Related papers: Note: low-rank tensor train completion with side i…

Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…

This paper is concerned with the problem of recovering third-order tensor data from limited samples. A recently proposed tensor decomposition (BMD) method has been shown to efficiently compress third-order spatiotemporal data. Using the…

This paper studies tensors that admit decomposition in the Extended Tensor Train (ETT) format, with a key focus on the case where some decomposition factors are constrained to be equal. This factor sharing introduces additional challenges,…

Radio maps are important enablers for many applications in wireless networks, ranging from network planning and optimization to fingerprint based localization. Sampling the complete map is prohibitively expensive in practice, so methods for…

Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…

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…

In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…

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,…

Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…

We consider machine learning tasks with low-rank functional tree tensor networks (TTN) as the learning model. While in the case of least-squares regression, low-rank functional TTNs can be efficiently optimized using alternating…

Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…

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…

Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…

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…

The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…

Tensor data, or multi-dimensional arrays, is a data format popular in multiple fields such as social network analysis, recommender systems, and brain imaging. It is not uncommon to observe tensor data containing missing values, and tensor…

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…

In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality…

In this paper, we propose a new approach to solve low-rank tensor completion and robust tensor PCA. Our approach is based on some novel notion of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly…

We establish theoretical recovery guarantees of a family of Riemannian optimization algorithms for low rank matrix recovery, which is about recovering an $m\times n$ rank $r$ matrix from $p < mn$ number of linear measurements. The…