Related papers: A Randomized Block Krylov Method for Tensor Train …
We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…
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,…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…
This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…
We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…
Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers…
We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discrete element method (DEM) simulations, demonstrating its…
Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…
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…
Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…
Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete…
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…
Based on sketching techniques, we propose two randomized algorithms for tensor ring (TR) decomposition. Specifically, by defining new tensor products and investigating their properties, we apply the Kronecker sub-sampled randomized Fourier…