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Solving sparse non-negative tensor equations： algorithms and applications

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Frontiers of Mathematics in China 2015年第3期10卷 649-680页

作者： Xutao LI michael k. ng School of Computer Engineering Nanyang Technological University Singapore 639798 Singapore Centre for Mathematical Imaging and Vision and Department of MathematicsHong Kong Baptist University Hong Kong China

We study iterative methods for solving a set of sparse non-negative tensor equations （multivariate polynomial systems） arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional network.. By mak.ng use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional network. are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.

关键词： Nonnegative tensor multi-dimensional network information retrieval community iterative method multivariate polynomial equation

MODIFIED NEWTON＇S ALGORITHM FOR COMPUTIng THE GROUP INVERSES OF SIngULAR TOEPLITZ MATRICES

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Journal of Computational Mathematics 2006年第5期24卷 647-656页

作者： Jian-feng Cai michael k. ng Yi-min Wei Department of Mathematics The Chinese University of Hong Kong Hong Kong Department of Mathematics Hong Kong Baptist University Hong Kong School of Mathematical Sciences Fudan University Shanghai 200433 China ~ Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University) Ministry of Education

Newton＇s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton＇s iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.

关键词： Newton's iteration Group inverse Toeplitz matrix Displacement rank.

BLOCk.TRIAngULAR PRECONDITIONERS FOR SYSTEMS ARISIng FROM EDGE-PRESERVIng IMAGE RESTORATION

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Journal of Computational Mathematics 2010年第6期28卷 848-863页

作者： Zhong-Zhi Bai Yu-Mei Huang michael k. ng LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China School of Mathematics and Statistics Lanzhou University Lanzhou 730000 China Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

Signal and image restoration problems are often solved by minimizing a cost function consisting of an l2 data-fidelity term and a regularization term. We consider a class of convex and edge-preserving regularization functions. In specific, half-quadratic regularization as a fixed-point iteration method is usually employed to solve this problem. The main aim of this paper is to solve the above-described signal and image restoration problems with the half-quadratic regularization technique by mak.ng use of the Newton method. At each iteration of the Newton method, the Newton equation is a structured system of linear equations of a symmetric positive definite coefficient matrix, and may be efficiently solved by the preconditioned conjugate gradient method accelerated with the modified block.SSOR preconditioner. Our experimental results show that the modified block.SSOR preconditioned conjugate gradient method is feasible and effective for further improving the numerical performance of the half-quadratic regularization approach.

关键词： Block.system of equations Matrix preconditioner Edge-preserving Image restoration Half-quadratic regularization.

Uniqueness and perturbation bounds for sparse non-negative tensor equations

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Frontiers of Mathematics in China 2018年第4期13卷 849-874页

作者： Dongdong LIU Wen LI michael k. ng Seak.Weng VOng School of Applied Mathematics Guangdong University of Technology Guangzhou 510006 China School of Mathematical Sciences South China Normal University Guangzhou 510631China Department of Mathematics Hong Kong Baptist University Hong Kong China Department of Mathematics University of Macao Macao China

We discuss the uniqueness and the perturbation analysis for sparse non-negative tensor equations arriving from data sciences. By two different techniques, we may get better ranges of parameters to guarantee the uniqueness of the solution of the tensor equation. On the other hand, we present some perturbation bounds for the tensor equation. Numerical examples are given to show the efficiency of the theoretical results.

关键词： Stochastic tensor tensor equation uniqueness perturbation

A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization

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Numerical Mathematics(Theory,Methods and Applications) 2009年第4期2卷 377-402页

作者： Zheng-Jian Bai michael k. ng Liqun Qi School of Mathematical Sciences Xiamen University Xiamen 361005 China Centre for Mathematical Imaging and Vision and Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong Department of Applied Mathematics The Hong Kong Polytechnic University Hung Horn Hong Kong

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex *** find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex *** a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence *** also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method.

关键词： Coordinate descent global convergence linear convergence rate

Spectral Analysis for HSS Preconditioners

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Numerical Mathematics(Theory,Methods and Applications) 2008年第1期1卷 57-77页

作者： Lung Chak.Chan michael k. ng Nam k.u Tsing Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th *** study an approximation of the spectra of HSS preconditioned matrices and use these results to illustrate and explain the spectra obtained from numerical examples,where the previous spectral analysis of HSS precon- ditioned matrices does not cover.

关键词： Saddle point problems iterative methods preconditioning eigenvalues

Stability and Generalization of Hypergraph Collaborative Network.

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Machine Intelligence Research 2024年第1期21卷 184-196页

作者： michael k.ng Hanrui Wu Andy Yip Institute of Data Science The University of Hong KongHong KongChina Department of Mathematics The University of Hong KongHong KongChina College of Information Science and Technology Jinan UniversityGuangzhou 510006China

Graph neural network. have been shown to be very effective in utilizing pairwise relationships across ***,there have been several successful proposals to generalize graph neural network. to hypergraph neural network. to exploit more com-plex *** particular,the hypergraph collaborative network. yield superior results compared to other hypergraph neural net-work. for various semi-supervised learning *** collaborative network.can provide high quality vertex embeddings and hyperedge embeddings together by formulating them as a joint optimization problem and by using their consistency in reconstructing the given *** this paper,we aim to establish the algorithmic stability of the core layer of the collaborative network.and provide generaliz--ation *** analysis sheds light on the design of hypergraph filters in collaborative network.,for instance,how the data and hypergraph filters should be scaled to achieve uniform stability of the learning *** experimental results on real-world datasets are presented to illustrate the theory.

关键词： Hypergraphs vertices hyperedges collaborative network. graph convolutional neural network.(CNNs) stability generalization guarantees

EFFICIENT BOX-CONSTRAINED TV-TYPE-l^1 ALGORITHMS FOR RESTORIng IMAGES WITH IMPULSE NOISE

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Journal of Computational Mathematics 2013年第3期31卷 249-270页

作者： Liyan Ma michael k. ng Jian Yu Tieyong Zeng School of Computer and Information Technology Beijing Jiaotong University Beijing 100044 China Department of Mathematics Hong Kong Baptist University Hong Kong China

In this paper, we study the restoration of images simultaneously corrupted by blur and impulse noise via variational approach with a box constraint on the pixel values of an image. In the literature, the TV-l^1 variational model which contains a total variation （TV） regularization term and an l^1 data-fidelity term, has been proposed and developed. Several numerical methods have been studied and experimental results have shown that these methods lead to very promising results. However, these numerical methods are designed based on approximation or penalty approaches, and do not consider the box constraint. The addition of the box constraint mak.s the problem more difficult to handle. The main contribution of this paper is to develop numerical algorithms based on the derivation of exact total variation and the use of proximal operators. Both one-phase and two-phase methods are considered, and both TV and nonlocal TV versions are designed. The box constraint [0, 1] on the pixel values of an image can be efficiently handled by the proposed algorithms. The numerical experiments demonstrate that the proposed methods are efficient in computational time and effective in restoring images with impulse noise.

关键词： Image restoration Impulse noise Total variation Nonlocal total variation Proximal Operators.

Single-pilot operations in commercial flight:Effects on neural activity and visual behaviour under abnormalities and emergencies

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Chinese Journal of Aeronautics 2024年第8期37卷 277-292页

作者： Qinbiao LI Chun-Hsien CHEN k.m k.H.ng Xin YUAN Cho Yin YIU Human Factors and Ergonomics Laboratory Department of Aeronautical and Aviation EngineeringThe Hong Kong Polytechnic UniversityHong Kong Special Administrative Region 100872China School of Mechanical&Aerospace Engineering Nanyang Technological UniversitySingapore 639798Singapore

With cutting-edge technologies and considering airline human-resource-saving,a single pilot in commercial jets could be technically *** changes in captains’natural behaviours are initially required to comprehend the specific safe human performance envelope for safeguarding single-pilot flight,particularly in high-risk.*** paper investigates how captains’performance transforms for fixing emergencies when operating from Dual-Pilot Operations(DPO)to Single-Pilot Operations(SPO)through a physiological-based *** pilots flew an emergency-included flight with/without first officers’*** neural activities and scanning behaviours were recorded using a 32-channel Electroencephalogram(EEG)and glasses-based eye track.r,with the observation and post-experiment questionnaires to evaluate the flight operations and pilots’*** alone,there was a significantly increased cortical activity in h and b waves over the frontal,parietal,and temporal lobes during the more complicated emergencies,and pilots focused less on the primary flight display while spending significantly more time scanning the other *** physiological fluctuating patterns associated with risk. operations in SPO were highlighted by cross-correlating multimodal *** experimental-based noteworthy insights may wish to inform commercial SPO measures to lessen the persistent physiological fluctuation,assisting airlines in creating SPO-oriented intelligent flight systems to give captains adequate support for assuring safer air transportation.

关键词： Aviation engineering Single pilot operations Behaviour changes Eye track.r Electroencephalogram