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Related papers: Hierarchical Tensor Ring Completion

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In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…

Machine Learning · Statistics 2020-10-30 Yunfeng Cai , Ping Li

Tensor completion recovers missing entries of multiway data. Teh missing of entries could often be caused during teh data acquisition and transformation. In dis paper, we provide an overview of recent development in low rank tensor…

Numerical Analysis · Computer Science 2018-05-11 Zhen Long , Yipeng Liu , Longxi Chen , Ce Zhu

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Information Theory · Computer Science 2016-02-18 Holger Rauhut , Reinhold Schneider , Zeljka Stojanac

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

Numerical Analysis · Mathematics 2021-04-13 Liyu Su

In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…

Computer Vision and Pattern Recognition · Computer Science 2020-05-07 Haijin Zeng , Xiaozhen Xie , Jifeng Ning

Tensor completion recovers a multi-dimensional array from a limited number of measurements. Using the recently proposed tensor ring (TR) decomposition, in this paper we show that a d-order tensor of dimensional size n and TR rank r can be…

Machine Learning · Computer Science 2020-03-17 Huyan Huang , Yipeng Liu , Ce Zhu

In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…

Numerical Analysis · Computer Science 2018-03-23 Longhao Yuan , Qibin Zhao , Jianting Cao

The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…

Computer Vision and Pattern Recognition · Computer Science 2020-04-30 Meng Ding , Ting-Zhu Huang , Xi-Le Zhao , Michael K. Ng , Tian-Hui Ma

This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic…

Machine Learning · Computer Science 2017-08-03 Jonathan Q. Jiang , Michael K. Ng

In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We call such a decomposition the triple decomposition, and the…

Numerical Analysis · Mathematics 2020-03-03 Liqun Qi , Yannan Chen , Mayank Bakshi , Xinzhen Zhang

In recent studies, the tensor ring (TR) rank has shown high effectiveness in tensor completion due to its ability of capturing the intrinsic structure within high-order tensors. A recently proposed TR rank minimization method is based on…

Computer Vision and Pattern Recognition · Computer Science 2020-05-21 Meng Ding , Ting-Zhu Huang , Xi-Le Zhao , Tian-Hui Ma

Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD…

Machine Learning · Computer Science 2023-05-22 Wenjin Qin , Hailin Wang , Feng Zhang , Weijun Ma , Jianjun Wang , Tingwen Huang

This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…

Machine Learning · Computer Science 2023-05-22 Jingjing Zheng , Wenzhe Wang , Xiaoqin Zhang , Xianta Jiang

Tensor completion is a challenging problem with various applications. Many related models based on the low-rank prior of the tensor have been proposed. However, the low-rank prior may not be enough to recover the original tensor from the…

Numerical Analysis · Mathematics 2019-11-20 Ping-Ping Wang , Liang Li , Guang-Hui Cheng

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

Machine Learning · Statistics 2022-03-18 Yuning Qiu , Guoxu Zhou , Qibin Zhao , Shengli Xie

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor…

Computer Vision and Pattern Recognition · Computer Science 2017-08-04 Lei Zhang , Wei Wei , Qinfeng Shi , Chunhua Shen , Anton van den Hengel , Yanning Zhang

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

Numerical Analysis · Computer Science 2017-09-15 Longhao Yuan , Qibin Zhao , Jianting Cao

This paper focus on recovering multi-dimensional data called tensor from randomly corrupted incomplete observation. Inspired by reweighted $l_1$ norm minimization for sparsity enhancement, this paper proposes a reweighted singular value…

Computer Vision and Pattern Recognition · Computer Science 2017-07-11 Baburaj M. , Sudhish N. George

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

Numerical Analysis · Computer Science 2016-08-24 Linxiao Yang , Jun Fang , Hongbin Li , Bing Zeng

This paper considers the completion problem for a tensor (also referred to as a multidimensional array) from limited sampling. Our greedy method is based on extending the low-rank approximation pursuit (LRAP) method for matrix completions…

Numerical Analysis · Mathematics 2020-04-21 An-Bao Xu