Related papers: Efficient Algorithms for Low Tubal Rank Tensor App…

This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as…

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called the Tensor Train Matrix format. Our tensor network randomized…

In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…

We propose a novel approach for hyperspectral super-resolution, that is based on low-rank tensor approximation for a coupled low-rank multilinear (Tucker) model. We show that the correct recovery holds for a wide range of multilinear ranks.…

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this…

We present an efficient low-rank approximation algorithm for non-negative tensors. The algorithm is derived from our two findings: First, we show that rank-1 approximation for tensors can be viewed as a mean-field approximation by treating…

The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…

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…

Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms…

Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…

The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized,…

The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…

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…

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…

In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…

Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…

In this paper, we propose a conservative low rank tensor method to approximate nonlinear Vlasov solutions. The low rank approach is based on our earlier work (arxiv: 2106.08834). It takes advantage of the fact that the differential…