Message-passing neural networks (MPNNs) have been successfully applied to representation learning on graphs in a variety of real-world applications. However, two fundamental weaknesses of MPNNs' aggregators limit their ability to represent graph-structured data: losing the structural information of nodes in neighborhoods and lacking the ability to capture long-range dependencies in disassortative graphs. Few studies have noticed the weaknesses from different perspectives. From the observations on classical neural network and network geometry, we propose a novel geometric aggregation scheme for graph neural networks to overcome the two weaknesses. The behind basic idea is the aggregation on a graph can benefit from a continuous space underlying the graph. The proposed aggregation scheme is permutation-invariant and consists of three modules, node embedding, structural neighborhood, and bi-level aggregation. We also present an implementation of the scheme in graph convolutional networks, termed Geom-GCN, to perform transductive learning on graphs. Experimental results show the proposed Geom-GCN achieved state-of-the-art performance on a wide range of open datasets of graphs.

现代图形神经网络（GNNS）通过多层本地聚合学习节点嵌入，并在各种图形应用中取得巨大成功。但是，对辅音图的任务通常需要非局部聚合。此外，我们发现本地聚合对某些抵消图表甚至有害。在这项工作中，我们提出了一个简单但有效的非本地聚合框架，具有高效的GNN的关注排序。基于它，我们开发各种非本地GNN。我们进行彻底的实验，以分析Disasstative图数据集并评估我们的非本地GNN。实验结果表明，在模型性能和效率方面，我们的非本地GNN在七个基准数据集上显着优于七个基准数据集。

消息传递已作为设计图形神经网络（GNN）的有效工具的发展。但是，消息传递的大多数现有方法简单地简单或平均所有相邻的功能更新节点表示。它们受到两个问题的限制，即（i）缺乏可解释性来识别对GNN的预测重要的节点特征，以及（ii）特征过度混合，导致捕获长期依赖和无能为力的过度平滑问题在异质或低同质的下方处理图。在本文中，我们提出了一个节点级胶囊图神经网络（NCGNN），以通过改进的消息传递方案来解决这些问题。具体而言，NCGNN表示节点为节点级胶囊组，其中每个胶囊都提取其相应节点的独特特征。对于每个节点级胶囊，开发了一个新颖的动态路由过程，以适应适当的胶囊，以从设计的图形滤波器确定的子图中聚集。 NCGNN聚集仅有利的胶囊并限制无关的消息，以避免交互节点的过度混合特征。因此，它可以缓解过度平滑的问题，并通过同粒或异质的图表学习有效的节点表示。此外，我们提出的消息传递方案本质上是可解释的，并免于复杂的事后解释，因为图形过滤器和动态路由过程确定了节点特征的子集，这对于从提取的子分类中的模型预测最为重要。关于合成和现实图形的广泛实验表明，NCGNN可以很好地解决过度光滑的问题，并为半监视的节点分类产生更好的节点表示。它的表现优于同质和异质的艺术状态。

图形神经网络（GNNS）在各种基于图形的应用中显示了优势。大多数现有的GNNS假设图形结构的强大奇妙并应用邻居的置换不变本地聚合以学习每个节点的表示。然而，它们未能概括到异质图，其中大多数相邻节点具有不同的标签或特征，并且相关节点远处。最近的几项研究通过组合中央节点的隐藏表示（即，基于多跳的方法）的多个跳数来解决这个问题，或者基于注意力分数对相邻节点进行排序（即，基于排名的方法）来解决这个问题。结果，这些方法具有一些明显的限制。一方面，基于多跳的方法没有明确区分相关节点的大量多跳社区，导致严重的过平滑问题。另一方面，基于排名的模型不与结束任务进行联合优化节点排名，并导致次优溶液。在这项工作中，我们呈现图表指针神经网络（GPNN）来解决上述挑战。我们利用指针网络从大量的多跳邻域选择最相关的节点，这根据与中央节点的关系来构造有序序列。然后应用1D卷积以从节点序列中提取高级功能。 GPNN中的基于指针网络的Ranker是以端到端的方式与其他部件进行联合优化的。在具有异质图的六个公共节点分类数据集上进行了广泛的实验。结果表明，GPNN显着提高了最先进方法的分类性能。此外，分析还揭示了拟议的GPNN在过滤出无关邻居并减少过平滑的特权。

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。

Various graph neural networks (GNNs) have been proposed to solve node classification tasks in machine learning for graph data. GNNs use the structural information of graph data by aggregating the features of neighboring nodes. However, they fail to directly characterize and leverage the structural information. In this paper, we propose multi-duplicated characterization of graph structures using information gain ratio (IGR) for GNNs (MSI-GNN), which enhances the performance of node classification by using an i-hop adjacency matrix as the structural information of the graph data. In MSI-GNN, the i-hop adjacency matrix is adaptively adjusted by two methods: (i) structural features in the matrix are selected based on the IGR, and (ii) the selected features in (i) for each node are duplicated and combined flexibly. In an experiment, we show that our MSI-GNN outperforms GCN, H2GCN, and GCNII in terms of average accuracies in benchmark graph datasets.

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance. * Equal contribution. † Work partially performed while in Tokyo, visiting Prof. Ken-ichi Kawarabayashi.

基于图形卷积的方法已成功应用于同质图上的表示学习，其中具有相同标签或相似属性的节点往往相互连接。由于这些方法使用的图形卷积网络（GCN）的同义假设，它们不适合异质图，其中具有不同标记或不同属性的节点往往相邻。几种方法试图解决这个异质问题，但是它们没有改变GCN的基本聚合机制，因为它们依靠求和操作员来汇总邻近节点的信息，这隐含地遵守同质假设。在这里，我们介绍了一种新颖的聚合机制，并开发了基于随机步行聚集的图形神经网络（称为RAW-GNN）方法。提出的方法将随机步行策略与图神经网络集成在一起。新方法利用广度优先的随机步行搜索来捕获同质信息和深度优先搜索以收集异性信息。它用基于路径的社区取代了传统社区，并基于经常性神经网络引入了新的基于路径的聚合器。这些设计使RAW-GNN适用于同质图和异质图。广泛的实验结果表明，新方法在各种同质图和异质图上实现了最先进的性能。

图形神经网络（GNN）已成功用于许多涉及图形结构数据的问题，从而实现了最新的性能。 GNN通常采用消息通话方案，其中每个节点都使用置换不变的聚合函数从其邻居中汇总信息。标准良好的选择（例如平均值或总和函数）具有有限的功能，因为它们无法捕获邻居之间的相互作用。在这项工作中，我们使用信息理论框架正式化了这些交互，该框架特别包括协同信息。在此定义的驱动下，我们介绍了图排序注意（山羊）层，这是一种新型的GNN组件，可捕获邻域中的节点之间的相互作用。这是通过通过注意机制学习局部节点顺序并使用复发性神经网络聚合器来处理订购表示的来实现的。这种设计使我们能够利用置换敏感的聚合器，同时维持所提出的山羊层的排列量表。山羊模型展示了其在捕获复杂信息（例如中心中心性和节点的有效大小）中的建模图指标中提高的性能。在实用用例中，通过在几个现实世界节点分类基准中成功证实了其出色的建模能力。

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.

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.

图表神经网络（GNNS）最近提出了用于处理图形结构数据的神经网络结构。由于他们所采用的邻国聚合策略，现有的GNNS专注于捕获节点级信息并忽略高级信息。因此，现有的GNN受到本地置换不变性（LPI）问题引起的代表性限制。为了克服这些限制并丰富GNN捕获的特征，我们提出了一种新的GNN框架，称为两级GNN（TL-GNN）。这与节点级信息合并子图级信息。此外，我们提供了对LPI问题的数学分析，这表明子图级信息有利于克服与LPI相关的问题。还提出了一种基于动态编程算法的子图计数方法，并且该具有时间复杂度是O（n ^ 3），n是图的节点的数量。实验表明，TL-GNN优于现有的GNN，实现了最先进的性能。

Graph neural networks (GNNs) have been widely used under semi-supervised settings. Prior studies have mainly focused on finding appropriate graph filters (e.g., aggregation schemes) to generalize well for both homophilic and heterophilic graphs. Even though these approaches are essential and effective, they still suffer from the sparsity in initial node features inherent in the bag-of-words representation. Common in semi-supervised learning where the training samples often fail to cover the entire dimensions of graph filters (hyperplanes), this can precipitate over-fitting of specific dimensions in the first projection matrix. To deal with this problem, we suggest a simple and novel strategy; create additional space by flipping the initial features and hyperplane simultaneously. Training in both the original and in the flip space can provide precise updates of learnable parameters. To the best of our knowledge, this is the first attempt that effectively moderates the overfitting problem in GNN. Extensive experiments on real-world datasets demonstrate that the proposed technique improves the node classification accuracy up to 40.2 %

图表学习目的旨在将节点内容与图形结构集成以学习节点/图表示。然而，发现许多现有的图形学习方法在具有高异性级别的数据上不能很好地工作，这是不同类标签之间很大比例的边缘。解决这个问题的最新努力集中在改善消息传递机制上。但是，尚不清楚异质性是否确实会损害图神经网络（GNNS）的性能。关键是要展现一个节点与其直接邻居之间的关系，例如它们是异性还是同质性？从这个角度来看，我们在这里研究了杂质表示在披露连接节点之间的关系之前/之后的杂音表示的作用。特别是，我们提出了一个端到端框架，该框架既学习边缘的类型（即异性/同质性），并利用边缘类型的信息来提高图形神经网络的表现力。我们以两种不同的方式实施此框架。具体而言，为了避免通过异质边缘传递的消息，我们可以通过删除边缘分类器鉴定的异性边缘来优化图形结构。另外，可以利用有关异性邻居的存在的信息进行特征学习，因此，设计了一种混合消息传递方法来汇总同质性邻居，并根据边缘分类使异性邻居多样化。广泛的实验表明，在整个同质级别的多个数据集上，通过在多个数据集上提出的框架对GNN的绩效提高了显着提高。

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。

Recent deep learning approaches for representation learning on graphs follow a neighborhood aggregation procedure. We analyze some important properties of these models, and propose a strategy to overcome those. In particular, the range of "neighboring" nodes that a node's representation draws from strongly depends on the graph structure, analogous to the spread of a random walk. To adapt to local neighborhood properties and tasks, we explore an architecture -jumping knowledge (JK) networks -that flexibly leverages, for each node, different neighborhood ranges to enable better structure-aware representation. In a number of experiments on social, bioinformatics and citation networks, we demonstrate that our model achieves state-of-the-art performance. Furthermore, combining the JK framework with models like Graph Convolutional Networks, GraphSAGE and Graph Attention Networks consistently improves those models' performance.

图形神经网络已成为从图形结构数据学习的不可缺少的工具之一，并且它们的实用性已在各种各样的任务中显示。近年来，建筑设计的巨大改进，导致各种预测任务的性能更好。通常，这些神经架构在同一层中使用可知的权重矩阵组合节点特征聚合和特征转换。这使得分析从各种跳过的节点特征和神经网络层的富有效力来挑战。由于不同的图形数据集显示在特征和类标签分布中的不同级别和异常级别，因此必须了解哪些特征对于没有任何先前信息的预测任务是重要的。在这项工作中，我们将节点特征聚合步骤和深度与图形神经网络分离，并经验分析了不同的聚合特征在预测性能中发挥作用。我们表明，并非通过聚合步骤生成的所有功能都很有用，并且通常使用这些较少的信息特征可能对GNN模型的性能有害。通过我们的实验，我们表明学习这些功能的某些子集可能会导致各种数据集的性能更好。我们建议使用Softmax作为常规器，并从不同跳距的邻居聚合的功能的“软选择器”;和L2 - GNN层的标准化。结合这些技术，我们呈现了一个简单浅的模型，特征选择图神经网络（FSGNN），并经验展示所提出的模型比九个基准数据集中的最先进的GNN模型实现了可比或甚至更高的准确性节点分类任务，具有显着的改进，可达51.1％。

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.

通过递归将整个社区的节点特征汇总，空间图卷积运算符已被宣布为图形神经网络（GNNS）成功的关键。然而，尽管GNN方法跨任务和应用程序进行了繁殖，但此聚合操作对其性能的影响尚未得到广泛的分析。实际上，尽管努力主要集中于优化神经网络的体系结构，但更少的工作试图表征（a）不同类别的空间卷积操作员，（b）特定类别的选择如何与数据的属性相关，以及（c）它对嵌入空间的几何形状的影响。在本文中，我们建议通过将现有操作员分为两个主要类（对称性与行规范的空间卷积）来回答所有三个问题，并展示它们如何转化为数据性质的不同隐性偏见。最后，我们表明，这种聚合操作员实际上是可调的，并且明确的制度在其中某些操作员（因此，嵌入几何形状）的某些选择可能更合适。

图形神经网络（GNNS）依赖于图形结构来定义聚合策略，其中每个节点通过与邻居的信息组合来更新其表示。已知GNN的限制是，随着层数的增加，信息被平滑，压扁并且节点嵌入式变得无法区分，对性能产生负面影响。因此，实用的GNN模型雇用了几层，只能在每个节点周围的有限邻域利用图形结构。不可避免地，实际的GNN不会根据图的全局结构捕获信息。虽然有几种研究GNNS的局限性和表达性，但是关于图形结构数据的实际应用的问题需要全局结构知识，仍然没有答案。在这项工作中，我们通过向几个GNN模型提供全球信息并观察其对下游性能的影响来认证解决这个问题。我们的研究结果表明，全球信息实际上可以为共同的图形相关任务提供显着的好处。我们进一步确定了一项新的正规化策略，导致所有考虑的任务的平均准确性提高超过5％。