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Cluster-preserving sampling algorithm for large-scale graphs

Science China(Information Sciences) 2023年第1期66卷 60-76页

作者： Jianpeng ZHANG Hongchang CHEN Dingjiu YU Yulong PEI Yingjun DENG National Digital Switching System E&T Research Center Information Engineering University Network Systems Department of the Strategic Support Force School of Computer Science and Technology Eindhoven University of Technology Center for Applied Mathematics Tianjin University

Graph sampling is a very effective method to deal with scalability issues when analyzing largescale graphs. Lots of sampling algorithms have been proposed, and sampling qualities have been quantified using explicit properties(e.g., degree distribution) of the sample. However, the existing sampling techniques are inadequate for the current sampling task: sampling the clustering structure, which is a crucial property of the current networks. In this paper, using different expansion strategies, two novel top-leader sampling methods(i.e., TLS-e and TLS-i) are proposed to obtain representative samples, and they are capable of effectively preserving the clustering structure. The rationale behind them is to select top-leader nodes of most clusters into the sample and then heuristically incorporate peripheral nodes into the sample using specific expansion strategies. Extensive experiments are conducted to investigate how well sampling techniques preserve the clustering structure of graphs. Our empirical results show that the proposed sampling algorithms can preserve the population's clustering structure well and provide feasible solutions to sample the clustering structure from large-scale graphs.

关键词： graph sampling clustering structure top-leader nodes expansion strategies large-scale graphs

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Unsupervised multiplex graph diffusion networks with multi-level canonical correlation analysis for multiplex graph representation learning

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Science China(Information Sciences) 2025年第3期68卷 66-79页

作者： Sichao FU Qinmu PENG Yange HE Baokun DU Bin ZOU Xiao-Yuan JING Xinge YOU School of Electronic Information and Communications Huazhong University of Science and Technology Platform Operation and Marketing Center JD Retail Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University School of Computer Science Wuhan University

In recent years, unsupervised multiplex graph representation learning(UMGRL) has received increasing research interest, which aims to learn discriminative node features from the multiplex graphs supervised by data without the guidance of labels. Although these designed UMGRL methods have obtained great success in various graph-related tasks, most existing UMGRL models still have the following issues: highly depending on complex self-supervised strategies(i.e., data augmentation,pretext tasks, and negative pairs sampling), restricted receptive fields, and only aggregating low-frequency information between nodes. In this paper, we propose a simple unsupervised multiplex graph diffusion network(UMGDN) with the aid of multi-level canonical correlation analysis to solve the above issues. Specifically, we first decouple the feature transform and propagation processes of the graph convolution layer to further improve the generalization of the learnable parameters. And then, we propose adaptive diffusion propagation to capture long-range dependency relationships between nodes, not the local neighborhood interactions. Finally, a multi-level canonical correlation analysis loss on both the feature transform and propagation processes is proposed to maximize the correlation of the same node features from multiple graphs for guiding model optimization. Compared to the existing UMGRL models, our proposed UMGDN does not need to introduce any data augmentation, negative pairs sampling techniques, complex pretext tasks, and also adaptively aggregates the optimal frequency information between nodes to generate more robust node embeddings. Extensive experiments on four popular datasets and two graph-related tasks demonstrate the effectiveness of the proposed method.

关键词： unsupervised multiplex graph representation learning graph neural networks node classification node clustering

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Gradient-based algorithms for multi-objective bi-level optimization

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Science China mathematics 2024年第6期67卷 1419-1438页

作者： Xinmin Yang Wei Yao Haian Yin Shangzhi Zeng Jin Zhang National Center for Applied Mathematics in Chongqing Chongqing401331China School of Mathematical Sciences Chongqing Normal UniversityChongqing401331China Department of Mathematics Southern University of Science and TechnologyShenzhen518055China National Center for Applied Mathematics Shenzhen Shenzhen518000China Department of Mathematics and Statistics University of VictoriaVictoriaBCV8W 2Y2Canada

Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of ***,its multi-objective and hierarchical bi-level nature makes it notably ***-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement ***,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical *** address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and ***,we demonstrate the theoretical validity by accomplishing the desirable Pareto *** experiments confirm the practical efficiency of the proposed method and verify the theoretical *** accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA *** results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.

关键词： multi-objective bi-level optimization convergence analysis Pareto stationary learning to optimize

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A Corrected H_(N)^(T)-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations

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Communications on applied mathematics and Computation 2025年第2期7卷 689-717页

作者： Song Jiang Qi Li Wenjun Sun National Key Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing100094China Center for Applied Physics and Technology College of EngineeringPeking UniversityBeijing100871China

In this paper,the corrected method to the original H_(N)^(T)-unified gas kinetic scheme(H_(N)^(T)-UGKS)is developed in order to solve the nonlinear radiative transfer equations with boundary *** H_(N)^(T)-UGKS is an asymptotic preserving(AP)scheme that uses UGKS for spatial discretization and the hybrid H_(N)^(T)method for angular discretization which is constructed in the paper(Li et *** ***.198(5):993-1020,2024).First,the correction idea in Mieussens(***.253:138-156,2013)is adopted,such that H_(N)^(T)-UGKS can correctly simulate the linear radiative transfer equation with boundary ***,for the nonlinear radiative transfer equations with boundary layers,the transformation from the implicit Monte Carlo(IMC)method is introduced to rewrite the nonlinear transfer equations into a linearized *** is the key point in the construction of the current scheme to use this linearized system to construct the numerical boundary *** this way,the boundary density is included in the numerical fluxes,and consequently,the modification method for the linear radiative transfer equation can be used to deal with the nonlinear problem studied in this paper.A number of numerical examples are presented to demonstrate the accuracy and effectiveness of the current scheme for resolving boundary layers in both linear and nonlinear radiative transfer problems.

关键词： Nonlinear radiative transfer Boundary layer -UGKS Implicit Monte Carlo(IMC)method

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A survey of fine-grained visual categorization based on deep learning

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Journal of Systems Engineering and Electronics 2024年第6期35卷 1337-1356页

作者： XIE Yuxiang GONG Quanzhi LUAN Xidao YAN Jie ZHANG Jiahui College of System Engineering National University of Defense TechnologyChangsha 410000China College of Computer Engineering and Applied Mathematics Changsha UniversityChangsha 410003China

Deep learning has achieved excellent results in various tasks in the field of computer vision,especially in fine-grained visual *** aims to distinguish the subordinate categories of the label-level *** to high intra-class variances and high inter-class similarity,the fine-grained visual categorization is extremely *** paper first briefly introduces and analyzes the related public *** that,some of the latest methods are *** on the feature types,the feature processing methods,and the overall structure used in the model,we divide them into three types of methods:methods based on general convolutional neural network(CNN)and strong supervision of parts,methods based on single feature processing,and meth-ods based on multiple feature *** methods of the first type have a relatively simple structure,which is the result of the initial *** methods of the other two types include models that have special structures and training processes,which are helpful to obtain discriminative *** conduct a specific analysis on several methods with high accuracy on pub-lic *** addition,we support that the focus of the future research is to solve the demand of existing methods for the large amount of the data and the computing *** terms of tech-nology,the extraction of the subtle feature information with the burgeoning vision transformer(ViT)network is also an important research direction.

关键词： deep learning fine-grained visual categorization convolutional neural network(CNN) visual attention

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Alleviating limit cycling in training GANs with an optimization technique

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Science China mathematics 2024年第6期67卷 1287-1316页

作者： Keke Li Liping Tang Xinmin Yang National Center for Applied Mathematics in Chongqing Chongqing Normal UniversityChongqing401331China School of Mathematical Sciences University of Electronic Science and Technology of ChinaChengdu611731China

In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCAA).Specifically,we first derive the upper and lower complexity bounds of PCAA for a general bilinear game,with the last-iterate convergence rate notably improving upon previous ***,we combine PCAA with the adaptive moment estimation algorithm(Adam)to propose PCAA-Adam,for practical training of GANs to enhance their generalization ***,we validate the effectiveness of the proposed algorithm through experiments conducted on bilinear games,multivariate Gaussian distributions,and the CelebA dataset,respectively.

关键词： GANs general bilinear game predictive centripetal acceleration algorithm lower and upper complexity bounds PCAA-Adam

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Comparing UAV camera data with satellite imagery for global localization 7

Comparing UAV camera data with satellite imagery for global ...

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7th IEEE International Conference on Actual Problems of Unmanned Aerial Vehicles Development, APUAVD 2024

作者： Kozachuk, Oleksandr Prystavka, Pylyp National Aviation University Faculty of Computer Science and Technology Department of Applied Mathematics Kyiv03058 Ukraine

ISBN: (纸本)9798331534141

Global visual localization is critical for UAVs operating in environments where global navigation satellite systems (GNSS) are unreliable or unavailable. While many methods, such as visual odometry (VIO), rely on optical flow for localization, they often require prior knowledge of the current coordinates. In this paper, we propose an enhanced UAV localization method using the vector of locally aggregated descriptors (VLAD) combined with a cycle generative adversarial network (GAN) architecture. Unlike traditional approaches, our method does not require knowledge of the current coordinates;it only requires a pre-downloaded flight map, enabling location determination through image matching. © 2024 IEEE.

关键词： Satellite imagery

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Spline Approaches for Anomaly Detection in UAV-Based Aerial Surveillance 7

Spline Approaches for Anomaly Detection in UAV-Based Aerial ...

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7th IEEE International Conference on Actual Problems of Unmanned Aerial Vehicles Development, APUAVD 2024

作者： Zhultynska, Anhelina Prystavka, Pylyp National Aviation University Faculty of Computer Science and Technology Department of Applied Mathematics Kyiv03058 Ukraine

ISBN: (纸本)9798331534141

This article presents a new approach to detecting anomalies in data obtained from unmanned aerial vehicles using spline models. The relevance of the study is driven by the need for fast and accurate identification of anomalies in real time, which is critical for military intelligence and civilian monitoring. The proposed model is based on the use of momentary characteristics, such as average illumination intensity and standard deviation, which allows for effective data parameterization and detection of anomalous observations. The advantage of the spline model is its ability to adapt to complex and heterogeneous image textures, which significantly reduces the risk of missing critical anomalies. The model also demonstrates high robustness to variations in the data, making it a reliable tool for analyzing images in different lighting and landscape conditions. Experiments using forest, road, and car textures have shown that the spline model is able to accurately identify anomalies, which increases the efficiency of analysis and allows for a quick response to detected changes. © 2024 IEEE.

关键词： Splines

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Comparative Analysis of Detector-Tracker Architecture for Object Tracking Based on SBC for UAV 7

Comparative Analysis of Detector-Tracker Architecture for Ob...

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7th IEEE International Conference on Actual Problems of Unmanned Aerial Vehicles Development, APUAVD 2024

作者： Prystavka, Pylyp Shevchenko, Andrii Rokitianska, Irina National Aviation University Faculty of Computer Science and Technology Department of Applied Mathematics Kyiv03058 Ukraine

ISBN: (纸本)9798331534141

This paper investigates the tracking technology of moving objects from a UAV camera (or streaming video) for systems with limited computational resources, such as modern SBCs. A detector-tracker architecture is proposed, combining the advantages of object detection methods and tracking algorithms. A comparative analysis of the performance and accuracy of various detector and tracker combinations on modern SBCs is conducted. The results demonstrate the high efficiency of the proposed approach for object-tracking tasks under limited computational resources, which has practical significance for UAV-based systems. © 2024 IEEE.

关键词： Object tracking

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Monte Carlo Integration Using Elliptic Curves

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Chinese Annals of mathematics,Series B 2025年第2期46卷 241-260页

作者： Chung Pang MOK Huimin ZHENG Shanghai Institute for Mathematics and Interdisciplinary Sciences Shanghai200438China Department of Mathematics Nanjing UniversityNanjing210093China Jiangsu National Center for Applied Mathematics Nanjing210023China College of Information and Network Engineering Anhui Science and Technology UniversityBengbu233030AnhuiChina

The authors carry out numerical experiments with regard to the Monte Carlo integration method,using as input the pseudorandom vectors that are generated by the algorithm proposed in[Mok,C.P.,Pseudorandom Vector Generation Using Elliptic Curves and Applications to Wiener Processes,Finite Fields and Their Applications,85,2023,102129],which is based on the arithmetic theory of elliptic curves over finite *** consider integration in the following two cases:The case of Lebesgue measure on the unit hypercube[0,1]d,and as well as the case of Wiener *** the case of Wiener measure,the construction gives discrete time simulation of an independent sequence of standard Wiener processes,which is then used for the numerical evaluation of Feynman-Kac formulas.

关键词： Pseudorandom vectors Elliptic curves Finite fields Monte Carlo integration Feynman-Kac formulas

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