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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…
Currently, the size of scientific data is growing at an unprecedented rate. Data in the form of tensors exhibit high-order, high-dimensional, and highly sparse features. Although tensor-based analysis methods are very effective, the large…
In this work, we propose a method for the compression of the coupling matrix in volume\hyp surface integral equation (VSIE) formulations. VSIE methods are used for electromagnetic analysis in magnetic resonance imaging (MRI) applications,…
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…
Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…
The paper introduces a hybrid approach to the CUR-type decomposition of tensors in the Tucker format. The idea of the hybrid algorithm is to write a tensor $\mathcal{X}$ as a product of a core tensor $\mathcal{S}$, a matrix $C$ obtained by…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…
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…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…
The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper,…
Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there…
VoxCap, a fast Fourier transform (FFT)-accelerated and Tucker-enhanced integral equation simulator for capacitance extraction of voxelized structures, is proposed. The VoxCap solves the surface integral equations (SIEs) for conductor and…
This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…
The evaluation of Fock exchange is often the computationally most expensive part of hybrid functional density functional theory calculations in a systematically improvable, complete basis. In this work, we employ a Tucker tensor based…
We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical…