Related papers: Quaternion tensor singular value decomposition usi…
This document explores the connections between singular value decomposition (SVD) and various tensor operations in the context of quantum state calculations and tensor networks. The relationships between SVD and quantities such as trace,…
We approximated the evaluation function for the game Tic-Tac-Toe by singular value decomposition (SVD) and investigated the effect of approximation accuracy on winning rate. We first prepared the perfect evaluation function of Tic-Tac-Toe…
In this work, a quaternion-valued model is proposed in lieu of the Clarke's \alpha, \beta transformation to convert three-phase quantities to a hypercomplex single-phase signal. The concatenated signal can be used for harmonic distortion…
In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…
Singular Value Decomposition (SVD) has become an important technique for reducing the computational burden of Vision Language Models (VLMs), which play a central role in tasks such as image captioning and visual question answering. Although…
We present a fully differential next-to-next-to-leading order calculation of t-channel single top-quark production and decay at the LHC under narrow-width approximation and neglecting cross-talk between incoming protons. We focus on the…
This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the…
Recently, the connectionist temporal classification (CTC) model coupled with recurrent (RNN) or convolutional neural networks (CNN), made it easier to train speech recognition systems in an end-to-end fashion. However in real-valued models,…
In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…
Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order…
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…
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…
Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to…
Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…
We demonstrate a novel technique to obtain singular-value decomposition (SVD) of the coupled-cluster triple excitations amplitudes, $t_{ijk}^{abc}$. The presented method is based on the Golub-Kahan bidiagonalisation strategy and does not…
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…
This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…
Exact recovery of tensor decomposition (TD) methods is a desirable property in both unsupervised learning and scientific data analysis. The numerical defects of TD methods, however, limit their practical applications on real-world data. As…
An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…