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。

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.

由于其几何特性，双曲线空间可以支持树木和图形结构化数据的高保真嵌入。结果，已经开发了各种双曲线网络，这些网络在许多任务上都超过了欧几里得网络：例如双曲线图卷积网络（GCN）在某些图形学习任务上的表现可以胜过香草GCN。但是，大多数现有的双曲线网络都是复杂的，计算昂贵的，并且在数值上不稳定 - 由于这些缺点，它们无法扩展到大图。提出了越来越多的双曲线网络，越来越不清楚什么关键组成部分使模型行为。在本文中，我们提出了HYLA，这是一种简单而最小的方法，用于在网络中使用双曲线空间：Hyla地图一次从双曲空空间从嵌入荷兰的嵌入到欧几里得空间，并通过双曲线空间中的Laplacian操作员的特征函数。我们在图形学习任务上评估HYLA，包括节点分类和文本分类，其中HYLA可以与任何图神经网络一起使用。当与线性模型一起使用时，HYLA对双曲线网络和其他基线显示出显着改善。

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。

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.

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。

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。

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。

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。

图表表示学习是一种快速增长的领域，其中一个主要目标是在低维空间中产生有意义的图形表示。已经成功地应用了学习的嵌入式来执行各种预测任务，例如链路预测，节点分类，群集和可视化。图表社区的集体努力提供了数百种方法，但在所有评估指标下没有单一方法擅长，例如预测准确性，运行时间，可扩展性等。该调查旨在通过考虑算法来评估嵌入方法的所有主要类别的图表变体，参数选择，可伸缩性，硬件和软件平台，下游ML任务和多样化数据集。我们使用包含手动特征工程，矩阵分解，浅神经网络和深图卷积网络的分类法组织了图形嵌入技术。我们使用广泛使用的基准图表评估了节点分类，链路预测，群集和可视化任务的这些类别算法。我们在Pytorch几何和DGL库上设计了我们的实验，并在不同的多核CPU和GPU平台上运行实验。我们严格地审查了各种性能指标下嵌入方法的性能，并总结了结果。因此，本文可以作为比较指南，以帮助用户选择最适合其任务的方法。

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.

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.

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.

In recent years, graph neural networks (GNNs) have emerged as a promising tool for solving machine learning problems on graphs. Most GNNs are members of the family of message passing neural networks (MPNNs). There is a close connection between these models and the Weisfeiler-Leman (WL) test of isomorphism, an algorithm that can successfully test isomorphism for a broad class of graphs. Recently, much research has focused on measuring the expressive power of GNNs. For instance, it has been shown that standard MPNNs are at most as powerful as WL in terms of distinguishing non-isomorphic graphs. However, these studies have largely ignored the distances between the representations of nodes/graphs which are of paramount importance for learning tasks. In this paper, we define a distance function between nodes which is based on the hierarchy produced by the WL algorithm, and propose a model that learns representations which preserve those distances between nodes. Since the emerging hierarchy corresponds to a tree, to learn these representations, we capitalize on recent advances in the field of hyperbolic neural networks. We empirically evaluate the proposed model on standard node and graph classification datasets where it achieves competitive performance with state-of-the-art models.

图形神经网络已用于各种学习任务，例如链接预测，节点分类和节点群集。其中，链接预测是一项相对研究的图形学习任务，其当前最新模型基于浅层图自动编码器（GAE）体系结构的一层或两层。在本文中，我们专注于解决链接预测的当前方法的局限性，该预测只能使用浅的GAE和变分GAE，并创建有效的方法来加深（变异）GAE架构以实现稳定和竞争性的性能。我们提出的方法是创新的方法将标准自动编码器（AES）纳入GAE的体系结构，在该体系结构中，标准AE被利用以通过无缝整合邻接信息和节点来学习必要的，低维的表示，而GAE则进一步构建了多尺度的低规模的低尺度低尺度的低尺度。通过残差连接的维度表示，以学习紧凑的链接预测的整体嵌入。从经验上讲，在各种基准测试数据集上进行的广泛实验验证了我们方法的有效性，并证明了我们加深的图形模型以进行链接预测的竞争性能。从理论上讲，我们证明我们的深度扩展包括具有不同阶的多项式过滤器。

网络完成是一个比链接预测更难的问题，因为它不仅尝试推断丢失的链接，还要推断节点。已经提出了不同的方法来解决此问题，但是很少有人使用结构信息 - 局部连接模式的相似性。在本文中，我们提出了一个名为C-GIN的模型，以根据图形自动编码器框架从网络的观察到的部分捕获局部结构模式，该框架配备了图形同构网络模型，并将这些模式推广到完成整个图形。对来自不同领域的合成和现实世界网络的实验和分析表明，C-Gin可以实现竞争性能，而所需的信息较少，并且在大多数情况下，与基线预测模型相比，可以获得更高的准确性。我们进一步提出了一个基于网络结构的“可达聚类系数（CC）”。实验表明，我们的模型在具有较高可及的CC的网络上表现更好。

图表是一个宇宙数据结构，广泛用于组织现实世界中的数据。像交通网络，社交和学术网络这样的各种实际网络网络可以由图表代表。近年来，目睹了在网络中代表顶点的快速发展，进入低维矢量空间，称为网络表示学习。表示学习可以促进图形数据上的新算法的设计。在本调查中，我们对网络代表学习的当前文献进行了全面审查。现有算法可以分为三组：浅埋模型，异构网络嵌入模型，图形神经网络的模型。我们为每个类别审查最先进的算法，并讨论这些算法之间的基本差异。调查的一个优点是，我们系统地研究了不同类别的算法底层的理论基础，这提供了深入的见解，以更好地了解网络表示学习领域的发展。

Graph Neural Networks (GNNs) have become increasingly important in recent years due to their state-of-the-art performance on many important downstream applications. Existing GNNs have mostly focused on learning a single node representation, despite that a node often exhibits polysemous behavior in different contexts. In this work, we develop a persona-based graph neural network framework called PersonaSAGE that learns multiple persona-based embeddings for each node in the graph. Such disentangled representations are more interpretable and useful than a single embedding. Furthermore, PersonaSAGE learns the appropriate set of persona embeddings for each node in the graph, and every node can have a different number of assigned persona embeddings. The framework is flexible enough and the general design helps in the wide applicability of the learned embeddings to suit the domain. We utilize publicly available benchmark datasets to evaluate our approach and against a variety of baselines. The experiments demonstrate the effectiveness of PersonaSAGE for a variety of important tasks including link prediction where we achieve an average gain of 15% while remaining competitive for node classification. Finally, we also demonstrate the utility of PersonaSAGE with a case study for personalized recommendation of different entity types in a data management platform.

数据增强已广泛用于图像数据和语言数据，但仍然探索图形神经网络（GNN）。现有方法专注于从全局视角增强图表数据，并大大属于两个类型：具有特征噪声注入的结构操纵和对抗训练。但是，最近的图表数据增强方法忽略了GNNS“消息传递机制的本地信息的重要性。在这项工作中，我们介绍了本地增强，这通过其子图结构增强了节点表示的局部。具体而言，我们将数据增强模拟为特征生成过程。鉴于节点的功能，我们的本地增强方法了解其邻居功能的条件分布，并生成更多邻居功能，以提高下游任务的性能。基于本地增强，我们进一步设计了一个新颖的框架：La-GNN，可以以即插即用的方式应用于任何GNN模型。广泛的实验和分析表明，局部增强一致地对各种基准的各种GNN架构始终如一地产生性能改进。

图形神经网络（GNNS）显着改善了图形结构数据的表示功率。尽管最近GNN的成功，大多数GNN的图表卷积都有两个限制。由于图形卷积在输入图上的小本地邻域中执行，因此固有地无法捕获距离节点之间的远程依赖性。另外，当节点具有属于不同类别的邻居时，即，异常，来自它们的聚合消息通常会影响表示学习。为了解决图表卷积的两个常见问题，在本文中，我们提出了可变形的图形卷积网络（可变形GCNS），可在多个潜在空间中自适应地执行卷积并捕获节点之间的短/远程依赖性。与节点表示（特征）分开，我们的框架同时学习节点位置嵌入式嵌入式（坐标）以确定节点之间以端到端的方式之间的关系。根据节点位置，卷积内核通过变形向量变形并将不同的变换应用于其邻居节点。我们广泛的实验表明，可变形的GCNS灵活地处理异常的处理，并在六个异化图数据集中实现节点分类任务中的最佳性能。