复杂网络分析的最新进展为不同领域的应用开辟了广泛的可能性。网络分析的功能取决于节点特征。基于拓扑的节点特征是对局部和全局空间关系和节点连接结构的实现。因此，收集有关节点特征的正确信息和相邻节点的连接结构在复杂网络分析中在节点分类和链接预测中起着最突出的作用。目前的工作介绍了一种新的特征抽象方法，即基于嵌入匿名随机步行向量上的匿名随机步行，即过渡概率矩阵（TPM）。节点特征向量由从预定义半径中的一组步行中获得的过渡概率组成。过渡概率与局部连接结构直接相关，因此正确嵌入到特征向量上。在节点识别/分类中测试了建议的嵌入方法的成功，并在三个常用的现实世界网络上进行了链接预测。在现实世界网络中，具有相似连接结构的节点很常见。因此，从类似网络中获取新网络预测的信息是一种显着特征，它使所提出的算法在跨网络概括任务方面优于最先进的算法。

图形嵌入，代表数值向量的本地和全局邻域信息，是广泛的现实系统数学建模的关键部分。在嵌入算法中，事实证明，基于步行的随机算法非常成功。这些算法通过创建许多随机步行，并重新定义步骤来收集信息。创建随机步行是嵌入过程中最苛刻的部分。计算需求随着网络的规模而增加。此外，对于现实世界网络，考虑到相同基础上的所有节点，低度节点的丰度都会造成不平衡的数据问题。在这项工作中，提出了一种计算较少且节点连接性统一抽样方法。在提出的方法中，随机步行的数量与节点的程度成比例地创建。当将算法应用于大图时，所提出的算法的优点将变得更加增强。提出了使用两个网络（即Cora和Citeseer）进行比较研究。与固定数量的步行情况相比，提出的方法需要减少50％的计算工作，以达到节点分类和链接预测计算的相同精度。

网络表示学习（NRL）方法在过去几年中受到了重大关注，因此由于它们在几个图形分析问题中的成功，包括节点分类，链路预测和聚类。这种方法旨在以一种保留网络的结构信息的方式将网络的每个顶点映射到低维空间中。特别感兴趣的是基于随机行走的方法;这些方法将网络转换为节点序列的集合，旨在通过预测序列内每个节点的上下文来学习节点表示。在本文中，我们介绍了一种通用框架，以增强通过基于主题信息的随机行走方法获取的节点的嵌入。类似于自然语言处理中局部单词嵌入的概念，所提出的模型首先将每个节点分配给潜在社区，并有利于各种统计图模型和社区检测方法，然后了解增强的主题感知表示。我们在两个下游任务中评估我们的方法：节点分类和链路预测。实验结果表明，通过纳入节点和社区嵌入，我们能够以广泛的广泛的基线NRL模型表明。

图表上的表示学习（也称为图形嵌入）显示了其对一系列机器学习应用程序（例如分类，预测和建议）的重大影响。但是，现有的工作在很大程度上忽略了现代应用程序中图和边缘的属性（或属性）中包含的丰富信息，例如，属性图表示的节点和边缘。迄今为止，大多数现有的图形嵌入方法要么仅关注具有图形拓扑的普通图，要么仅考虑节点上的属性。我们提出了PGE，这是一个图形表示学习框架，该框架将节点和边缘属性都包含到图形嵌入过程中。 PGE使用节点聚类来分配偏差来区分节点的邻居，并利用多个数据驱动的矩阵来汇总基于偏置策略采样的邻居的属性信息。 PGE采用了流行的邻里聚合归纳模型。我们通过显示PGE如何实现更好的嵌入结果的详细分析，并验证PGE的性能，而不是最新的嵌入方法嵌入方法在基准应用程序上的嵌入方法，例如节点分类和对现实世界中的链接预测数据集。

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。

Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating prediction by learning the features themselves. However, present feature learning approaches are not expressive enough to capture the diversity of connectivity patterns observed in networks.Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks. In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node's network neighborhood and design a biased random walk procedure, which efficiently explores diverse neighborhoods. Our algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and we argue that the added flexibility in exploring neighborhoods is the key to learning richer representations.We demonstrate the efficacy of node2vec over existing state-ofthe-art techniques on multi-label classification and link prediction in several real-world networks from diverse domains. Taken together, our work represents a new way for efficiently learning stateof-the-art task-independent representations in complex networks.

在过去的二十年中，我们目睹了以图形或网络形式构建的有价值的大数据的大幅增长。为了将传统的机器学习和数据分析技术应用于此类数据，有必要将图形转换为基于矢量的表示，以保留图形最重要的结构属性。为此，文献中已经提出了大量的图形嵌入方法。它们中的大多数产生了适用于各种应用的通用嵌入，例如节点聚类，节点分类，图形可视化和链接预测。在本文中，我们提出了两个新的图形嵌入算法，这些算法是基于专门为节点分类问题设计的随机步道。已设计算法的随机步行采样策略旨在特别注意集线器 - 高度节点，这些节点在大规模图中具有最关键的作用。通过分析对现实世界网络嵌入的三种分类算法的分类性能，对所提出的方法进行实验评估。获得的结果表明，与当前最流行的随机步行方法相比，我们的方法可大大提高所检查分类器的预测能力（NODE2VEC）。

在低维空间中节点的学习表示是一项至关重要的任务，在网络分析中具有许多有趣的应用，包括链接预测，节点分类和可视化。解决此问题的两种流行方法是矩阵分解和基于步行的随机模型。在本文中，我们旨在将两全其美的最好的人融合在一起，以学习节点表示。特别是，我们提出了一个加权矩阵分解模型，该模型编码有关网络节点的随机步行信息。这种新颖的表述的好处是，它使我们能够利用内核函数，而无需意识到确切的接近矩阵，从而增强现有矩阵分解方法的表达性，并减轻其计算复杂性。我们通过多个内核学习公式扩展了方法，该公式提供了学习内核作为以数据驱动方式的词典的线性组合的灵活性。我们在现实世界网络上执行经验评估，表明所提出的模型优于基线节点嵌入下游机器学习任务中的算法。

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.

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.

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。

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.

复杂的网络是代表现实生活系统的图形，这些系统表现出独特的特征，这些特征在纯粹的常规或完全随机的图中未发现。由于基础过程的复杂性，对此类系统的研究至关重要，但具有挑战性。然而，由于大量网络数据的可用性，近几十年来，这项任务变得更加容易。复杂网络中的链接预测旨在估计网络中缺少两个节点之间的链接的可能性。由于数据收集的不完美或仅仅是因为它们尚未出现，因此可能会缺少链接。发现网络数据中实体之间的新关系吸引了研究人员在社会学，计算机科学，物理学和生物学等各个领域的关注。大多数现有研究的重点是无向复杂网络中的链接预测。但是，并非所有现实生活中的系统都可以忠实地表示为无向网络。当使用链接预测算法时，通常会做出这种简化的假设，但不可避免地会导致有关节点之间关系和预测性能中降解的信息的丢失。本文介绍了针对有向网络的明确设计的链接预测方法。它基于相似性范式，该范式最近已证明在无向网络中成功。提出的算法通过在相似性和受欢迎程度上将其建模为不对称性来处理节点关系中的不对称性。鉴于观察到的网络拓扑结构，该算法将隐藏的相似性近似为最短路径距离，并使用边缘权重捕获并取消链接的不对称性和节点的受欢迎程度。在现实生活中评估了所提出的方法，实验结果证明了其在预测各种网络数据类型和大小的丢失链接方面的有效性。

近年来，对图表的研究受到了极大的关注。但是，到目前为止，大多数研究都集中在单层图的嵌入上。涉及多层结构的表示问题问题的少数研究取决于以下强烈的假设：层间链接是已知的，这限制了可能的应用范围。在这里，我们提出了多层，这是允许嵌入多重网络的图形算法的概括。我们表明，多层能够重建层内和层间连接性，超过了图形，该图是为简单图形而设计的。接下来，通过全面的实验分析，我们还以简单和多重网络中的嵌入性能阐明，表明图的密度或链接的随机性都会强烈影响嵌入的质量。

网络嵌入任务是将网络中的节点表示为低维矢量，同时结合了拓扑和结构信息。大多数现有方法通过直接或隐式分配接近性矩阵来解决此问题。在这项工作中，我们从新的角度介绍了一种网络嵌入方法，该方法利用现代Hopfield网络（MHN）进行关联学习。我们的网络学习每个节点的内容与该节点的邻居之间的关联。这些关联是MHN中的回忆。鉴于该节点的邻居，网络的复发动力学使得可以恢复蒙版节点。我们提出的方法对不同的下游任务进行评估，例如节点分类和链接预测。与常见的矩阵分解技术和基于深度学习的方法相比，结果表明竞争性能。

Community detection is the task of discovering groups of nodes sharing similar patterns within a network. With recent advancements in deep learning, methods utilizing graph representation learning and deep clustering have shown great results in community detection. However, these methods often rely on the topology of networks (i) ignoring important features such as network heterogeneity, temporality, multimodality, and other possibly relevant features. Besides, (ii) the number of communities is not known a priori and is often left to model selection. In addition, (iii) in multimodal networks all nodes are assumed to be symmetrical in their features; while true for homogeneous networks, most of the real-world networks are heterogeneous where feature availability often varies. In this paper, we propose a novel framework (named MGTCOM) that overcomes the above challenges (i)--(iii). MGTCOM identifies communities through multimodal feature learning by leveraging a new sampling technique for unsupervised learning of temporal embeddings. Importantly, MGTCOM is an end-to-end framework optimizing network embeddings, communities, and the number of communities in tandem. In order to assess its performance, we carried out an extensive evaluation on a number of multimodal networks. We found out that our method is competitive against state-of-the-art and performs well in inductive inference.

时间图代表实体之间的动态关系，并发生在许多现实生活中的应用中，例如社交网络，电子商务，通信，道路网络，生物系统等。他们需要根据其生成建模和表示学习的研究超出与静态图有关的研究。在这项调查中，我们全面回顾了近期针对处理时间图提出的神经时间依赖图表的学习和生成建模方法。最后，我们确定了现有方法的弱点，并讨论了我们最近发表的论文提格的研究建议[24]。

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.

图形嵌入是图形节点到一组向量的转换。良好的嵌入应捕获图形拓扑，节点与节点的关系以及有关图，其子图和节点的其他相关信息。如果实现了这些目标，则嵌入是网络中有意义的，可理解的，可理解的压缩表示形式，可用于其他机器学习工具，例如节点分类，社区检测或链接预测。主要的挑战是，需要确保嵌入很好地描述图形的属性。结果，选择最佳嵌入是一项具有挑战性的任务，并且通常需要领域专家。在本文中，我们在现实世界网络和人为生成的网络上进行了一系列广泛的实验，并使用选定的图嵌入算法进行了一系列的实验。根据这些实验，我们制定了两个一般结论。首先，如果需要在运行实验之前选择一种嵌入算法，则Node2Vec是最佳选择，因为它在我们的测试中表现最好。话虽如此，在所有测试中都没有单一的赢家，此外，大多数嵌入算法都具有应该调整并随机分配的超参数。因此，如果可能的话，我们对从业者的主要建议是生成几个问题的嵌入，然后使用一个通用框架，该框架为无监督的图形嵌入比较提供了工具。该框架（最近在文献中引入并在GitHub存储库中很容易获得）将分歧分数分配给嵌入，以帮助区分好的分数和不良的分数。

Traditional network embedding primarily focuses on learning a continuous vector representation for each node, preserving network structure and/or node content information, such that off-the-shelf machine learning algorithms can be easily applied to the vector-format node representations for network analysis. However, the learned continuous vector representations are inefficient for large-scale similarity search, which often involves finding nearest neighbors measured by distance or similarity in a continuous vector space. In this paper, we propose a search efficient binary network embedding algorithm called BinaryNE to learn a binary code for each node, by simultaneously modeling node context relations and node attribute relations through a three-layer neural network. BinaryNE learns binary node representations through a stochastic gradient descent based online learning algorithm. The learned binary encoding not only reduces memory usage to represent each node, but also allows fast bit-wise comparisons to support faster node similarity search than using Euclidean distance or other distance measures. Extensive experiments and comparisons demonstrate that BinaryNE not only delivers more than 25 times faster search speed, but also provides comparable or better search quality than traditional continuous vector based network embedding methods. The binary codes learned by BinaryNE also render competitive performance on node classification and node clustering tasks. The source code of this paper is available at https://github.com/daokunzhang/BinaryNE.