Related papers: Nonconvex Robust High-Order Tensor Completion Usin…
Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
The oriented singular value decomposition (O-SVD) proposed by Zeng and Ng provides a hybrid approach to the t-product based third-order tensor singular value decomposition with the transform matrix being a factor matrix of the higher order…
Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness…
There are several factorizations of multi-dimensional tensors into lower-dimensional components, known as `tensor networks'. We consider the popular `tensor-train' (TT) format and ask: How efficiently can we compute a low-rank approximation…
We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…
In order to compute the best low-rank tensor approximation using the Multilinear Tensor Decomposition (MTD) model, it is essential to estimate the rank of the underlying multilinear tensor from the noisy observation tensor. In this paper,…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition…
Tensor numerical methods, based on the rank-structured tensor representation of $d$-variate functions and operators, are designed to provide $O(dn)$ complexity of numerical calculations on $n^{\otimes d }$ grids contrary to $O(n^d)$ scaling…
The low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information, which has attracted significant interest in a wide range of practical applications such as image processing and computer vision.…
In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…
This paper studies the rank-1 tensor completion problem for cubic tensors when there are noises for observed tensor entries. First, we propose a robust biquadratic optimization model for obtaining rank-1 completing tensors. When the…
We consider convex relaxations for recovering low-rank tensors based on constrained minimization over a ball induced by the tensor nuclear norm, recently introduced in \cite{tensor_tSVD}. We build on a recent line of results that considered…
We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
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…
In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…