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Related papers: Noisy Tensor Completion via Low-rank Tensor Ring

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Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…

Computer Vision and Pattern Recognition · Computer Science 2019-03-22 Jinshi Yu , Chao Li , Qibin Zhao , Guoxu Zhou

Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…

Machine Learning · Computer Science 2024-12-03 Xiongjun Zhang , Michael K. Ng

In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the…

Machine Learning · Statistics 2021-10-22 Xiongjun Zhang , Michael K. Ng

On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…

Information Theory · Computer Science 2009-03-19 Emmanuel J. Candes , Yaniv Plan

Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…

Numerical Analysis · Mathematics 2021-01-03 Abdul Ahad , Zhen Long , Ce Zhu , Yipeng Liu

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

Real-world spatio-temporal data is often incomplete or inaccurate due to various data loading delays. For example, a location-disease-time tensor of case counts can have multiple delayed updates of recent temporal slices for some locations…

Machine Learning · Computer Science 2021-05-13 Cheng Qian , Nikos Kargas , Cao Xiao , Lucas Glass , Nicholas Sidiropoulos , Jimeng Sun

The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…

Methodology · Statistics 2018-11-28 Anru Zhang

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…

Machine Learning · Statistics 2013-11-12 Akshay Krishnamurthy , Aarti Singh

Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…

Machine Learning · Statistics 2021-04-07 Zhen Long , Ce Zhu , Jiani Liu , Yipeng Liu

The goal of tensor completion is to fill in missing entries of a partially known tensor under a low-rank constraint. In this paper, we mainly study low rank third-order tensor completion problems by using Riemannian optimization methods on…

Optimization and Control · Mathematics 2020-11-24 Guang-Jing Song , Xue-Zhong Wang , Michael K. Ng

We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…

Machine Learning · Statistics 2021-11-04 Chanwoo Lee , Miaoyan Wang

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

Machine Learning · Computer Science 2016-10-12 Xiao-Yang Liu , Shuchin Aeron , Vaneet Aggarwal , Xiaodong Wang

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…

Machine Learning · Computer Science 2017-07-27 Wenqi Wang , Vaneet Aggarwal , Shuchin Aeron

Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…

Machine Learning · Statistics 2014-05-09 Ming Yuan , Cun-Hui Zhang

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Statistics Theory · Mathematics 2016-07-05 Olga Klopp , Karim Lounici , Alexandre B. Tsybakov

We consider a novel algorithm, for the completion of partially observed low-rank tensors, where each entry of the tensor can be chosen from a discrete finite alphabet set, such as in common image processing problems, where the entries…

Signal Processing · Electrical Eng. & Systems 2026-02-06 Niclas Führling , Getuar Rexhepi , Giuseppe Abreu

In the noisy tensor completion problem we observe $m$ entries (whose location is chosen uniformly at random) from an unknown $n_1 \times n_2 \times n_3$ tensor $T$. We assume that $T$ is entry-wise close to being rank $r$. Our goal is to…

Machine Learning · Computer Science 2016-02-19 Boaz Barak , Ankur Moitra

In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from applications, including tensor regression, tensor completion,…

Machine Learning · Statistics 2023-07-11 Yuetian Luo , Anru R. Zhang

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