Related papers: Randomized Interpolative Decomposition of Separate…
Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…
Tensor Train~(TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate…
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…
We introduce a new tensor norm, the average spectrum norm, to study sample complexity of tensor completion problems based on the canonical polyadic decomposition (CPD). Properties of the average spectrum norm and its dual norm are…
Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous…
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…
Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…
We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as Higher Order Interpolatory Decomposition (HOID). Given a tensor $\mathcal{X}$, the algorithm provides a set of…
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…
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…
In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, e.g., when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does…
Canonical polyadic decomposition (CPD) is at the core of fast matrix multiplication, a computational problem with widespread implications across several seemingly unrelated problems in computer science. Much recent progress in this field…
The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…
We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…
The primary bottleneck towards obtaining good recognition performance in IR images is the lack of sufficient labeled training data, owing to the cost of acquiring such data. Realizing that object detection methods for the RGB modality are…
Linear least-squares regression with a "design" matrix A approximates a given matrix B via minimization of the spectral- or Frobenius-norm discrepancy ||AX-B|| over every conformingly sized matrix X. Another popular approximation is…
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…
Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank…
Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…
Tensor decompositions, such as CANDECOMP/PARAFAC (CP), are widely used in a variety of applications, such as chemometrics, signal processing, and machine learning. A broadly used method for computing such decompositions relies on the…