相关论文: Low-rank Tensor Train Decomposition Using TensorSk…

A numerical algorithm to decompose an exact low-rank skew-symmetric tensor into a sum of elementary (rank-$1$) skew-symmetric tensors is introduced. The algorithm uncovers this Grassmann decomposition based on linear relations that are…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

Sketching uses randomized Hash functions for dimensionality reduction and acceleration. The existing sketching methods, such as count sketch (CS), tensor sketch (TS), and higher-order count sketch (HCS), either suffer from low accuracy or…

This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

Learning neural fields has been an active topic in deep learning research, focusing, among other issues, on finding more compact and easy-to-fit representations. In this paper, we introduce a novel low-rank representation termed Tensor…

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…

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,…

We study low rank approximation of tensors, focusing on the tensor train and Tucker decompositions, as well as approximations with tree tensor networks and more general tensor networks. For tensor train decomposition, we give a bicriteria…

Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

We consider the problem of online subspace tracking of a partially observed high-dimensional data stream corrupted by noise, where we assume that the data lie in a low-dimensional linear subspace. This problem is cast as an online low-rank…

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…

Alternating least squares (ALS) is often considered the workhorse algorithm for computing the rank-R canonical tensor approximation, but for certain problems its convergence can be very slow. The nonlinear conjugate gradient (NCG) method…

Convolutional neural networks show outstanding results in a variety of computer vision tasks. However, a neural network architecture design usually faces a trade-off between model performance and computational/memory complexity. For some…

Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…

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…

In this paper, we propose a new unified optimization algorithm for general tensor decomposition which is formulated as an inverse problem for low-rank tensors in the general linear observation models. The proposed algorithm supports three…