基于Graph Transformer的半监督异配图表示学习模型

现有的图卷积网络(GCN)模型基于同配性假设,无法直接应用于异配图的表示学习,且许多异配图表示学习的研究工作受消息传递机制的限制,导致节点特征混淆和特征过度挤压而出现过平滑问题。针对这些问题,提出一种基于Graph Transformer的半监督异配图表示学习模型HPGT(HeteroPhilic Graph Transformer)。首先,使用度连接概率矩阵采样节点的路径邻域,再通过自注意力机制自适应地聚合路径上的节点异配连接模式,编码得到节点的结构信息,用节点的原始属性信息和结构信息构建Transformer层的自注意力模块;其次,将每个节点自身的隐层表示与它的邻域节点的隐层表示分离更新以避免节点通过自注意力模块聚合过量的自身信息,再把每个节点表示与它的邻域表示连接,得到单个Transformer层的输出,另外,将所有的Transformer层的输出跳连到最终的节点隐层表示以防止中间层信息丢失;最后,使用线性层和Softmax层将节点的隐层表示映射到节点的预测标签。实验结果表明,与无结构编码(SE)的模型相比,基于度连接概率的SE能为Transformer层的自注意力模块提供有效的偏差信息,HPGT平均准确率提升0.99%~11.98%;与对比模型相比,在异配数据集(Texas、Cornell、Wisconsin和Actor)上,模型节点分类准确率提升0.21%~1.69%,在同配数据集(Cora、CiteSeer和PubMed)上,节点分类准确率分别达到了0.8379、0.7467和0.8862。以上结果验证了HPGT具有较强的异配图表示学习能力,尤其适用于强异配图节点分类任务。

A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

A Value for Games Defined on Graphs

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

Heterophilic Graph Neural Network Based on Spatial and Frequency Domain Adaptive Embedding Mechanism

Graph Neural Networks(GNNs)play a significant role in tasks related to homophilic graphs.Traditional GNNs,based on the assumption of homophily,employ low-pass filters for neighboring nodes to achieve information aggregation and embedding.However,in heterophilic graphs,nodes from different categories often establish connections,while nodes of the same category are located further apart in the graph topology.This characteristic poses challenges to traditional GNNs,leading to issues of“distant node modeling deficiency”and“failure of the homophily assumption”.In response,this paper introduces the Spatial-Frequency domain Adaptive Heterophilic Graph Neural Networks(SFA-HGNN),which integrates adaptive embedding mechanisms for both spatial and frequency domains to address the aforementioned issues.Specifically,for the first problem,we propose the“Distant Spatial Embedding Module”,aiming to select and aggregate distant nodes through high-order randomwalk transition probabilities to enhance modeling capabilities.For the second issue,we design the“Proximal Frequency Domain Embedding Module”,constructing adaptive filters to separate high and low-frequency signals of nodes,and introduce frequency-domain guided attention mechanisms to fuse the relevant information,thereby reducing the noise introduced by the failure of the homophily assumption.We deploy the SFA-HGNN on six publicly available heterophilic networks,achieving state-of-the-art results in four of them.Furthermore,we elaborate on the hyperparameter selection mechanism and validate the performance of each module through experimentation,demonstrating a positive correlation between“node structural similarity”,“node attribute vector similarity”,and“node homophily”in heterophilic networks.

Weighted Forwarding in Graph Convolution Networks for Recommendation Information Systems

Recommendation Information Systems(RIS)are pivotal in helping users in swiftly locating desired content from the vast amount of information available on the Internet.Graph Convolution Network(GCN)algorithms have been employed to implement the RIS efficiently.However,the GCN algorithm faces limitations in terms of performance enhancement owing to the due to the embedding value-vanishing problem that occurs during the learning process.To address this issue,we propose a Weighted Forwarding method using the GCN(WF-GCN)algorithm.The proposed method involves multiplying the embedding results with different weights for each hop layer during graph learning.By applying the WF-GCN algorithm,which adjusts weights for each hop layer before forwarding to the next,nodes with many neighbors achieve higher embedding values.This approach facilitates the learning of more hop layers within the GCN framework.The efficacy of the WF-GCN was demonstrated through its application to various datasets.In the MovieLens dataset,the implementation of WF-GCN in LightGCN resulted in significant performance improvements,with recall and NDCG increasing by up to+163.64%and+132.04%,respectively.Similarly,in the Last.FM dataset,LightGCN using WF-GCN enhanced with WF-GCN showed substantial improvements,with the recall and NDCG metrics rising by up to+174.40%and+169.95%,respectively.Furthermore,the application of WF-GCN to Self-supervised Graph Learning(SGL)and Simple Graph Contrastive Learning(SimGCL)also demonstrated notable enhancements in both recall and NDCG across these datasets.

An End-To-End Hyperbolic Deep Graph Convolutional Neural Network Framework

Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.

BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).

A Sharding Scheme Based on Graph Partitioning Algorithm for Public Blockchain

Blockchain technology,with its attributes of decentralization,immutability,and traceability,has emerged as a powerful catalyst for enhancing traditional industries in terms of optimizing business processes.However,transaction performance and scalability has become the main challenges hindering the widespread adoption of blockchain.Due to its inability to meet the demands of high-frequency trading,blockchain cannot be adopted in many scenarios.To improve the transaction capacity,researchers have proposed some on-chain scaling technologies,including lightning networks,directed acyclic graph technology,state channels,and shardingmechanisms,inwhich sharding emerges as a potential scaling technology.Nevertheless,excessive cross-shard transactions and uneven shard workloads prevent the sharding mechanism from achieving the expected aim.This paper proposes a graphbased sharding scheme for public blockchain to efficiently balance the transaction distribution.Bymitigating crossshard transactions and evening-out workloads among shards,the scheme reduces transaction confirmation latency and enhances the transaction capacity of the blockchain.Therefore,the scheme can achieve a high-frequency transaction as well as a better blockchain scalability.Experiments results show that the scheme effectively reduces the cross-shard transaction ratio to a range of 35%-56%and significantly decreases the transaction confirmation latency to 6 s in a blockchain with no more than 25 shards.

Algorithm for Visualization of Zero Divisor Graphs of the Ring ℤn Using MAPLE Coding

This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤn modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.

Feature Matching via Topology-Aware Graph Interaction Model

Feature matching plays a key role in computer vision. However, due to the limitations of the descriptors, the putative matches are inevitably contaminated by massive outliers.This paper attempts to tackle the outlier filtering problem from two aspects. First, a robust and efficient graph interaction model,is proposed, with the assumption that matches are correlated with each other rather than independently distributed. To this end, we construct a graph based on the local relationships of matches and formulate the outlier filtering task as a binary labeling energy minimization problem, where the pairwise term encodes the interaction between matches. We further show that this formulation can be solved globally by graph cut algorithm. Our new formulation always improves the performance of previous localitybased method without noticeable deterioration in processing time,adding a few milliseconds. Second, to construct a better graph structure, a robust and geometrically meaningful topology-aware relationship is developed to capture the topology relationship between matches. The two components in sum lead to topology interaction matching(TIM), an effective and efficient method for outlier filtering. Extensive experiments on several large and diverse datasets for multiple vision tasks including general feature matching, as well as relative pose estimation, homography and fundamental matrix estimation, loop-closure detection, and multi-modal image matching, demonstrate that our TIM is more competitive than current state-of-the-art methods, in terms of generality, efficiency, and effectiveness. The source code is publicly available at http://github.com/YifanLu2000/TIM.

Insider threat detection approach for tobacco industry based on heterogeneous graph embedding

In the tobacco industry,insider employee attack is a thorny problem that is difficult to detect.To solve this issue,this paper proposes an insider threat detection method based on heterogeneous graph embedding.First,the interrelationships between logs are fully considered,and log entries are converted into heterogeneous graphs based on these relationships.Second,the heterogeneous graph embedding is adopted and each log entry is represented as a low-dimensional feature vector.Then,normal logs and malicious logs are classified into different clusters by clustering algorithm to identify malicious logs.Finally,the effectiveness and superiority of the method is verified through experiments on the CERT dataset.The experimental results show that this method has better performance compared to some baseline methods.

A Bitcoin Address Multi-Classification Mechanism Based on Bipartite Graph-Based Maximization Consensus

Bitcoin is widely used as the most classic electronic currency for various electronic services such as exchanges,gambling,marketplaces,and also scams such as high-yield investment projects.Identifying the services operated by a Bitcoin address can help determine the risk level of that address and build an alert model accordingly.Feature engineering can also be used to flesh out labeled addresses and to analyze the current state of Bitcoin in a small way.In this paper,we address the problem of identifying multiple classes of Bitcoin services,and for the poor classification of individual addresses that do not have significant features,we propose a Bitcoin address identification scheme based on joint multi-model prediction using the mapping relationship between addresses and entities.The innovation of the method is to(1)Extract as many valuable features as possible when an address is given to facilitate the multi-class service identification task.(2)Unlike the general supervised model approach,this paper proposes a joint prediction scheme for multiple learners based on address-entity mapping relationships.Specifically,after obtaining the overall features,the address classification and entity clustering tasks are performed separately,and the results are subjected to graph-basedmaximization consensus.The final result ismade to baseline the individual address classification results while satisfying the constraint of having similarly behaving entities as far as possible.By testing and evaluating over 26,000 Bitcoin addresses,our feature extraction method captures more useful features.In addition,the combined multi-learner model obtained results that exceeded the baseline classifier reaching an accuracy of 77.4%.

Privacy-Preserving Multi-Keyword Fuzzy Adjacency Search Strategy for Encrypted Graph in Cloud Environment

In a cloud environment,outsourced graph data is widely used in companies,enterprises,medical institutions,and so on.Data owners and users can save costs and improve efficiency by storing large amounts of graph data on cloud servers.Servers on cloud platforms usually have some subjective or objective attacks,which make the outsourced graph data in an insecure state.The issue of privacy data protection has become an important obstacle to data sharing and usage.How to query outsourcing graph data safely and effectively has become the focus of research.Adjacency query is a basic and frequently used operation in graph,and it will effectively promote the query range and query ability if multi-keyword fuzzy search can be supported at the same time.This work proposes to protect the privacy information of outsourcing graph data by encryption,mainly studies the problem of multi-keyword fuzzy adjacency query,and puts forward a solution.In our scheme,we use the Bloom filter and encryption mechanism to build a secure index and query token,and adjacency queries are implemented through indexes and query tokens on the cloud server.Our proposed scheme is proved by formal analysis,and the performance and effectiveness of the scheme are illustrated by experimental analysis.The research results of this work will provide solid theoretical and technical support for the further popularization and application of encrypted graph data processing technology.

Survey and Prospect for Applying Knowledge Graph in Enterprise Risk Management

Enterprise risk management holds significant importance in fostering sustainable growth of businesses and in serving as a critical element for regulatory bodies to uphold market order.Amidst the challenges posed by intricate and unpredictable risk factors,knowledge graph technology is effectively driving risk management,leveraging its ability to associate and infer knowledge from diverse sources.This review aims to comprehensively summarize the construction techniques of enterprise risk knowledge graphs and their prominent applications across various business scenarios.Firstly,employing bibliometric methods,the aim is to uncover the developmental trends and current research hotspots within the domain of enterprise risk knowledge graphs.In the succeeding section,systematically delineate the technical methods for knowledge extraction and fusion in the standardized construction process of enterprise risk knowledge graphs.Objectively comparing and summarizing the strengths and weaknesses of each method,we provide recommendations for addressing the existing challenges in the construction process.Subsequently,categorizing the applied research of enterprise risk knowledge graphs based on research hotspots and risk category standards,and furnishing a detailed exposition on the applicability of technical routes and methods.Finally,the future research directions that still need to be explored in enterprise risk knowledge graphs were discussed,and relevant improvement suggestions were proposed.Practitioners and researchers can gain insights into the construction of technical theories and practical guidance of enterprise risk knowledge graphs based on this foundation.

On traceable iterated line graph and hamiltonian path index

Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.

Analysis on the Changes of Research Hotspots in the Prevention and Treatment of COVID-19 by Traditional Chinese Medicine Based on Knowledge Graph

Objective: To grasp the changing trend of research hotspots of traditional Chinese medicine in the prevention and treatment of COVID-19, and to better play the role of traditional Chinese medicine in the prevention and treatment of COVID-19 and other diseases. Methods: The research literature from 2020 to 2022 was searched in the CNKI database, and CiteSpace software was used for visual analysis. Results: The papers on the prevention and treatment of COVID-19 by traditional Chinese medicine changed from cases, overviews, reports, and efficacy studies to more in-depth mechanism research, theoretical exploration, and social impact analysis, and finally formed a theory-clinical-society Influence-institutional change and other multi-dimensional achievement systems. Conclusion: Analyzing the changing trends of TCM hotspots in the prevention and treatment of COVID-19 can fully understand the important value of TCM, take the coordination of TCM and Western medicine as an important means to deal with public health security incidents, and promote the exploration of the potential efficacy of TCM, so as to enhance the role of TCM in Applications in social stability, emergency security, clinical practice, etc.

Multi-modal knowledge graph inference via media convergence and logic rule

Media convergence works by processing information from different modalities and applying them to different domains.It is difficult for the conventional knowledge graph to utilise multi-media features because the introduction of a large amount of information from other modalities reduces the effectiveness of representation learning and makes knowledge graph inference less effective.To address the issue,an inference method based on Media Convergence and Rule-guided Joint Inference model(MCRJI)has been pro-posed.The authors not only converge multi-media features of entities but also introduce logic rules to improve the accuracy and interpretability of link prediction.First,a multi-headed self-attention approach is used to obtain the attention of different media features of entities during semantic synthesis.Second,logic rules of different lengths are mined from knowledge graph to learn new entity representations.Finally,knowledge graph inference is performed based on representing entities that converge multi-media features.Numerous experimental results show that MCRJI outperforms other advanced baselines in using multi-media features and knowledge graph inference,demonstrating that MCRJI provides an excellent approach for knowledge graph inference with converged multi-media features.

Predicting Traffic Flow Using Dynamic Spatial-Temporal Graph Convolution Networks

Traffic flow prediction plays a key role in the construction of intelligent transportation system.However,due to its complex spatio-temporal dependence and its uncertainty,the research becomes very challenging.Most of the existing studies are based on graph neural networks that model traffic flow graphs and try to use fixed graph structure to deal with the relationship between nodes.However,due to the time-varying spatial correlation of the traffic network,there is no fixed node relationship,and these methods cannot effectively integrate the temporal and spatial features.This paper proposes a novel temporal-spatial dynamic graph convolutional network(TSADGCN).The dynamic time warping algorithm(DTW)is introduced to calculate the similarity of traffic flow sequence among network nodes in the time dimension,and the spatiotemporal graph of traffic flow is constructed to capture the spatiotemporal characteristics and dependencies of traffic flow.By combining graph attention network and time attention network,a spatiotemporal convolution block is constructed to capture spatiotemporal characteristics of traffic data.Experiments on open data sets PEMSD4 and PEMSD8 show that TSADGCN has higher prediction accuracy than well-known traffic flow prediction algorithms.

Learning to Branch in Combinatorial Optimization With Graph Pointer Networks

Traditional expert-designed branching rules in branch-and-bound(B&B) are static, often failing to adapt to diverse and evolving problem instances. Crafting these rules is labor-intensive, and may not scale well with complex problems.Given the frequent need to solve varied combinatorial optimization problems, leveraging statistical learning to auto-tune B&B algorithms for specific problem classes becomes attractive. This paper proposes a graph pointer network model to learn the branch rules. Graph features, global features and historical features are designated to represent the solver state. The graph neural network processes graph features, while the pointer mechanism assimilates the global and historical features to finally determine the variable on which to branch. The model is trained to imitate the expert strong branching rule by a tailored top-k Kullback-Leibler divergence loss function. Experiments on a series of benchmark problems demonstrate that the proposed approach significantly outperforms the widely used expert-designed branching rules. It also outperforms state-of-the-art machine-learning-based branch-and-bound methods in terms of solving speed and search tree size on all the test instances. In addition, the model can generalize to unseen instances and scale to larger instances.

Combining Deep Learning with Knowledge Graph for Design Knowledge Acquisition in Conceptual Product Design

The acquisition of valuable design knowledge from massive fragmentary data is challenging for designers in conceptual product design.This study proposes a novel method for acquiring design knowledge by combining deep learning with knowledge graph.Specifically,the design knowledge acquisition method utilises the knowledge extraction model to extract design-related entities and relations from fragmentary data,and further constructs the knowledge graph to support design knowledge acquisition for conceptual product design.Moreover,the knowledge extraction model introduces ALBERT to solve memory limitation and communication overhead in the entity extraction module,and uses multi-granularity information to overcome segmentation errors and polysemy ambiguity in the relation extraction module.Experimental comparison verified the effectiveness and accuracy of the proposed knowledge extraction model.The case study demonstrated the feasibility of the knowledge graph construction with real fragmentary porcelain data and showed the capability to provide designers with interconnected and visualised design knowledge.