In this paper, we extend the definition of tensor products from using an invertible matrix to utilising right-invertible matrices, exploring the algebraic properties of these new tensor products. Based on this novel definition, we define the concepts...
In this paper, we derive and propose basic differential operations and generalized Green’s integral theorems applicable to multidimensional spaces based on Cartesian tensor analysis to solve some nonlinear problems in smooth spaces in the neces...
Over the past few decades, there have been rapid advances in solid-state technology as well as a reduction in cost. This, coupled with the functionality and efficiency improvements they afford, has resulted in a massive increase in the use of electro...
Tensor Robust Principal Component Analysis (TRPCA) plays a critical role in handling high multi-dimensional data sets, aiming to recover the low-rank and sparse components both accurately and efficiently. In this paper, different from current approac...
The ground Penetrating Radar (GPR) is a promising remote sensing modality for Antipersonnel Mine (APM) detection. However, detection of the buried APMs are impaired by strong clutter, especially the reflection caused by rough ground surfaces. In this...
Dimensionality reduction is of great importance which aims at reducing the spectral dimensionality while keeping the desirable intrinsic structure information of hyperspectral images. Tensor analysis which can retain both spatial and spectral informa...
A scalar–tensor theory of gravity was considered, wherein the gravitational coupling G and the speed of light c were admitted as space–time functions and combined to form the definition of the scalar field
Traditional target detection (TD) algorithms for hyperspectral imagery (HSI) typically suffer from background interference. To alleviate this problem, we propose a novel preprocessing method based on tensor principal component analysis (TPCA) to sepa...
Being capable of high-resolution imaging and non-contact measurement, Ground Penetrating Radar (GPR) is a promising technology for the detection of unexploded ordnance (UXO). However, UXO detection is severely hindered by clutter, particularly in env...
We have derived the tensor amplitudes for partial wave analysis of
The research on the quality of employment in China holds immense significance for attaining high-quality employment development. Firstly, enhancing the quality of employment facilitates the optimization of labor resource allocation and enhances econo...
6 July 2020
For a long time, various epidemics, such as lower respiratory infections and diarrheal diseases, have caused serious social losses and costs. Various methods for analyzing infectious disease occurrences have been proposed for effective prevention and...
To solve the problem of multi-fault blind source separation (BSS) in the case that the observed signals are under-determined, a novel approach for single channel blind source separation (SCBSS) based on the improved tensor-based singular spectrum ana...
Background/Objectives: The glymphatic system plays a crucial role in clearing brain metabolic waste, and its dysfunction has been correlated to various neurological disorders. The Diffusion Tensor Imaging Analysis Along the Perivascular Space (DTI-AL...
Aquaculture plays an important role in China’s total fisheries production nowadays, and it leads to a few problems, for example water quality degradation, which has damaging effect on the sustainable development of environment. Among the many forms o...
In this paper, the symmetric character of the thermal conductivity tensor for anisotropic materials is established based on arguments from tensor analysis and the physical constraints on the domain of definition of the conductivity tensor. The non-si...
It is difficult to identify histone modification from datasets that contain high-throughput sequencing data. Although multiple methods have been developed to identify histone modification, most of these methods are not specific to histone modificatio...
In this paper, we aim to develop an efficient algorithm for the solving Tensor Robust Principal Component Analysis (TRPCA) problem, which focuses on obtaining a low-rank approximation of a tensor by separating sparse and impulse noise. A common appro...
Modern Shape Analysis integrates mathematical and statistical methods to study morphology using geometric data from 2D and 3D digitization. Beyond visualization, local deformation analysis offers deeper insight into longitudinal changes like ontogene...
In order to compare and analyze the positioning efficiency of the magnetic tensor location method, this paper studies the blind spots of the magnetic tensor location method. By constructing two magnetic tensor localization models, the localization pr...
Symmetry principles of several distinct kinds are revealingly engaged in an analysis focussing on third harmonic scattering, a current focus of research on nonlinear optics in chiral media. Analysis in terms of irreducible Cartesian tensors elucidate...
Tensor-structured multi-scale longitudinal data are quite prevalent in epidemiological, clinical, and other follow-up research. A key challenge in their statistical analysis is to simultaneously realize dimension reduction and longitudinal correlatio...
Recently, sparse and low-rank graph-based discriminant analysis (SLGDA) has yielded satisfactory results in hyperspectral image (HSI) dimensionality reduction (DR), for which sparsity and low-rankness are simultaneously imposed to capture both local...
Wind power forecasting plays a vital role in renewable energy production. Accurately forecasting wind energy is a significant challenge due to the uncertain and complex behavior of wind signals. For this purpose, accurate prediction methods are requi...
Low-rank tensors have received more attention in hyperspectral image (HSI) recovery. Minimizing the tensor nuclear norm, as a low-rank approximation method, often leads to modeling bias. To achieve an unbiased approximation and improve the robustness...
Technological developments coupled with socioeconomic changes are driving a rapid transformation of the fifth-generation (5G) cellular network landscape. This evolution has led to versatile applications with fast data-transfer capabilities. The integ...
Integration of gene expression (GE) and protein–protein interaction (PPI) is not straightforward because the former is provided as a matrix, whereas the latter is provided as a network. In many cases, genes processed with GE analysis are refine...
The characterisation of small-scale turbulence has been an active area of research for decades and this includes, particularly, the analysis of small-scale isotropy, as postulated by Kolmogorov. In particular, the question if the dissipation tensor i...
Deep learning-based morphometric analysis of zebrafish is widely utilized for non-destructively identifying abnormalities and diagnosing diseases. However, obtaining discriminative and continuous organ category decision boundaries poses a significant...
The detection of dipole-like sources, such as unexploded ordnances (UXO) and other metallic objects, based on a magnetic gradiometer system, has been increasingly applied in recent years. In this paper, a novel dipole-like source detection algorithm,...
Excellent performance, real time and strong robustness are three vital requirements for infrared small target detection. Unfortunately, many current state-of-the-art methods merely achieve one of the expectations when coping with highly complex scene...
Background: Depression is a prominent and highly prevalent nonmotor feature in patients with Parkinson’s disease (PD). The neural and pathophysiologic mechanisms of PD with depression (DPD) remain unclear. The current diagnosis of DPD largely d...
This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that un...
Analyzing deep neural networks (DNNs) via information plane (IP) theory has gained tremendous attention recently to gain insight into, among others, DNNs’ generalization ability. However, it is by no means obvious how to estimate the mutual inf...
In today’s complex embedded systems targeting internet of things (IoT) applications, there is a greater need for embedded digital signal processing algorithms that can effectively and efficiently process complex data sets. A typical application...
Analysis of single-cell multiomics datasets is a novel topic and is considerably challenging because such datasets contain a large number of features with numerous missing values. In this study, we implemented a recently proposed tensor-decomposition...
In this work, we present a new hierarchical decomposition aimed at the decorrelation of a cubical tensor of size 2n, based on the 3D Frequency-Ordered Hierarchical KLT (3D FO-HKLT). The decomposition is executed in three consecutive stages. In the fi...
Hippocampal-sparing radiotherapy (HSR) is a promising approach to alleviate cognitive side effects following cranial radiotherapy. Microstructural brain changes after irradiation have been demonstrated using Diffusion Tensor Imaging (DTI). However, e...
The normalized difference vegetation index (NDVI) contains important data for providing vegetation-cover information and supporting environmental analyses. However, understanding long-term vegetation cover dynamics remains challenging due to data out...
Given the broad range of applications from video surveillance to human–computer interaction, human action learning and recognition analysis based on 3D skeleton data are currently a popular area of research. In this paper, we propose a method f...
We have proposed the reduction in triple integral to double integral that is used in multiple shear mechanism model for faster 3D nonlinear ground motion analysis. In this study, we propose reformulation of the mechanism which results in the expressi...
We prove that vector fields described by the generalized Proca class of theories do not admit consistent coupling with a gravitational sector defined by a scalar–tensor theory of the degenerate type. Under the assumption that there exists a frame in...
The paper proposes a method of visual attention-based emotion classification through eye gaze analysis. Concretely, tensor-based emotional category classification via visual attention-based heterogeneous convolutional neural network (CNN) feature fus...
Multimodal sentiment analysis is an actively growing field of research, where tensor-based techniques have demonstrated great expressive efficiency in previous research. However, existing sequential sentiment analysis methods only focus on a single f...
Over the past decades, there has been an increase of attention to adapting machine learning methods to fully exploit the higher order structure of tensorial data. One problem of great interest is tensor classification, and in particular the extension...
In the field of gene expression analysis, methods of integrating multiple gene expression profiles are still being developed and the existing methods have scope for improvement. The previously proposed tensor decomposition-based unsupervised feature...
Background/Objectives: Recent theories of the neurocognitive architecture of semantic memory have included a distinction between semantic control in the left inferior frontal gyrus (LIFG) and semantic representation in the left anterior temporal lobe...
This paper presents an Enhanced Multilinear Principal Component Analysis (EMPCA) algorithm, an improved variant of the traditional Multilinear Principal Component Analysis (MPCA) tailored for efficient dimensionality reduction in high-dimensional dat...
Fine-grained urban cultural perception is critical for GIScience, yet traditional social media studies struggle with complex cultural semantics and heterogeneous factor integration. Addressing Beijing’s “Capital Culture,” this study...
Background/Objectives: The integration of microbiome and metabolome data could unveil profound insights into biological processes. However, widely used multi-omic data analyses often employ a stepwise mining approach, failing to harness the full pote...
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