图形神经网络（GNNS）传统上由于1）建模邻域和2）保留不对称，因此由于1）的显着挑战，传统上具有较差的图形（DIGRAPH）的性能。在本文中，我们通过利用从多订购和分区社区的双曲线协作学习以及由社会心理因素的启发的常规方来解决传统GNN中的这些挑战。我们所产生的形式主义，Digraph双曲线网络（D-Hypr）学习双曲线空间中的节点表示，以避免真实世界的结构和语义扭曲。我们对4个任务进行全面的实验：链路预测，节点分类，标志预测和嵌入可视化。D-HYPR在大多数任务和数据集上统计上显着优于本领域的当前状态，同时实现竞争性能。我们的代码和数据将可用。

Hyperbolic space is emerging as a promising learning space for representation learning, owning to its exponential growth volume. Compared with the flat Euclidean space, the curved hyperbolic space is far more ambient and embeddable, particularly for datasets with implicit tree-like architectures, such as hierarchies and power-law distributions. On the other hand, the structure of a real-world network is usually intricate, with some regions being tree-like, some being flat, and others being circular. Directly embedding heterogeneous structural networks into a homogeneous embedding space unavoidably brings inductive biases and distortions. Inspiringly, the discrete curvature can well describe the local structure of a node and its surroundings, which motivates us to investigate the information conveyed by the network topology explicitly in improving geometric learning. To this end, we explore the properties of the local discrete curvature of graph topology and the continuous global curvature of embedding space. Besides, a Hyperbolic Curvature-aware Graph Neural Network, HCGNN, is further proposed. In particular, HCGNN utilizes the discrete curvature to lead message passing of the surroundings and adaptively adjust the continuous curvature simultaneously. Extensive experiments on node classification and link prediction tasks show that the proposed method outperforms various competitive models by a large margin in both high and low hyperbolic graph data. Case studies further illustrate the efficacy of discrete curvature in finding local clusters and alleviating the distortion caused by hyperbolic geometry.

嵌入现实世界网络提出挑战，因为它不清楚如何识别其潜在的几何形状。嵌入了诸如无尺度网络的辅音网络，以欧几里德空间显示出造成的扭曲。将无缝的网络嵌入到双曲线空间提供令人兴奋的替代方案，但在将各种网络与潜在几何图中嵌入不同的几何形状时，扭曲的障碍。我们提出了一种归纳模型，可以利用GCNS和琐碎束的表现力来学习有或没有节点特征的网络的归纳节点表示。琐碎的束是一种简单的纤维束的情况，这是全球的空间，其基础空间和光纤的产品空间。基础空间和纤维的坐标可用于表达产生边缘的分类和抵消因子。因此，该模型能够学习可以表达这些因素的嵌入物。在实践中，与Euclidean和双曲线GCN相比，它会减少链路预测和节点分类的错误。

双曲线神经网络由于对几个图形问题的有希望的结果，包括节点分类和链接预测，因此最近引起了极大的关注。取得成功的主要原因是双曲空间在捕获图数据集的固有层次结构方面的有效性。但是，在非层次数据集方面，它们在概括，可伸缩性方面受到限制。在本文中，我们对双曲线网络进行了完全正交的观点。我们使用Poincar \'e磁盘对双曲线几何形状进行建模，并将其视为磁盘本身是原始的切线空间。这使我们能够用欧几里院近似替代非尺度的M \“ Obius Gyrovector操作，因此将整个双曲线模型简化为具有双曲线归一化功能的欧几里得模型。它仍然在Riemannian歧管中起作用，因此我们称其为伪poincar \'e框架。我们将非线性双曲线归一化应用于当前的最新均质和多关系图网络，与欧几里得和双曲线对应物相比，性能的显着改善。这项工作的主要影响在于其在欧几里得空间中捕获层次特征的能力，因此可以替代双曲线网络而不会损失性能指标，同时利用欧几里得网络的功能，例如可解释性和有效执行各种模型组件。

Clustering is a fundamental problem in network analysis that finds closely connected groups of nodes and separates them from other nodes in the graph, while link prediction is to predict whether two nodes in a network are likely to have a link. The definition of both naturally determines that clustering must play a positive role in obtaining accurate link prediction tasks. Yet researchers have long ignored or used inappropriate ways to undermine this positive relationship. In this article, We construct a simple but efficient clustering-driven link prediction framework(ClusterLP), with the goal of directly exploiting the cluster structures to obtain connections between nodes as accurately as possible in both undirected graphs and directed graphs. Specifically, we propose that it is easier to establish links between nodes with similar representation vectors and cluster tendencies in undirected graphs, while nodes in a directed graphs can more easily point to nodes similar to their representation vectors and have greater influence in their own cluster. We customized the implementation of ClusterLP for undirected and directed graphs, respectively, and the experimental results using multiple real-world networks on the link prediction task showed that our models is highly competitive with existing baseline models. The code implementation of ClusterLP and baselines we use are available at https://github.com/ZINUX1998/ClusterLP.

将包含文本和不同边缘类型的文本的信息节点连接的异质网络通常用于在各种现实世界应用程序中存储和处理信息。图形神经网络（GNNS）及其双曲线变体提供了一种有希望的方法，可以通过邻域聚集和分层特征提取在低维的潜在空间中编码此类网络。但是，这些方法通常忽略Metapath结构和可用的语义信息。此外，这些方法对训练数据中存在的噪声很敏感。为了解决这些局限性，在本文中，我们提出了富含文本的稀疏双曲图卷积网络（TESH-GCN），以使用语义信号捕获图形的Metapath结构，并进一步改善大型异质图中的预测。在TESH-GCN中，我们提取语义节点信息，该信息连接信号是从稀疏的双曲线图卷积层中从稀疏邻接张量中提取相关节点的局部邻域和图形级Metapath特征。这些提取的功能与语言模型的语义特征（用于鲁棒性）结合使用，用于最终下游任务。各种异质图数据集的实验表明，我们的模型在链接预测任务上的大幅度优于当前最新方法。我们还报告说，与现有的双曲线方法相比，训练时间和模型参数均减少了，通过重新的双曲线图卷积。此外，我们通过在图形结构和文本中使用不同级别的模拟噪声来说明模型的鲁棒性，并通过分析提取的Metapaths来解释Tesh-GCN的预测机制。

图表神经网络（GNNS）在各种机器学习任务中获得了表示学习的提高。然而，应用邻域聚合的大多数现有GNN通常在图中的图表上执行不良，其中相邻的节点属于不同的类。在本文中，我们示出了在典型的异界图中，边缘可以被引导，以及是否像是处理边缘，也可以使它们过度地影响到GNN模型的性能。此外，由于异常的限制，节点对来自本地邻域之外的类似节点的消息非常有益。这些激励我们开发一个自适应地学习图表的方向性的模型，并利用潜在的长距离相关性节点之间。我们首先将图拉普拉斯概括为基于所提出的特征感知PageRank算法向数字化，该算法同时考虑节点之间的图形方向性和长距离特征相似性。然后，Digraph Laplacian定义了一个图形传播矩阵，导致一个名为{\ em diglaciangcn}的模型。基于此，我们进一步利用节点之间的通勤时间测量的节点接近度，以便在拓扑级别上保留节点的远距离相关性。具有不同级别的10个数据集的广泛实验，同意级别展示了我们在节点分类任务任务中对现有解决方案的有效性。

异质图卷积网络在解决异质网络数据的各种网络分析任务方面已广受欢迎，从链接预测到节点分类。但是，大多数现有作品都忽略了多型节点之间的多重网络的关系异质性，而在元路径中，元素嵌入中关系的重要性不同，这几乎无法捕获不同关系跨不同关系的异质结构信号。为了应对这一挑战，这项工作提出了用于异质网络嵌入的多重异质图卷积网络（MHGCN）。我们的MHGCN可以通过多层卷积聚合自动学习多重异质网络中不同长度的有用的异质元路径相互作用。此外，我们有效地将多相关结构信号和属性语义集成到学习的节点嵌入中，并具有无监督和精选的学习范式。在具有各种网络分析任务的五个现实世界数据集上进行的广泛实验表明，根据所有评估指标，MHGCN与最先进的嵌入基线的优势。

图表可以模拟实体之间的复杂交互，它在许多重要的应用程序中自然出现。这些应用程序通常可以投入到标准图形学习任务中，其中关键步骤是学习低维图表示。图形神经网络（GNN）目前是嵌入方法中最受欢迎的模型。然而，邻域聚合范例中的标准GNN患有区分\ EMPH {高阶}图形结构的有限辨别力，而不是\ EMPH {低位}结构。为了捕获高阶结构，研究人员求助于主题和开发的基于主题的GNN。然而，现有的基于主基的GNN仍然仍然遭受较少的辨别力的高阶结构。为了克服上述局限性，我们提出了一个新颖的框架，以更好地捕获高阶结构的新框架，铰接于我们所提出的主题冗余最小化操作员和注射主题组合的新颖框架。首先，MGNN生成一组节点表示W.R.T.每个主题。下一阶段是我们在图案中提出的冗余最小化，该主题在彼此相互比较并蒸馏出每个主题的特征。最后，MGNN通过组合来自不同图案的多个表示来执行节点表示的更新。特别地，为了增强鉴别的功率，MGNN利用重新注射功能来组合表示的函数w.r.t.不同的主题。我们进一步表明，我们的拟议体系结构增加了GNN的表现力，具有理论分析。我们展示了MGNN在节点分类和图形分类任务上的七个公共基准上表现出最先进的方法。

链接预测是一项重要的任务，在各个域中具有广泛的应用程序。但是，大多数现有的链接预测方法都假定给定的图遵循同质的假设，并设计基于相似性的启发式方法或表示学习方法来预测链接。但是，许多现实世界图是异性图，同义假设不存在，这挑战了现有的链接预测方法。通常，在异性图中，有许多引起链接形成的潜在因素，并且两个链接的节点在一个或两个因素中往往相似，但在其他因素中可能是不同的，导致总体相似性较低。因此，一种方法是学习每个节点的分离表示形式，每个矢量捕获一个因子上的节点的潜在表示，这铺平了一种方法来模拟异性图中的链接形成，从而导致更好的节点表示学习和链接预测性能。但是，对此的工作非常有限。因此，在本文中，我们研究了一个新的问题，该问题是在异性图上进行链接预测的分离表示学习。我们提出了一种新颖的框架分解，可以通过建模链接形成并执行感知因素的消息来学习以促进链接预测来学习解开的表示形式。在13个现实世界数据集上进行的广泛实验证明了Disenlink对异性恋和血友病图的链接预测的有效性。我们的代码可从https://github.com/sjz5202/disenlink获得

Graph Neural Networks (GNNs) have attracted increasing attention in recent years and have achieved excellent performance in semi-supervised node classification tasks. The success of most GNNs relies on one fundamental assumption, i.e., the original graph structure data is available. However, recent studies have shown that GNNs are vulnerable to the complex underlying structure of the graph, making it necessary to learn comprehensive and robust graph structures for downstream tasks, rather than relying only on the raw graph structure. In light of this, we seek to learn optimal graph structures for downstream tasks and propose a novel framework for semi-supervised classification. Specifically, based on the structural context information of graph and node representations, we encode the complex interactions in semantics and generate semantic graphs to preserve the global structure. Moreover, we develop a novel multi-measure attention layer to optimize the similarity rather than prescribing it a priori, so that the similarity can be adaptively evaluated by integrating measures. These graphs are fused and optimized together with GNN towards semi-supervised classification objective. Extensive experiments and ablation studies on six real-world datasets clearly demonstrate the effectiveness of our proposed model and the contribution of each component.

Inferring missing links or detecting spurious ones based on observed graphs, known as link prediction, is a long-standing challenge in graph data analysis. With the recent advances in deep learning, graph neural networks have been used for link prediction and have achieved state-of-the-art performance. Nevertheless, existing methods developed for this purpose are typically discriminative, computing features of local subgraphs around two neighboring nodes and predicting potential links between them from the perspective of subgraph classification. In this formalism, the selection of enclosing subgraphs and heuristic structural features for subgraph classification significantly affects the performance of the methods. To overcome this limitation, this paper proposes a novel and radically different link prediction algorithm based on the network reconstruction theory, called GraphLP. Instead of sampling positive and negative links and heuristically computing the features of their enclosing subgraphs, GraphLP utilizes the feature learning ability of deep-learning models to automatically extract the structural patterns of graphs for link prediction under the assumption that real-world graphs are not locally isolated. Moreover, GraphLP explores high-order connectivity patterns to utilize the hierarchical organizational structures of graphs for link prediction. Our experimental results on all common benchmark datasets from different applications demonstrate that the proposed method consistently outperforms other state-of-the-art methods. Unlike the discriminative neural network models used for link prediction, GraphLP is generative, which provides a new paradigm for neural-network-based link prediction.

Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph structure so that it can be easily exploited by machine learning models. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural information about a graph (e.g., degree statistics or kernel functions). However, recent years have seen a surge in approaches that automatically learn to encode graph structure into low-dimensional embeddings, using techniques based on deep learning and nonlinear dimensionality reduction. Here we provide a conceptual review of key advancements in this area of representation learning on graphs, including matrix factorization-based methods, random-walk based algorithms, and graph neural networks. We review methods to embed individual nodes as well as approaches to embed entire (sub)graphs. In doing so, we develop a unified framework to describe these recent approaches, and we highlight a number of important applications and directions for future work.

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into four categories, namely recurrent graph neural networks, convolutional graph neural networks, graph autoencoders, and spatial-temporal graph neural networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes, benchmark data sets, and model evaluation of graph neural networks. Finally, we propose potential research directions in this rapidly growing field.

Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the represented problem. To address cutting-edge problems based on graph data, the research field of Graph Neural Networks (GNNs) has emerged. Despite the field's youth and the speed at which new models are developed, many recent surveys have been published to keep track of them. Nevertheless, it has not yet been gathered which GNN can process what kind of graph types. In this survey, we give a detailed overview of already existing GNNs and, unlike previous surveys, categorize them according to their ability to handle different graph types and properties. We consider GNNs operating on static and dynamic graphs of different structural constitutions, with or without node or edge attributes. Moreover, we distinguish between GNN models for discrete-time or continuous-time dynamic graphs and group the models according to their architecture. We find that there are still graph types that are not or only rarely covered by existing GNN models. We point out where models are missing and give potential reasons for their absence.

在异质图上的自我监督学习（尤其是对比度学习）方法可以有效地摆脱对监督数据的依赖。同时，大多数现有的表示学习方法将异质图嵌入到欧几里得或双曲线的单个几何空间中。这种单个几何视图通常不足以观察由于其丰富的语义和复杂结构而观察到异质图的完整图片。在这些观察结果下，本文提出了一种新型的自我监督学习方法，称为几何对比度学习（GCL），以更好地表示监督数据是不可用时的异质图。 GCL同时观察了从欧几里得和双曲线观点的异质图，旨在强烈合并建模丰富的语义和复杂结构的能力，这有望为下游任务带来更多好处。 GCL通过在局部局部和局部全球语义水平上对比表示两种几何视图之间的相互信息。在四个基准数据集上进行的广泛实验表明，在三个任务上，所提出的方法在包括节点分类，节点群集和相似性搜索在内的三个任务上都超过了强基础，包括无监督的方法和监督方法。

在时间图上的表示学习吸引了大量的研究注意力，因为它在各种各样的现实应用程序中的基本重要性。尽管许多研究成功地获得了时间依赖的表示，但它仍然面临重大挑战。一方面，大多数现有方法都以一定的曲率限制了嵌入空间。然而，实际上，潜在的几何形状随着时间的推移而变化的曲率超球，零曲率欧几里得和负曲率双曲空间发生了变化。另一方面，这些方法通常需要丰富的标签来学习时间表示，从而明显限制了它们在真实应用程序的未标记图中的广泛使用。为了弥合这一差距，我们首次尝试研究一般的Riemannian空间中自我监督的时间图表示学习的问题，从而支持随时间变化的曲率在超球，欧几里得和双曲线空间之间转移。在本文中，我们提出了一种新颖的自我监督的Riemannian图神经网络（SEXTRGNN）。具体而言，我们设计了具有理论上的时间编码的曲率变化的Riemannian GNN，并随着时间的推移制定功能性曲率，以模拟正，零和负曲率空间之间的演变转换。为了启用自我监督的学习，我们提出了一种新颖的重新处理自我对比的方法，探索Riemannian空间本身而无需增强，并提出了一种基于边缘的自我监督的曲率学习，并使用RICCI曲率进行。广泛的实验表明了SelfRGNN的优越性，此外，案例研究表明了现实中时间图的时变曲率。

Learning node embeddings that capture a node's position within the broader graph structure is crucial for many prediction tasks on graphs. However, existing Graph Neural Network (GNN) architectures have limited power in capturing the position/location of a given node with respect to all other nodes of the graph. Here we propose Position-aware Graph Neural Networks (P-GNNs), a new class of GNNs for computing position-aware node embeddings. P-GNN first samples sets of anchor nodes, computes the distance of a given target node to each anchor-set, and then learns a non-linear distance-weighted aggregation scheme over the anchor-sets. This way P-GNNs can capture positions/locations of nodes with respect to the anchor nodes. P-GNNs have several advantages: they are inductive, scalable, and can incorporate node feature information. We apply P-GNNs to multiple prediction tasks including link prediction and community detection. We show that P-GNNs consistently outperform state of the art GNNs, with up to 66% improvement in terms of the ROC AUC score.Node embedding methods can be categorized into Graph Neural Networks (GNNs) approaches (Scarselli et al., 2009),

Graph convolutional networks (GCNs) are powerful frameworks for learning embeddings of graph-structured data. GCNs are traditionally studied through the lens of Euclidean geometry. Recent works find that non-Euclidean Riemannian manifolds provide specific inductive biases for embedding hierarchical or spherical data. However, they cannot align well with data of mixed graph topologies. We consider a larger class of pseudo-Riemannian manifolds that generalize hyperboloid and sphere. We develop new geodesic tools that allow for extending neural network operations into geodesically disconnected pseudo-Riemannian manifolds. As a consequence, we derive a pseudo-Riemannian GCN that models data in pseudo-Riemannian manifolds of constant nonzero curvature in the context of graph neural networks. Our method provides a geometric inductive bias that is sufficiently flexible to model mixed heterogeneous topologies like hierarchical graphs with cycles. We demonstrate the representational capabilities of this method by applying it to the tasks of graph reconstruction, node classification and link prediction on a series of standard graphs with mixed topologies. Empirical results demonstrate that our method outperforms Riemannian counterparts when embedding graphs of complex topologies.

图表表示学习近年来收到了增加的注意。大多数现有方法忽略了图形结构的复杂性，并限制了单个恒定曲率表示空间中的图形，这仅适用于特定类型的图形结构。此外，这些方法遵循监督或半监督的学习范例，从而显着限制其在实际应用中的未标记图中的部署。为了解决这些上述限制，我们首次尝试研究混合曲率空间中的自我监督的图表表示学习。在本文中，我们提出了一种新颖的自我监督的混合曲率图神经网络（SelfMGNN）。我们不是在一个单一的恒定曲率空间上工作，我们通过多个riemannian组件空间的笛卡尔乘积构建混合曲率空间，并设计分层注意机制，用于学习和融合这些组件空间的表示。为了实现自我超标学习，我们提出了一种新的双重对比方法。混合曲率的黎曼空间实际上为对比学习提供了多个黎曼观点。我们介绍了一个riemananian投影机来揭示这些观点，并利用精心设计的riemananian判别者，以便在里莫安尼亚视图中单独和跨越对比学习。最后，广泛的实验表明SelfMGNN捕获了现实中的复杂图形结构，优于最先进的基线。