Related papers: A mixed EIM-SVD tensor decomposition for bivariate…

In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices. By constructing the Gram matrix in higher precision and…

The empirical mode decomposition (EMD) has achieved its reputation by providing a multi-scale time-frequency representation of nonlinear and/or nonstationary signals. To extend this method to vector-valued signals (VvS) in multidimensional…

Singular value decomposition (SVD) is widely used in wireless systems, including multiple-input multiple-output (MIMO) processing and dimension reduction in distributed MIMO (D-MIMO). However, the iterative nature of decomposition methods…

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…

Motivated by the challenges of analyzing high-dimensional ($p \gg n$) sequencing data from longitudinal microbiome studies, where samples are collected at multiple time points from each subject, we propose supervised functional tensor…

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

Recently, numerous tensor singular value decomposition (t-SVD)-based tensor recovery methods have shown promise in processing visual data, such as color images and videos. However, these methods often suffer from severe performance…

We introduce the tubal tensor train (TTT) decomposition, a tensor-network model that combines the t-product algebra of the tensor singular value decomposition (T-SVD) with the low-order core structure of the tensor train (TT) format. For an…

This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…

This paper introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular modes. The problem is motivated by high-order longitudinal data…

This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient…

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…

An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed…

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is,…

A CUR factorization is often utilized as a substitute for the singular value decomposition (SVD), especially when a concrete interpretation of the singular vectors is challenging. Moreover, if the original data matrix possesses properties…

The Singular Value Decomposition (SVD) of linear functions facilitates the calculation of their 2-induced norm and row and null spaces, hallmarks of linear control theory. In this work, we present a function representation that, similar to…

The data bottleneck has emerged as a fundamental challenge in learning based image restoration methods. Researchers have attempted to generate synthesized training data using paired or unpaired samples to address this challenge. This study…

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…