACTIONS ON IMAGE PROCESSING, 2018, 27 (03) : 1152 - 1163
  • [6] Iterative tensor eigen rank minimization for low-rank tensor completion
    Su, Liyu
    Liu, Jing
    Tian, Xiaoqing
    Huang, Kaiyu
    Tan, Shuncheng
    INFORMATION SCIENCES, 2022, 616 : 303 - 329
  • [7] Low-rank tensor completion via smooth matrix factorization
    Zheng, Yu-Bang
    Huang, Ting-Zhu
    Ji, Teng-Yu
    Zhao, Xi-Le
    Jiang, Tai-Xiang
    Ma, Tian-Hui
    APPLIED MATHEMATICAL MODELLING, 2019, 70 : 677 - 695
  • [8] Low-Rank Tensor Completion Method for Implicitly Low-Rank Visual Data
    Ji, Teng-Yu
    Zhao, Xi-Le
    Sun, Dong-Lin
    IEEE SIGNAL PROCESSING LETTERS, 2022, 29 : 1162 - 1166
  • [9] Low-Rank Tensor Completion Using Matrix Factorization Based on Tensor Train Rank and Total Variation
    Ding, Meng
    Huang, Ting-Zhu
    Ji, Teng-Yu
    Zhao, Xi-Le
    Yang, Jing-Hua
    JOURNAL OF SCIENTIFIC COMPUTING, 2019, 81 (02) : 941 - 964
  • [10] Low-Rank Tensor Completion Using Matrix Factorization Based on Tensor Train Rank and Total Variation
    Meng Ding
    Ting-Zhu Huang
    Teng-Yu Ji
    Xi-Le Zhao
    Jing-Hua Yang
    Journal of Scientific Computing, 2019, 81 : 941 - 964
12345