相关论文: Towards Efficient and Accurate Approximation: Tens…
Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…
We propose a new algorithm called higher-order QR iteration (HOQRI) for computing low multilinear rank approximation (LMLRA), also known as the Tucker decomposition, of large and sparse tensors. Compared to the celebrated higher-order…
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…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…
Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…
Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard…
The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…
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…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
We present a low-scaling algorithm for the random phase approximation (RPA) with \textbf{k}-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a…
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…
This paper is devoted to studying the application of the block Krylov subspace method for approximation of the truncated tensor SVD (T-SVD). The theoretical results of the proposed randomized approach are presented. Several experimental…
Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…
The paper is concerned with methods for computing the best low multilinear rank approximation of large and sparse tensors. Krylov-type methods have been used for this problem; here block versions are introduced. For the computation of…
Low-rank approximation of tensors has been widely used in high-dimensional data analysis. It usually involves singular value decomposition (SVD) of large-scale matrices with high computational complexity. Sketching is an effective data…