Related papers: A dual framework for low-rank tensor completion

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the…

Matrix and tensor completion are frameworks for a wide range of problems, including collaborative filtering, missing data, and image reconstruction. Missing entries are estimated by leveraging an assumption that the matrix or tensor is…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

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,…

This paper studies stability and symmetry preserving $H^2$ optimal model reduction problems of linear systems which include linear gradient systems as a special case. The problem is formulated as a nonlinear optimization problem on the…

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…

The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…

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…

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…

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…

Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…

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…

Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…

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…

In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…

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…

Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…

We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace…