Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs-a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DIFFPOOL, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DIFFPOOL learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DIFFPOOL yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.

近年来，图形神经网络（GNNS）被出现为一个强大的神经结构，以学习在监督的端到端时尚中的节点和图表的矢量表示。到目前为止，只有经验评估GNNS - 显示有希望的结果。以下工作从理论的角度调查了GNN，并将它们与1美元 - 二维韦斯美犬 - Leman Graph同构Heuristic（1美元-WL）相关联。我们表明GNNS在区分非同义（子）图表中，GNN具有与1美元-WL相同的表现力。因此，这两种算法也具有相同的缺点。基于此，我们提出了GNN的概括，所谓的$ k $ -dimensional gnns（$ k $ -gnns），这可以考虑多个尺度的高阶图结构。这些高阶结构在社交网络和分子图的表征中起重要作用。我们的实验评估证实了我们的理论调查结果，并确认了更高阶信息在图形分类和回归的任务中有用。

Advanced methods of applying deep learning to structured data such as graphs have been proposed in recent years. In particular, studies have focused on generalizing convolutional neural networks to graph data, which includes redefining the convolution and the downsampling (pooling) operations for graphs. The method of generalizing the convolution operation to graphs has been proven to improve performance and is widely used. However, the method of applying downsampling to graphs is still difficult to perform and has room for improvement. In this paper, we propose a graph pooling method based on selfattention. Self-attention using graph convolution allows our pooling method to consider both node features and graph topology. To ensure a fair comparison, the same training procedures and model architectures were used for the existing pooling methods and our method. The experimental results demonstrate that our method achieves superior graph classification performance on the benchmark datasets using a reasonable number of parameters.

建议图表神经网络（GNNS）在不考虑训练和测试图之间的不可知分布的情况下，诱导GNN的泛化能力退化在分布外（OOD）设置。这种退化的根本原因是大多数GNN是基于I.I.D假设开发的。在这种设置中，GNN倾向于利用在培训中存在的微妙统计相关性用于预测，即使它是杂散的相关性。然而，这种杂散的相关性可能在测试环境中改变，导致GNN的失败。因此，消除了杂散相关的影响对于稳定的GNN来说是至关重要的。为此，我们提出了一个普遍的因果代表框架，称为稳定凝球。主要思想是首先从图数据中提取高级表示，并诉诸因因果推理的显着能力，以帮助模型摆脱虚假相关性。特别是，我们利用图形池化层以提取基于子图的表示作为高级表示。此外，我们提出了一种因果变量区别，以纠正偏置训练分布。因此，GNN将更多地集中在稳定的相关性上。对合成和现实世界ood图数据集的广泛实验良好地验证了所提出的框架的有效性，灵活性和可解释性。

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.

随着各个领域的深度学习的巨大成功，图形神经网络（GNNS）也成为图形分类的主要方法。通过全局读出操作，只会聚合所有节点（或节点群集）表示，现有的GNN分类器获得输入图的图级表示，并使用表示来预测其类标签。但是，这种全局聚合不考虑每个节点的结构信息，这导致全局结构的信息丢失。特别地，它通过对所有节点表示来强制执行分类器的相同权重参数来限制辨别力;在实践中，他们中的每一个都有助于不同于其结构语义的目标类别。在这项工作中，我们提出了结构性语义读数（SSREAD）来总结位置级节点表示，这允许为分类模拟特定位置的权重参数，以及有效地捕获与全局结构相关的图形语义。给定输入图，SSREAD旨在通过使用其节点与结构原型之间的语义对齐来识别结构上有意义的位置，该结构原型编码每个位置的原型特征。结构原型经过优化，以最小化所有训练图的对准成本，而其他GNN参数训练以预测类标签。我们的实验结果表明，SSREAD显着提高了GNN分类器的分类性能和可解释性，同时兼容各种聚合函数，GNN架构和学习框架。

Pre-publication draft of a book to be published byMorgan & Claypool publishers. Unedited version released with permission. All relevant copyrights held by the author and publisher extend to this pre-publication draft.

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.

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。

近年来，基于Weisfeiler-Leman算法的算法和神经架构，是一个众所周知的Graph同构问题的启发式问题，它成为具有图形和关系数据的机器学习的强大工具。在这里，我们全面概述了机器学习设置中的算法的使用，专注于监督的制度。我们讨论了理论背景，展示了如何将其用于监督的图形和节点表示学习，讨论最近的扩展，并概述算法的连接（置换 - ）方面的神经结构。此外，我们概述了当前的应用和未来方向，以刺激进一步的研究。

随着传感技术的进步，多元时间序列分类（MTSC）最近受到了相当大的关注。基于深度学习的MTSC技术主要依赖于卷积或经常性神经网络，主要涉及单时间序列的时间依赖性。结果，他们努力直接在多变量变量中表达成对依赖性。此外，基于图形神经网络（GNNS）的当前空间 - 时间建模（例如，图形分类）方法本质上是平的，并且不能以分层方式聚合集线器数据。为了解决这些限制，我们提出了一种基于新的图形汇集框架MTPOOL，以获得MTS的表现力全球表示。我们首先通过采用通过图形结构学习模块的相互作用来将MTS切片转换为曲线图，并通过时间卷积模块获得空间 - 时间图节点特征。为了获得全局图形级表示，我们设计了基于“编码器 - 解码器”的变形图池池模块，用于为群集分配创建自适应质心。然后我们将GNN和我们所提出的变分图层汇集层组合用于联合图表示学习和图形粗糙化，之后该图逐渐赋予一个节点。最后，可差异化的分类器将此粗糙的表示来获取最终预测的类。 10个基准数据集的实验表明MTPOOL优于MTSC任务中最先进的策略。

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神经网络（GNN）最近已成为使用图的机器学习的主要范式。对GNNS的研究主要集中于消息传递神经网络（MPNNS）的家族。与同构的Weisfeiler-Leman（WL）测试类似，这些模型遵循迭代的邻域聚合过程以更新顶点表示，并通过汇总顶点表示来更新顶点图表。尽管非常成功，但在过去的几年中，对MPNN进行了深入的研究。因此，需要新颖的体系结构，这将使该领域的研究能够脱离MPNN。在本文中，我们提出了一个新的图形神经网络模型，即所谓的$ \ pi $ -gnn，该模型学习了每个图的“软”排列（即双随机）矩阵，从而将所有图形投影到一个共同的矢量空间中。学到的矩阵在输入图的顶点上强加了“软”顺序，并基于此顺序，将邻接矩阵映射到向量中。这些向量可以被送入完全连接或卷积的层，以应对监督的学习任务。在大图的情况下，为了使模型在运行时间和记忆方面更有效，我们进一步放松了双随机矩阵，以使其排列随机矩阵。我们从经验上评估了图形分类和图形回归数据集的模型，并表明它与最新模型达到了性能竞争。

Graph classification is an important area in both modern research and industry. Multiple applications, especially in chemistry and novel drug discovery, encourage rapid development of machine learning models in this area. To keep up with the pace of new research, proper experimental design, fair evaluation, and independent benchmarks are essential. Design of strong baselines is an indispensable element of such works. In this thesis, we explore multiple approaches to graph classification. We focus on Graph Neural Networks (GNNs), which emerged as a de facto standard deep learning technique for graph representation learning. Classical approaches, such as graph descriptors and molecular fingerprints, are also addressed. We design fair evaluation experimental protocol and choose proper datasets collection. This allows us to perform numerous experiments and rigorously analyze modern approaches. We arrive to many conclusions, which shed new light on performance and quality of novel algorithms. We investigate application of Jumping Knowledge GNN architecture to graph classification, which proves to be an efficient tool for improving base graph neural network architectures. Multiple improvements to baseline models are also proposed and experimentally verified, which constitutes an important contribution to the field of fair model comparison.

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。

对于学习图表表示，并非图中的所有详细结构都与给定的图形任务相关。与任务相关的结构可以是$本地化的$或$稀疏$，仅参与子图或以子图的交互作用（层次结构的角度）。图神经网络应该能够有效提取与任务相关的结构并与无关的部分不变，这对于通用消息传递GNN来说是具有挑战性的。在这项工作中，我们建议从原始图的一系列子图中学习图表表示，以更好地捕获与任务相关的子结构或分层结构，并跳过$ noisy $零件。为此，我们设计了软遮罩GNN层，以通过掩模机制提取所需的子图。软遮罩是在连续空间中定义的，以维持不同部分的重量并表征不同部分的权重。与现有的子图或分层表示方法和图形合并操作相比，软掩模GNN层不受固定样品或降低比率的限制，因此更灵活地提取具有任意尺寸的子图。公共图基准测试的广泛实验表明，软罩机制可以提高性能。它还提供了可解释性，使每个层中掩码的值可视化，使我们能够深入了解模型所学的结构。

图形内核是历史上最广泛使用的图形分类任务的技术。然而，由于图的手工制作的组合特征，这些方法具有有限的性能。近年来，由于其性能卓越，图形神经网络（GNNS）已成为与下游图形相关任务的最先进的方法。大多数GNN基于消息传递神经网络（MPNN）框架。然而，最近的研究表明，MPNN不能超过Weisfeiler-Lehman（WL）算法在图形同构术中的力量。为了解决现有图形内核和GNN方法的限制，在本文中，我们提出了一种新的GNN框架，称为\ Texit {内核图形神经网络}（Kernnns），该框架将图形内核集成到GNN的消息传递过程中。通过卷积神经网络（CNNS）中的卷积滤波器的启发，KERGNNS采用可训练的隐藏图作为绘图过滤器，该绘图过滤器与子图组合以使用图形内核更新节点嵌入式。此外，我们表明MPNN可以被视为Kergnns的特殊情况。我们将Kergnns应用于多个与图形相关的任务，并使用交叉验证来与基准进行公平比较。我们表明，与现有的现有方法相比，我们的方法达到了竞争性能，证明了增加GNN的表现能力的可能性。我们还表明，KERGNNS中的训练有素的图形过滤器可以揭示数据集的本地图形结构，与传统GNN模型相比，显着提高了模型解释性。

图形神经网络（GNN）已被广泛应用于各种领域，以通过图形结构数据学习。在各种任务（例如节点分类和图形分类）中，他们对传统启发式方法显示了显着改进。但是，由于GNN严重依赖于平滑的节点特征而不是图形结构，因此在链接预测中，它们通常比简单的启发式方法表现出差的性能，例如，结构信息（例如，重叠的社区，学位和最短路径）至关重要。为了解决这一限制，我们建议邻里重叠感知的图形神经网络（NEO-GNNS），这些神经网络（NEO-GNNS）从邻接矩阵中学习有用的结构特征，并估算了重叠的邻域以进行链接预测。我们的Neo-Gnns概括了基于社区重叠的启发式方法，并处理重叠的多跳社区。我们在开放图基准数据集（OGB）上进行的广泛实验表明，NEO-GNNS始终在链接预测中实现最新性能。我们的代码可在https://github.com/seongjunyun/neo_gnns上公开获取。

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.

最近，图形神经网络（GNNS）在各种现实情景中获得了普及。尽管取得了巨大成功，但GNN的建筑设计严重依赖于体力劳动。因此，自动化图形神经网络（Autopmn）引起了研究界的兴趣和关注，近年来显着改善。然而，现有的autopnn工作主要采用隐式方式来模拟并利用图中的链接信息，这对图中的链路预测任务不充分规范化，并限制了自动启动的其他图表任务。在本文中，我们介绍了一个新的Autognn工作，该工作明确地模拟了缩写为autogel的链接信息。以这种方式，AutoGel可以处理链路预测任务并提高Autognns对节点分类和图形分类任务的性能。具体地，AutoGel提出了一种新的搜索空间，包括层内和层间设计中的各种设计尺寸，并采用更强大的可分辨率搜索算法，以进一步提高效率和有效性。基准数据集的实验结果展示了自动池上的优势在几个任务中。