In this paper, we consider the tensor completion problem, which has many researchers in the machine learning particularly concerned. Our fast and precise method is built on extending the $L_{2,1}$-norm minimization and Qatar Riyal decomposition (LNM-QR) method for matrix completions to tensor completions, and is different from the popular tensor completion methods using the tensor singular value decomposition (t-SVD). In terms of shortening the computing time, t-SVD is replaced with the method computing an approximate t-SVD based on Qatar Riyal decomposition (CTSVD-QR), which can be used to compute the largest $r \left(r>0 \right)$ singular values (tubes) and their associated singular vectors (of tubes) iteratively. We, in addition, use the tensor $L_{2,1}$-norm instead of the tensor nuclear norm to minimize our model on account of it is easy to optimize. Then in terms of improving accuracy, ADMM, a gradient-search-based method, plays a crucial part in our method. Numerical experimental results show that our method is faster than those state-of-the-art algorithms and have excellent accuracy.
Alternating minimization algorithms for graph regularized tensor completion
Huawei European Research Institute（华为欧洲研究院）；LISN, INRIA, Université Paris-Saclay（法国国家信息与自动化研究所，巴黎萨克雷大学）；LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院科学与工程计算国家重点实验室）；Department of INMA, Université catholique de Louvain（鲁汶天主教大学）
Stable rank one matrix completion is solved by two rounds of semidefinite programming relaxation
Département de Mathématiques et Applications, Ecole Normale Supérieure, Ulm, Paris. PSL Research University（巴黎高等师范学院数学与应用系）；Department of Mathematics, Massachusetts Institute of Technology（麻省理工学院数学系）
Rank Minimization on Tensor Ring: A New Paradigm in Scalable Tensor Decomposition and Completion
Graduate School of Engineering, Saitama Institute of Technology, Japan（日本萨它马工学院工程研究生院）；Tensor Learning Unit, RIKEN Center for Advanced Intelligence Project (AIP), Japan（日本RIKEN高级智能项目（AIP）张量学习单元）；School of Automation, Guangdong University of Technology, China（中国广东技术大学自动化学院）；School of Computer Science and Technology, Hangzhou Dianzi University, China（中国杭州电子科技大学计算机科学与技术学院）；Department of Electrical and Electronic Engineering, Imperial College London, United Kingdom（英国伦敦帝国理工学院电子与电气工程系）
Accelerated alternating minimization algorithm for low-rank approximations in the Chebyshev norm
Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences（俄罗斯科学院马祖克数值数学研究所）；National Research University Higher School of Economics（国立高等经济大学）；Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）
Southeast University（东南大学）；Centre de Recherche en Information Biomédicale Sino-Français (CRIBs)（中法生物医学信息研究中心）；INSERM U 1099（法国国家健康与医学研究院U1099）；Laboratoire Traitement du Signal et de l’Image (LTSI)（信号图像处理实验室）；Université de Rennes 1（雷恩第一大学）
