Link prediction is a key problem for network-structured data. Link prediction heuristics use some score functions, such as common neighbors and Katz index, to measure the likelihood of links. They have obtained wide practical uses due to their simplicity, interpretability, and for some of them, scalability. However, every heuristic has a strong assumption on when two nodes are likely to link, which limits their effectiveness on networks where these assumptions fail. In this regard, a more reasonable way should be learning a suitable heuristic from a given network instead of using predefined ones. By extracting a local subgraph around each target link, we aim to learn a function mapping the subgraph patterns to link existence, thus automatically learning a "heuristic" that suits the current network. In this paper, we study this heuristic learning paradigm for link prediction. First, we develop a novel γ-decaying heuristic theory. The theory unifies a wide range of heuristics in a single framework, and proves that all these heuristics can be well approximated from local subgraphs. Our results show that local subgraphs reserve rich information related to link existence. Second, based on the γ-decaying theory, we propose a new method to learn heuristics from local subgraphs using a graph neural network (GNN). Its experimental results show unprecedented performance, working consistently well on a wide range of problems.

在本文中，我们提供了一种使用图形神经网络（GNNS）的理论，用于多节点表示学习（我们有兴趣学习一组多个节点的表示）。我们知道GNN旨在学习单节点表示。当我们想学习涉及多个节点的节点集表示时，先前作品中的常见做法是直接将GNN学习的多节点表示与节点集的关节表示。在本文中，我们显示了这种方法的基本限制，即无法捕获节点集中节点之间的依赖性，并且认为直接聚合各个节点表示不会导致多个节点的有效关节表示。然后，我们注意到，以前的一些成功的工作作品用于多节点表示学习，包括密封，距离编码和ID-GNN，所有使用的节点标记。这些方法根据应用GNN之前的与目标节点集的关系，首先标记图中的节点。然后，在标记的图表中获得的节点表示被聚合到节点集表示中。通过调查其内部机制，我们将这些节点标记技术统一到单个和最基本的形式，即标记技巧。我们证明，通过标记技巧，可以获得足够富有表现力的GNN学习最具表现力的节点集表示，因此原则上可以解决节点集的任何联合学习任务。关于一个重要的双节点表示学习任务，链接预测，验证了我们理论的实验。我们的工作建立了使用GNN在节点集上使用GNN进行联合预测任务的理论基础。

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。

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.

链接预测是图神经网络（GNN）的重要应用。链接预测的大多数现有GNN基于一维Weisfeiler-Lehman（1-WL）测试。 1-wl-gnn首先通过迭代的相邻节点特征来计算中心，然后通过汇总成对节点表示来获得链接表示。正如先前的作品所指出的那样，这两步过程会导致较低的区分功能，因为自然而然地学习节点级表示而不是链接级别。在本文中，我们研究了一种完全不同的方法，该方法可以基于\ textit {二维WEISFEILER-LEHMAN（2-WL）测试直接获得节点对（链接）表示。 2-WL测试直接使用链接（2个小说）作为消息传递单元而不是节点，因此可以直接获得链接表示。我们理论上分析了2-WL测试的表达能力以区分非晶状体链接，并证明其优越的链接与1-WL相比。基于不同的2-WL变体，我们提出了一系列用于链路预测的新型2-WL-GNN模型。在广泛的现实数据集上进行的实验证明了它们对最先进的基线的竞争性能以及优于普通1-WL-GNN的优势。

Link prediction is a crucial problem in graph-structured data. Due to the recent success of graph neural networks (GNNs), a variety of GNN-based models were proposed to tackle the link prediction task. Specifically, GNNs leverage the message passing paradigm to obtain node representation, which relies on link connectivity. However, in a link prediction task, links in the training set are always present while ones in the testing set are not yet formed, resulting in a discrepancy of the connectivity pattern and bias of the learned representation. It leads to a problem of dataset shift which degrades the model performance. In this paper, we first identify the dataset shift problem in the link prediction task and provide theoretical analyses on how existing link prediction methods are vulnerable to it. We then propose FakeEdge, a model-agnostic technique, to address the problem by mitigating the graph topological gap between training and testing sets. Extensive experiments demonstrate the applicability and superiority of FakeEdge on multiple datasets across various domains.

链接预测是图形结构数据（例如，社交网络，药物副作用网络等）的基本问题。图形神经网络为此问题提供了强大的解决方案，特别是通过学习封闭目标链接的子图的表示（即节点对）。但是，这些解决方案不能很好地扩展到大图，因为封闭子图的提取和操作在计算上是昂贵的，尤其是对于大图。本文提出了一个可扩展的链接预测解决方案，我们称之为缩放，该解决方案利用稀疏的封闭子图来做出预测。为了提取稀疏的封闭子图，缩放缩放从目标对节点进行多次随机步行，然后在所有访问的节点引起的采样封闭子图上操作。通过利用较小的采样封闭子图，缩放的缩放可以缩放到较大的图形，而在保持高精度的同时，缩小开销要少得多。缩放进一步提供了控制计算开销与准确性之间的权衡的灵活性。通过全面的实验，我们已经证明，缩放可以产生与现有子图表示学习框架报告的同时所报道的，同时计算要求较少的准确性。

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.

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.

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

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),

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。

能够推荐在线社交网络中用户之间的链接对于用户与志趣相投的个人以及利用社交媒体信息发展业务的平台本身和第三方联系很重要。预测通常基于无监督或监督的学习，通常利用简单而有效的图形拓扑信息，例如普通邻居的数量。但是，我们认为有关个人个人社会结构的更丰富信息可能会带来更好的预测。在本文中，我们建议利用良好的社会认知理论来提高链接预测绩效。根据这些理论，个人平均将自己的社会关系安排在五个同心圆下，以减少亲密关系。我们假设不同圈子中的关系在预测新链接方面具有不同的重要性。为了验证这一主张，我们专注于流行的功能萃取预测算法（既无监督和监督），并将其扩展到包括社交圈的意识。我们验证了这些圆圈感知算法对几个基准测试的预测性能（包括其基线版本以及基于节点的链接和GNN链接预测），利用了两个Twitter数据集，其中包括一个视频游戏玩家和通用用户的社区。我们表明，社会意识通常可以在预测绩效方面有重大改进，击败了Node2Vec和Seal等最新解决方案，而不会增加计算复杂性。最后，我们表明可以使用社交意识来代替针对特定类别用户的分类器（可能是昂贵或不切实际）的。

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。

Graph neural networks (GNNs) have received remarkable success in link prediction (GNNLP) tasks. Existing efforts first predefine the subgraph for the whole dataset and then apply GNNs to encode edge representations by leveraging the neighborhood structure induced by the fixed subgraph. The prominence of GNNLP methods significantly relies on the adhoc subgraph. Since node connectivity in real-world graphs is complex, one shared subgraph is limited for all edges. Thus, the choices of subgraphs should be personalized to different edges. However, performing personalized subgraph selection is nontrivial since the potential selection space grows exponentially to the scale of edges. Besides, the inference edges are not available during training in link prediction scenarios, so the selection process needs to be inductive. To bridge the gap, we introduce a Personalized Subgraph Selector (PS2) as a plug-and-play framework to automatically, personally, and inductively identify optimal subgraphs for different edges when performing GNNLP. PS2 is instantiated as a bi-level optimization problem that can be efficiently solved differently. Coupling GNNLP models with PS2, we suggest a brand-new angle towards GNNLP training: by first identifying the optimal subgraphs for edges; and then focusing on training the inference model by using the sampled subgraphs. Comprehensive experiments endorse the effectiveness of our proposed method across various GNNLP backbones (GCN, GraphSage, NGCF, LightGCN, and SEAL) and diverse benchmarks (Planetoid, OGB, and Recommendation datasets). Our code is publicly available at \url{https://github.com/qiaoyu-tan/PS2}

在本文中，我们旨在提供有效的成对学习神经链路预测（PLNLP）框架。该框架将链路预测视为对等级问题的成对学习，包括四个主要组件，即邻域编码器，链路预测器，负采样器和目标函数组成。该框架灵活地，任何通用图形神经卷积或链路预测特定神经结构都可以作为邻域编码器。对于链路预测器，我们设计不同的评分功能，可以基于不同类型的图表来选择。在否定采样器中，我们提供了几种采样策略，这些策略是特定的问题。至于目标函数，我们建议使用有效的排名损失，这大约最大化标准排名度量AUC。我们在4个链路属性预测数据集上评估了开放图基准的4个链接属性预测数据集，包括\ texttt {ogbl-ddi}，\ texttt {ogbl-collbab}，\ texttt {ogbl-ppa}和\ texttt {ogbl-ciation2}。 PLNLP在\ TextTt {ogbl-ddi}上实现前1个性能，以及仅使用基本神经架构的\ texttt {ogbl-collab}和\ texttt {ogbl-ciation2}的前2个性能。该性能展示了PLNLP的有效性。

最近提出了基于子图的图表学习（SGRL）来应对规范图神经网络（GNNS）遇到的一些基本挑战，并在许多重要的数据科学应用（例如链接，关系和主题预测）中证明了优势。但是，当前的SGRL方法遇到了可伸缩性问题，因为它们需要为每个培训或测试查询提取子图。扩大规范GNN的最新解决方案可能不适用于SGRL。在这里，我们通过共同设计学习算法及其系统支持，为可扩展的SGRL提出了一种新颖的框架Surel。 Surel采用基于步行的子图表分解，并将步行重新形成子图，从而大大降低了子图提取的冗余并支持并行计算。具有数百万个节点和边缘的六个同质，异质和高阶图的实验证明了Surel的有效性和可扩展性。特别是，与SGRL基线相比，Surel可以实现10 $ \ times $ Quad-Up，具有可比甚至更好的预测性能；与规范GNN相比，Surel可实现50％的预测准确性。

链接预测是图形上非常基本的任务。在本文中受到传统路径的方法的启发，我们提出了一种基于链路预测路径的一般和灵活的表示学习框架。具体地，我们将一对节点的表示定义为所有路径表示的广义和，每个路径表示为路径中的边缘表示的广义乘积。通过贝尔曼-Ford算法来解决最短路径问题，我们表明，所提出的路径配方可以通过广义的Bellman-Ford算法有效地解决。为了进一步提高路径制构的能力，我们提出了神经贝尔曼 - 福特网络（NBFNET），这是一种全图神经网络框架，其解决了通过广义Bellman-Ford算法中的学习运算符的路径制定。 NBFNET使用3个神经元件，即指示器，消息和聚合函数参数，即分别对应于边界条件，乘法运算符和求和运算符。 NBFNET非常一般，涵盖许多传统的基于路径的方法，并且可以应用于转导和归纳设置的同质图和多关系图（例如，知识图表）。两个均匀图表和知识图表的实验表明，所提出的NBFNET在转换和归纳设置中的大幅度优于现有方法，实现了新的最先进的结果。

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.

在过去十年中，图形内核引起了很多关注，并在结构化数据上发展成为一种快速发展的学习分支。在过去的20年中，该领域发生的相当大的研究活动导致开发数十个图形内核，每个图形内核都对焦于图形的特定结构性质。图形内核已成功地成功地在广泛的域中，从社交网络到生物信息学。本调查的目标是提供图形内核的文献的统一视图。特别是，我们概述了各种图形内核。此外，我们对公共数据集的几个内核进行了实验评估，并提供了比较研究。最后，我们讨论图形内核的关键应用，并概述了一些仍有待解决的挑战。