Related papers: Tensor Decompositions via Two-Mode Higher-Order SV…

A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…

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…

Kruskal's theorem states that a sum of product tensors constitutes a unique tensor rank decomposition if the so-called k-ranks of the product tensors are large. We prove a "splitting theorem" for sets of product tensors, in which the k-rank…

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…

Harmonic retrieval (HR) has a wide range of applications in the scenes where signals are modelled as a summation of sinusoids. Past works have developed a number of approaches to recover the original signals. Most of them rely on classical…

Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank…

In our paper, we have studied the tensor completion problem when the sampling pattern is deterministic. We first propose a simple but efficient weighted HOSVD algorithm for recovery from noisy observations. Then we use the weighted HOSVD…

In this paper we study the problem of decomposing a given tensor into a tensor train such that the tensors at the vertices are orthogonally decomposable. When the tensor train has length two, and the orthogonally decomposable tensors at the…

We consider the problem of recovering an orthogonally decomposable tensor with a subset of elements distorted by noise with arbitrarily large magnitude. We focus on the particular case where each mode in the decomposition is corrupted by…

To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…

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…

This paper presents an extension of Correspondence Analysis (CA) to tensors through High Order Singular Value Decomposition (HOSVD) from a geometric viewpoint. Correspondence analysis is a well-known tool, developed from principal component…

By singular value decomposition (SVD) of a numerically singular Hessian matrix and a numerically singular system of linear equations for the experimental data (accumulated in the respective ${\chi ^2}$ function) and constraints, least…

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…

This paper discusses the problem of symmetric tensor decomposition on a given variety $X$: decomposing a symmetric tensor into the sum of tensor powers of vectors contained in $X$. In this paper, we first study geometric and algebraic…

The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies…

We introduce the ``skew apolarity lemma'' and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in {$\bigwedge^dV_{\mathbb{C}}$ with $d\leq 3$ and $\dim V_{\mathbb{C}} \leq 8$}. New algorithms to…

Best rank-one approximation is one of the most fundamental tasks in tensor computation. In order to fully exploit modern multi-core parallel computers, it is necessary to develop decoupling algorithms for computing the best rank-one…

We present a simple yet novel parameterized form of linear mapping to achieves remarkable network compression performance: a pseudo SVD called Ternary SVD (TSVD). Unlike vanilla SVD, TSVD limits the $U$ and $V$ matrices in SVD to ternary…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…