基于元路径的图Transformer神经网络

图神经网络作为一种新的深度学习模型,被广泛运用在图数据中,并极大地推动了推荐系统、社交网络、知识图谱等应用的发展.现有的异构图神经网络通常事先定义了多条元路径来学习异构图中的复合关系.然而,这些模型通常在特征聚合步骤中只考虑单条元路径,导致模型只关注了元路径的局部结构,忽略了元路径之间的全局相关性;还有一些模型则是忽略掉了元路径的中间节点和边信息,导致模型无法学习到元路径内部的语义信息.针对以上问题,本文提出一种基于元路径的图Transformer神经网络(MaGTNN).该模型首先将异构图采样为基于元路径的多关系子图,利用提出的位置编码和边编码的方法来获取元路径中的语义信息.随后使用改进的图Transformer层计算出目标节点与其元邻居的相似度,并利用该相似度来聚合其所有的元邻居信息.在3个公开数据集的节点分类和节点聚类任务中, MaGTNN均高于最新的基准模型.     

Multi-view Contrastive Enhanced Heterogeneous Graph Structure Learning

As a learning method of heterogeneous graph representation, heterogeneous graph neural networks can effectively extract complex structural and semantic information from heterogeneous graphs, and perform excellently in node classification and link prediction tasks to provide strong support for the representation and analysis of knowledge graphs. Due to the existence of some noisy interactions or missing interactions in the heterogeneous graphs, the heterogeneous graph neural network incorporates erroneous neighbor features, thus affecting the overall performance of the model. To solve the above problems, in this paper we proposes a heterogeneous graph structure learning model enhanced by multi-view contrast. Firstly, the semantic information in the heterogeneous graph is maintained by the meta-path, and the similarity graph is generated by calculating the feature similarity among the nodes under each meta-path, which is fused with the meta-path graph to optimize the graph structure. By contrasting the similarity graph and meta-path graph as multiple views, the graph structure is optimized without supervision information, and the dependence on supervision signals is eliminated. Finally, for addressing the problem that the learning ability of the neural network model is insufficient at the initial training stage and there are often erroneous interactions in the generated graph structure, we design a progressive graph structure fusion method. Through incremental weighted addition of meta-path graphs and similarity graphs, the weight of similarity graphs in the fusion is changed. This not only prevents erroneous interactions from being introduced in the initial training stage but also achieves the purpose of employing the interactions in similarity graphs to suppress interference interactions or complete missing interactions, which leads to the optimized heterogeneous structure. Meanwhile, node classification and node clustering are selected as the verification tasks of graph structure learning. The experimental results on four real heterogeneous graph datasets prove that the proposed learning method is feasible and effective. Compared with the optimal comparison model, the performance of this model has been significantly improved under both tasks.     

Mapping the forms of meaning in small worlds

Prox is a stochastic method to map the local and global structures of real‐world complex networks, which are called small worlds. Prox transforms a graph into a Markov chain; the states of which are the nodes of the graph in question. Particles wander from one node to another within the graph by following the graph's edges. It is the dynamics of the particles' trajectories that map the structural properties of the graphs that are studied. Concrete examples are presented in a graph of synonyms to illustrate this approach. © 2008 Wiley Periodicals, Inc.     

A Taxonomy and Survey of Dynamic Graph Visualization

Dynamic graph visualization focuses on the challenge of representing the evolution of relationships between entities in readable, scalable and effective diagrams. This work surveys the growing number of approaches in this discipline. We derive a hierarchical taxonomy of techniques by systematically categorizing and tagging publications. While static graph visualizations are often divided into node‐link and matrix representations, we identify the representation of time as the major distinguishing feature for dynamic graph visualizations: either graphs are represented as animated diagrams or as static charts based on a timeline. Evaluations of animated approaches focus on dynamic stability for preserving the viewer's mental map or, in general, compare animated diagrams to timeline‐based ones. A bibliographic analysis provides insights into the organization and development of the field and its community. Finally, we identify and discuss challenges for future research. We also provide feedback from experts, collected with a questionnaire, which gives a broad perspective of these challenges and the current state of the field.     

Pre-Train and Learn:Preserving Global Information for Graph Neural Networks

Graph neural networks(GNNs) have shown great power in learning on graphs.However,it is still a challenge for GNNs to model information faraway from the source node.The ability to preserve global information can enhance graph representation and hence improve classification precision.In the paper,we propose a new learning framework named G-GNN(Global information for GNN) to address the challenge.First,the global structure and global attribute features of each node are obtained via unsupervised pre-training,and those global features preserve the global information associated with the node.Then,using the pre-trained global features and the raw attributes of the graph,a set of parallel kernel GNNs is used to learn different aspects from these heterogeneous features.Any general GNN can be used as a kernal and easily obtain the ability of preserving global information,without having to alter their own algorithms.Extensive experiments have shown that state-of-the-art models,e.g.,GCN,GAT,Graphsage and APPNP,can achieve improvement with G-GNN on three standard evaluation datasets.Specially,we establish new benchmark precision records on Cora(84.31％) and Pubmed(80.95％) when learning on attributed graphs.     

Shadow Graphs and 3D Texture Reconstruction

We present methods for recovering surface height fields such as geometric details of 3D textures by incorporating shadow constraints. We introduce shadow graphs which give a new graph-based representation for shadow constraints. It can be shown that the shadow graph alone is sufficient to solve the shape-from-shadow problem from a dense set of images. Shadow graphs provide a simpler and more systematic approach to represent and integrate shadow constraints from multiple images. To recover height fields from a sparse set of images, we propose a method for integrated shadow and shading constraints. Previous shape-from-shadow algorithms do not consider shading constraints while shape-from-shading usually assumes there is no shadow. Our method is based on collecting a set of images from a fixed viewpoint as a known light source changes its position. It first builds a shadow graph from shadow constraints from which an upper bound for each pixel can be derived if the height values of a small number of pixels are initialized correctly. Finally, a constrained optimization procedure is designed to make the results from shape-from-shading consistent with the height bounds derived from the shadow constraints. Our technique is demonstrated on both synthetic and real imagery.     

特殊图的图修正问题研究综述

图修正问题是指在一个图中进行删除点、删除边或加边操作,使这个图转变成另一个具有某种特殊性质的图。图修正问题一直被广泛研究,尤其对弦图、区间图以及单位区间图的图修正问题的研究更是如此。弦图是完美图中最重要的一类图,也是(单位)区间图的父类图,很多经典的NP难问题在弦图上都是多项式可解的。区间图以及单位区间图在生物计算上有着广泛的应用。对这几类图的图修正问题的研究对计算机理论和实践有很大的贡献。首先介绍并总结了关于弦图、区间图以及单位区间图的图修正问题的重要算法和技术,然后对这些问题的研究现状进行分析,并提出了今后研究中值得关注的问题。     

语义增强的大规模多元图简化可视分析方法

网络图可视化可以有效展示网络节点之间的连接关系,广泛应用于诸多领域,如社交网络、知识图谱、生物基因网络等.随着网络数据规模的不断增加,如何简化表达大规模网络图结构已成为图可视化领域中的研究热点.经典的网络图简化可视化方法主要包括图采样、边绑定和图聚类等技术,在减少大量点线交叉造成的视觉紊乱的基础上,提高用户对大规模网络结构的探索和认知效率.然而,上述方法主要侧重于网络图中的拓扑结构,却较少考虑和利用多元图节点的多维属性特征,难以有效提取和表达语义信息,从而无法帮助用户理解大规模多元网络的拓扑结构与多维属性之间的内在关联,为大规模多元图的认知和理解带来困难.因此,本文提出一种语义增强的大规模多元图简化可视分析方法,首先在基于模块度的图聚类算法基础上提取出网络图的层次结构;其次通过多维属性信息熵的计算和比较分析,对网络层次结构进行自适应划分,筛选出具有最优属性聚集特征的社团;进而设计交互便捷的多个关联视图来展示社团之间的拓扑结构、层次关系和属性分布,从不同角度帮助用户分析多维属性在社团形成和网络演化中的作用.大量实验结果表明,本文方法能够有效简化大规模多元图的视觉表达,可以快速分析不同应用领域大规模多元图的关联结构与语义构成,具有较强的实用性.     

基于关系图卷积网络的代码搜索方法

代码搜索是当下自然语言处理和软件工程交叉领域的一个重要分支. 开发高效的代码搜索算法能够显著提高代码重用的能力, 从而有效提高软件开发人员的工作效率. 代码搜索任务是以描述代码片段功能的自然语言作为输入, 在海量代码库中搜索得到相关代码片段的过程. 基于序列模型的代码搜索方法DeepCS虽然取得了很好的效果, 但这种方法不能捕捉代码的深层语义. 基于图嵌入的代码搜索方法GraphSearchNet能缓解这个问题, 但没有对代码与文本进行细粒度匹配, 也忽视了代码图和文本图的全局关系. 为了解决以上局限性, 提出基于关系图卷积网络的代码搜索方法, 对构建的文本图和代码图编码, 从节点层面对文本查询和代码片段进行细粒度匹配, 并应用神经张量网络捕捉它们的全局关系. 在两个公开数据集上的实验结果表明, 所提方法比先进的基线模型DeepCS和GraphSearchNet搜索精度更高.     

Mental map preserving graph drawing using simulated annealing

Visualizing graphs has been studied extensively in the community of graph drawing and information visualization over the years. In some applications, the user is required to interact with a graph by making slight changes to the underlying graph structure. To visualize graphs in such an interactive environment, it is desirable that the differences between the displays of the original and the modified graphs be kept minimal, allowing the user to comprehend the changes in the graph structure faster. As the mental map concept refers to the presentation of a person’s mind while exploring visual information, the better the mental map is preserved, the easier the structure change of a graph is understood. It is somewhat surprising that preserving the user’s mental map has largely been ignored in the graph drawing community in the past. We propose an effective mental-map-preserving graph drawing algorithm for straight-line drawings of general undirected graphs based on the simulated-annealing technique. Our experimental results and questionnaire analysis suggest this new approach to be promising.     

多视图对比增强的异质图结构学习方法

异质图神经网络作为一种异质图表示学习的方法,可以有效地抽取异质图中的复杂结构与语义信息,在节点分类和连接预测任务上取得了优异的表现,为知识图谱的表示与分析提供了有力的支撑.现有的异质图由于存在一定的噪声交互或缺失部分交互,导致异质图神经网络在节点聚合、更新时融入错误的邻域特征信息,从而影响模型的整体性能.为解决该问题,提出了多视图对比增强的异质图结构学习模型.该模型首先利用元路径保持异质图中的语义信息,并通过计算每条元路径下节点之间特征相似度生成相似度图,将其与元路径图融合,实现对图结构的优化.通过将相似度图与元路径图作为不同视图进行多视图对比,实现无监督信息的情况下优化图结构,摆脱对监督信号的依赖.最后,为解决神经网络模型在训练初期学习能力不足、生成的图结构中往往存在错误交互的问题,设计了一个渐进式的图结构融合方法.通过将元路径图和相似度图递增地加权相加,改变图结构融合过程中相似度图所占的比例,在抑制了因模型学习能力弱引入过多的错误交互的同时,达到了用相似度图中的交互抑制原有干扰交互或补全缺失交互的目的,实现了对异质图结构的优化.选择节点分类与节点聚类作为图结构学习的验证任务,在4种...     

基于Ncut准则的图分割的新算法

针对有权图分割时不能很好解决子图内部耦合度不高的问题,使用可以同时优化子图内部顶点耦合度和子图之间顶点耦合度的Ncut准则,提出了一种新的基于迭代改善策略的RNK分割算法。算法通过不断交换可以改善Ncut值的顶点对优化现有分割。与传统分割算法相比,可以同时保证子图内最大耦合度和子图间最小的耦合度。并提出一种散列技术,提高查找最优交换顶点对的效率。当图为稠密矩阵时,改善效果尤为明显。通过对随机图分割的实验结果表明,该算法较传统的KL算法可以得到更理想的分割结果。     

Genetic algorithm for the personnel assignment problem with multiple objectives

The assignment problem is a well-known graph optimization problem defined on weighted-bipartite graphs. The objective of the standard assignment problem is to maximize the summation of the weights of the matched edges of the bipartite graph. In the standard assignment problem, any node in one partition can be matched with any node in the other partition without any restriction. In this paper, variations of the standard assignment problem are defined with matching constraints by introducing structures in the partitions of the bipartite graph, and by defining constraints on these structures. According to the first constraint, the matching between the two partitions should respect the hierarchical-ordering constraints defined by forest and level graph structures produced by using the nodes of the two partitions respectively. In order to define the second constraint, the nodes of the partitions of the bipartite graph are distributed into mutually exclusive sets. The set-restriction constraint enforces the rule that in one of the partitions all the elements of each set should be matched with the elements of a set in the other partition. Even with one of these constraints the assignment problem becomes an NP-hard problem. Therefore, the extended assignment problem with both the hierarchical-ordering and set-restriction constraints becomes an NP-hard multi-objective optimization problem with three conflicting objectives; namely, minimizing the numbers of hierarchical-ordering and set-restriction violations, and maximizing the summation of the weights of the edges of the matching. Genetic algorithms are proven to be very successful for NP-hard multi-objective optimization problems. In this paper, we also propose genetic algorithm solutions for different versions of the assignment problem with multiple objectives based on hierarchical and set constraints, and we empirically show the performance of these solutions.     

Removing Node Overlapping in Graph Layout Using Constrained Optimization

Although graph drawing has been extensively studied, little attention has been paid to the problem of node overlapping. The problem arises because almost all existing graph layout algorithms assume that nodes are points. In practice, however, nodes may be labelled, and these labels may overlap. Here we investigate how such node overlapping can be removed in a subsequent layout adjustment phase. We propose four different approaches for removing node overlapping, all of which are based on constrained optimization techniques. The first is the simplest. It performs the minimal linear scaling which will remove node-overlapping. The second approach relies on formulating the node overlapping problem as a convex quadratic programming problem, which can then be solved by any quadratic solver. The disadvantage is that, since constraints must be linear, the node overlapping constraints cannot be expressed directly, but must be strengthened to obtain a linear constraint strong enough to ensure no node overlapping. The third and fourth approaches are based on local search methods. The third is an adaptation of the EGENET solver originally designed for solving general constraint satisfaction problems, while the fourth approach is a form of Lagrangian multiplier method, a well-known optimization technique used in operations research. Both the third and fourth method are able to handle the node overlapping constraints directly, and thus may potentially find better solutions. Their disadvantage is that no efficient global optimization methods are available for such problems, and hence we must accept a local minimum. We illustrate all of the above methods on a series of layout adjustment problems.     

A Lagrangian relaxation network for graph matching

A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing. Our approach is in the same spirit as a Lagrangian decomposition approach in that the row and column constraints are satisfied separately with a Lagrange multiplier used to equate the two "solutions". Due to the unavoidable symmetries in graph isomorphism (resulting in multiple global minima), we add a symmetry-breaking self-amplification term in order to obtain a permutation matrix. With the application of a fixpoint preserving algebraic transformation to both the distance measure and self-amplification terms, we obtain a Lagrangian relaxation network. The network performs minimization with respect to the Lagrange parameters and maximization with respect to the permutation matrix variables. Simulation results are shown on 100 node random graphs and for a wide range of connectivities.     

SetCoLa: High‐Level Constraints for Graph Layout

Constraints enable flexible graph layout by combining the ease of automatic layout with customizations for a particular domain. However, constraint‐based layout often requires many individual constraints defined over specific nodes and node pairs. In addition to the effort of writing and maintaining a large number of similar constraints, such constraints are specific to the particular graph and thus cannot generalize to other graphs in the same domain. To facilitate the specification of customized and generalizable constraint layouts, we contribute SetCoLa: a domain‐specific language for specifying high‐level constraints relative to properties of the backing data. Users identify node sets based on data or graph properties and apply high‐level constraints within each set. Applying constraints to node sets rather than individual nodes reduces specification effort and facilitates reapplication of customized layouts across distinct graphs. We demonstrate the conciseness, generalizability, and expressiveness of SetCoLa on a series of real‐world examples from ecological networks, biological systems, and social networks.     

图网络层级信息挖掘分类算法综述

深度学习作为人工智能的一个研究分支发展迅速,而研究数据主要是语音、图像和视频等,这些具有规则结构的数据通常在欧氏空间中表示。然而许多学习任务需要处理的数据是从非欧氏空间中生成,这些数据特征和其关系结构可以用图来定义。图卷积神经网络通过将卷积定理应用于图,完成节点之间的信息传播与聚合,成为建模图数据一种有效的方法。尽管图卷积神经网络取得了巨大成功,但针对图任务中的节点分类问题,由于深层图结构优化的特有难点——过平滑现象,现有的多数模型都只有两三层的浅层模型架构。在理论上,图卷积神经网络的深层结构可以获得更多节点表征信息,因此针对其层级信息进行研究,将层级结构算法迁移到图数据分析的核心在于图层级卷积算子构建和图层级间信息融合。本文对图网络层级信息挖掘算法进行综述,介绍图神经网络的发展背景、存在问题以及图卷积神经网络层级结构算法的发展,根据不同图卷积层级信息处理将现有算法分为正则化方法和架构调整方法。正则化方法通过重新构建图卷积算子更好地聚合邻域信息,而架构调整方法则融合层级信息丰富节点表征。图卷积神经网络层级特性实验表明,图结构中存在层级特性节点,现有图层级信息挖掘算法仍未对层级特性节点的图信息进行完全探索。最后,总结了图卷积神经网络层级信息挖掘模型的主要应用领域,并从计算效率、大规模数据、动态图和应用场景等方面提出进一步研究的方向。     

A survey on dynamic graph processing on GPUs: concepts,terminologies and systems

Graphs that are used to model real-world entities with vertices and relationships among entities with edges, have proven to be a powerful tool for describing real-world problems in applications. In most real-world scenarios, entities and their relationships are subject to constant changes. Graphs that record such changes are called dynamic graphs. In recent years, the widespread application scenarios of dynamic graphs have stimulated extensive research on dynamic graph processing systems that continuously ingest graph updates and produce up-to-date graph analytics results. As the scale of dynamic graphs becomes larger, higher performance requirements are demanded to dynamic graph processing systems. With the massive parallel processing power and high memory bandwidth, GPUs become mainstream vehicles to accelerate dynamic graph processing tasks. GPU-based dynamic graph processing systems mainly address two challenges: maintaining the graph data when updates occur (i.e., graph updating) and producing analytics results in time (i.e., graph computing). In this paper, we survey GPU-based dynamic graph processing systems and review their methods on addressing both graph updating and graph computing. To comprehensively discuss existing dynamic graph processing systems on GPUs, we first introduce the terminologies of dynamic graph processing and then develop a taxonomy to describe the methods employed for graph updating and graph computing. In addition, we discuss the challenges and future research directions of dynamic graph processing on GPUs.     

Parallel strong orientation of an undirected graph

A dominating set of an undirected graph G is a set D of nodes such that every node of G either is in D or is adjacent to some node of D. It is shown that the problem of finding a minimum cardinality dominating set is NP-complete for split graphs (a subclass of chordal graphs) and bipartite graphs.