Graph Neural Network for Traffic Forecasting: A Survey
用于交通预测的图神经网络：调查

Weiwei Jiang 蒋伟伟 Department of Electronic Engineering, Tsinghua University, Beijing, 100084, China
清华大学电子工程系, 北京, 100084 Jiayun Luo 罗佳云 School of Computer Science and Engineering, Nanyang Technological University, 639798, Singapore
南洋理工大学计算机科学与工程学院, 639798, 新加坡

Abstract 抽象的

Traffic forecasting is important for the success of intelligent transportation systems. Deep learning models, including convolution neural networks and recurrent neural networks, have been extensively applied in traffic forecasting problems to model spatial and temporal dependencies. In recent years, to model the graph structures in transportation systems as well as contextual information, graph neural networks have been introduced and have achieved state-of-the-art performance in a series of traffic forecasting problems. In this survey, we review the rapidly growing body of research using different graph neural networks, e.g. graph convolutional and graph attention networks, in various traffic forecasting problems, e.g. road traffic flow and speed forecasting, passenger flow forecasting in urban rail transit systems, and demand forecasting in ride-hailing platforms. We also present a comprehensive list of open data and source codes for each problem and identify future research directions. To the best of our knowledge, this paper is the first comprehensive survey that explores the application of graph neural networks for traffic forecasting problems. We have also created a public GitHub repository where the latest papers, open data, and source codes will be updated.
交通预测对于智能交通系统的成功非常重要。深度学习模型，包括卷积神经网络和循环神经网络，已广泛应用于交通预测问题中，以对空间和时间依赖性进行建模。近年来，为了对交通系统中的图结构以及上下文信息进行建模，引入了图神经网络，并在一系列交通预测问题中取得了最先进的性能。在这项调查中，我们回顾了使用不同图神经网络的快速增长的研究，例如图卷积和图注意力网络，用于各种流量预测问题，例如道路交通流量和速度预测、城市轨道交通系统客流预测、网约车平台需求预测。我们还提供了每个问题的开放数据和源代码的完整列表，并确定了未来的研究方向。据我们所知，本文是第一篇探索图神经网络在交通预测问题中的应用的综合调查。我们还创建了一个公共 GitHub 存储库，其中将更新最新论文、开放数据和源代码。

keywords:

Traffic Forecasting , Graph Neural Networks , Graph Convolution Network , Graph Attention Network , Deep Learning
关键词：流量预测、图神经网络、图卷积网络、图注意力网络、深度学习

^†^†journal: Journal of LaTeX Templates
期刊：LaTeX 模板期刊

1 Introduction 1简介

Transportation systems are among the most important infrastructure in modern cities, supporting the daily commuting and traveling of millions of people. With rapid urbanization and population growth, transportation systems have become more complex. Modern transportation systems encompass road vehicles, rail transport, and various shared travel modes that have emerged in recent years, including online ride-hailing, bike-sharing, and e-scooter sharing. Expanding cities face many transportation-related problems, including air pollution and traffic congestion. Early intervention based on traffic forecasting is seen as the key to improving the efficiency of a transportation system and to alleviate transportation-related problems. In the development and operation of smart cities and intelligent transportation systems (ITSs), traffic states are detected by sensors (e.g. loop detectors) installed on roads, subway and bus system transaction records, traffic surveillance videos, and even smartphone GPS (Global Positioning System) data collected in a crowd-sourced fashion. Traffic forecasting is typically based on consideration of historical traffic state data, together with the external factors which affect traffic states, e.g. weather and holidays.
交通系统是现代城市最重要的基础设施之一，支撑着数百万人的日常通勤和出行。随着快速城市化和人口增长，交通系统变得更加复杂。现代交通系统包括公路车辆、轨道交通以及近年来兴起的网约车、共享单车、共享电动车等多种共享出行方式。不断扩张的城市面临着许多与交通相关的问题，包括空气污染和交通拥堵。基于交通预测的早期干预被视为提高交通系统效率和缓解交通相关问题的关键。在智慧城市和智能交通系统（ITS）的开发和运营中，交通状态通过安装在道路上的传感器（例如环路探测器）、地铁和公交系统交易记录、交通监控视频，甚至智能手机GPS（全球定位系统）来检测。）以众包方式收集的数据。交通预测通常基于历史交通状态数据以及影响交通状态的外部因素（例如，交通状况）的考虑。天气和假期。

Both short-term and long-term traffic forecasting problems for various transport modes are considered in the literature. This survey focuses on the data-driven approach, which involves forecasting based on historical data. The traffic forecasting problem is more challenging than other time series forecasting problems because it involves large data volumes with high dimensionality, as well as multiple dynamics including emergency situations, e.g. traffic accidents. The traffic state in a specific location has both spatial dependency, which may not be affected only by nearby areas, and temporal dependency, which may be seasonal. Traditional linear time series models, e.g. auto-regressive and integrated moving average (ARIMA) models, cannot handle such spatiotemporal forecasting problems. Machine learning (ML) and deep learning techniques have been introduced in this area to improve forecasting accuracy, for example, by modeling the whole city as a grid and applying a convolutional neural network (CNN) as demonstrated by Jiang & Zhang [2018]. However, the CNN-based approach is not optimal for traffic foresting problems that have a graph-based form, e.g. road networks.
文献中考虑了各种运输方式的短期和长期交通预测问题。这项调查的重点是数据驱动的方法，其中涉及基于历史数据的预测。交通预测问题比其他时间序列预测问题更具挑战性，因为它涉及高维的大数据量，以及包括紧急情况在内的多种动态，例如紧急情况。交通意外。特定位置的交通状态既有空间依赖性（可能不仅仅受附近区域的影响），也有时间依赖性（可能是季节性的）。传统的线性时间序列模型，例如自回归和综合移动平均（ARIMA）模型无法处理此类时空预测问题。该领域已引入机器学习（ML）和深度学习技术来提高预测准确性，例如，通过将整个城市建模为网格并应用卷积神经网络（CNN），如Jiang和Zhang [2018]所示。然而，基于 CNN 的方法对于具有基于图的形式的流量森林问题来说并不是最佳的，例如道路网络。

In recent years, graph neural networks (GNNs) have become the frontier of deep learning research, showing state-of-the-art performance in various applications [Wu et al., 2020b]. GNNs are ideally suited to traffic forecasting problems because of their ability to capture spatial dependency, which is represented using non-Euclidean graph structures. For example, a road network is naturally a graph, with road intersections as the nodes and road connections as the edges. With graphs as the input, several GNN-based models have demonstrated superior performance to previous approaches on tasks including road traffic flow and speed forecasting problems. These include, for example, the diffusion convolutional recurrent neural network (DCRNN) [Li et al., 2018b] and Graph WaveNet [Wu et al., 2019] models. The GNN-based approach has also been extended to other transportation modes, utilizing various graph formulations and models.
近年来，图神经网络（GNN）已成为深度学习研究的前沿，在各种应用中显示出最先进的性能 [Wu et al., 2020b]。 GNN 非常适合交通预测问题，因为它们能够捕获空间依赖性（使用非欧几里得图结构表示）。例如，道路网络本质上是一个图，以道路交叉口为节点，以道路连接为边。以图为输入，一些基于 GNN 的模型在道路交通流量和速度预测问题等任务上表现出了优于之前方法的性能。例如，其中包括扩散卷积递归神经网络 (DCRNN) [Li et al., 2018b] 和 Graph WaveNet [Wu et al., 2019] 模型。基于 GNN 的方法还利用各种图形公式和模型扩展到其他交通模式。

To the best of the authors’ knowledge, this paper presents the first comprehensive literature survey of GNN-related approaches to traffic forecasting problems. While several relevant traffic forecasting surveys exist [Shi & Yeung, 2018, Pavlyuk, 2019, Yin et al., 2021, Luca et al., 2020, Fan et al., 2020, Boukerche & Wang, 2020a, Manibardo et al., 2021, Ye et al., 2020a, Lee et al., 2021, Xie et al., 2020a, George & Santra, 2020, Haghighat et al., 2020, Boukerche et al., 2020, Tedjopurnomo et al., 2020, Varghese et al., 2020], most of them are not GNN-focused with only one exception [Ye et al., 2020a]. For this survey, we reviewed 212 papers published in the years 2018 to 2020. Additionally, because this is a very rapidly developing research field, we also included preprints that have not yet gone through the traditional peer review process (e.g., arXiv papers) to present the latest progress. Based on these studies, we identify the most frequently considered problems, graph formulations, and models. We also investigate and summarize publicly available useful resources, including datasets, software, and open-sourced code, for GNN-based traffic forecasting research and application. Lastly, we identify the challenges and future directions of applying GNNs to the traffic forecasting problem.
据作者所知，本文首次对与 GNN 相关的交通预测问题方法进行了全面的文献调查。虽然存在一些相关的交通预测调查 [Shi & Yeung, 2018, Pavlyuk, 2019, Yin et al., 2021, Luca et al., 2020, Fan et al., 2020, Boukerche & Wang, 2020a, Manibardo et al., 2021，Ye 等人，2020a，Lee 等人，2021，Xie 等人，2020a，George & Santra，2020，Haghighat 等人，2020，Boukerche 等人，2020，Tedjopurnomo 等人，2020， Varghese 等人，2020]，其中大多数都不是以 GNN 为中心，只有一个例外 [Ye 等人，2020a]。在本次调查中，我们回顾了 2018 年至 2020 年发表的 212 篇论文。此外，由于这是一个非常快速发展的研究领域，我们还纳入了尚未经过传统同行评审流程的预印本（例如 arXiv 论文），以呈现最新进展。根据这些研究，我们确定了最常考虑的问题、图表公式和模型。我们还调查和总结了公开的有用资源，包括数据集、软件和开源代码，用于基于 GNN 的流量预测研究和应用。最后，我们确定了将 GNN 应用到流量预测问题的挑战和未来方向。

Instead of giving a whole picture of traffic forecasting, our aim is to provide a comprehensive summary of GNN-based solutions. This paper is useful for both the new researchers in this field who want to catch up with the progress of applying GNNs and the experienced researchers who are not familiar with these latest graph-based solutions. In addition to this paper, we have created an open GitHub repository on this topic ¹¹1https://github.com/jwwthu/GNN4Traffic
我们的目标不是提供流量预测的全貌，而是提供基于 GNN 的解决方案的全面总结。本文对于该领域想要了解 GNN 应用进展的新研究人员以及不熟悉这些最新的基于图的解决方案的经验丰富的研究人员来说都是有用的。除了本文之外，我们还创建了一个关于此主题的开放 GitHub 存储库 ¹ , where relevant content will be updated continuously.
，相关内容将持续更新。

Our contributions are summarized as follows:
我们的贡献总结如下：

1) Comprehensive Review: We present the most comprehensive review of graph-based solutions for traffic forecasting problems in the past three years (2018-2020).
1）全面回顾：我们对过去三年（2018-2020）基于图的流量预测问题解决方案进行了最全面的回顾。

2) Resource Collection: We provide the latest comprehensive list of open datasets and code resources for replication and comparison of GNNs in future work.
2）资源收集：我们提供最新的开放数据集和代码资源的综合列表，以便在未来的工作中复制和比较GNN。

3) Future Directions: We discuss several challenges and potential future directions for researchers in this field, when using GNNs for traffic forecasting problems.
3）未来方向：我们讨论了该领域研究人员在使用 GNN 解决流量预测问题时面临的几个挑战和潜在的未来方向。

The remainder of this paper is organized as follows. In Section 2, we compare our work with other relevant research surveys. In Section 3, we categorize the traffic forecasting problems that are involved with GNN-based models. In Section 4.1, we summarize the graphs and GNNs used in the reviewed studies. In Section 5, we outline the open resources. Finally, in Section 6, we point out challenges and future directions.
本文的其余部分安排如下。在第二节中，我们将我们的工作与其他相关研究调查进行比较。在第 3 节中，我们对基于 GNN 的模型涉及的流量预测问题进行了分类。在第 4.1 节中，我们总结了所审查研究中使用的图表和 GNN。在第 5 节中，我们概述了开放资源。最后，在第六节中，我们指出了挑战和未来的方向。

2 Related Research Surveys
2相关研究调查

In this section, we introduce the most recent relevant research surveys (most of which were published in 2020). The differences between our study and these existing surveys are pointed out when appropriate. We start with the surveys addressing wider ITS topics, followed by those focusing on traffic prediction problems and GNN application in particular.
在本节中，我们介绍最新的相关研究调查（其中大部分发表于 2020 年）。我们的研究与这些现有调查之间的差异会在适当的时候指出。我们从针对更广泛的 ITS 主题的调查开始，然后是针对流量预测问题和特别是 GNN 应用的调查。

Besides traffic forecasting, machine learning and deep learning methods have been widely used in ITSs as discussed in Haghighat et al. [2020], Fan et al. [2020], Luca et al. [2020]. In Haghighat et al. [2020], GNNs are only mentioned in the task of traffic characteristics prediction. Among the major milestones of deep-learning driven traffic prediction (summarized in Figure 2 of Fan et al. [2020]), the state-of-the-art models after 2019 are all based on GNNs, indicating that GNNs are indeed the frontier of deep learning-based traffic prediction research.
正如 Haghighat 等人所讨论的，除了交通预测之外，机器学习和深度学习方法也已广泛应用于 ITS。 [2020]，范等人。 [2020]，卢卡等人。 [2020]。在 Haghighat 等人中。 [2020]，GNN仅在流量特征预测任务中被提及。在深度学习驱动的流量预测的主要里程碑中（Fan等人[2020]的图2总结），2019年后最先进的模型都是基于GNN的，这表明GNN确实是前沿基于深度学习的交通预测研究。

Roughly speaking, five different types of traffic prediction methods are identified and categorized in previous surveys [Xie et al., 2020a, George & Santra, 2020], namely, statistics-based methods, traditional machine learning methods, deep learning-based methods, reinforcement learning-based methods, and transfer learning-based methods. Some comparisons between different categories have been considered, e.g., statistics-based models have better model interpretability, whereas ML-based models are more flexible as discussed in Boukerche et al. [2020]. Machine learning models for traffic prediction are further categorized in Boukerche & Wang [2020a], which include the regression model, example-based models (e.g., k-nearest neighbors), kernel-based models (e.g. support vector machine and radial basis function), neural network models, and hybrid models. Deep learning models are further categorized into five different generations in Lee et al. [2021], in which GCNs are classified as the fourth generation and other advanced techniques that have been considered but are not yet widely applied are merged into the fifth generation. These include transfer learning, meta learning, reinforcement learning, and the attention mechanism. Before these advanced techniques become mature in traffic prediction tasks, GNNs remain the state-of-the-art technique.
粗略地说，之前的调查识别并分类了五种不同类型的流量预测方法 [Xie et al., 2020a, George & Santra, 2020]，即基于统计的方法、传统机器学习方法、基于深度学习的方法、基于强化学习的方法和基于迁移学习的方法。已经考虑了不同类别之间的一些比较，例如，基于统计的模型具有更好的模型可解释性，而基于 ML 的模型更加灵活，如 Boukerche 等人所述。 [2020]。 Boukerche & Wang [2020a] 对流量预测的机器学习模型进行了进一步分类，包括回归模型、基于示例的模型（例如 k 最近邻）、基于内核的模型（例如支持向量机和径向基函数）、神经网络模型和混合模型。 Lee 等人将深度学习模型进一步分为五个不同的代。 [2021]，其中GCN被归类为第四代，其他已经考虑过但尚未广泛应用的先进技术被合并到第五代。其中包括迁移学习、元学习、强化学习和注意力机制。在这些先进技术在流量预测任务中变得成熟之前，GNN 仍然是最先进的技术。

Some of the relevant surveys only focus on the progress of deep learning-based methods [Tedjopurnomo et al., 2020], while the others prefer to compare them with the statistics-based and machine learning methods [Yin et al., 2021, Manibardo et al., 2021]. In Tedjopurnomo et al. [2020], 37 deep neural networks for traffic prediction are reviewed, categorized, and discussed. The authors conclude that encoder-decoder long short term-memory (LSTM) combined with graph-based methods is the state-of-the-art prediction technique. A detailed explanation of various data types and popular deep neural network architectures is also provided, along with challenges and future directions for traffic prediction. Conversely, it is found that deep learning is not always the best modeling technique in practical applications, where linear models and machine learning techniques with less computational complexity can sometimes be preferable [Manibardo et al., 2021].
一些相关调查仅关注基于深度学习的方法的进展 [Tedjopurnomo et al., 2020]，而其他调查则更喜欢将它们与基于统计和机器学习的方法进行比较 [Yin et al., 2021, Manibardo等人，2021]。在 Tedjopurnomo 等人中。 [2020]，对 37 个用于交通预测的深度神经网络进行了回顾、分类和讨论。作者得出的结论是，编码器-解码器长短期记忆 (LSTM) 与基于图的方法相结合是最先进的预测技术。还提供了各种数据类型和流行的深度神经网络架构的详细解释，以及流量预测的挑战和未来方向。相反，人们发现深度学习在实际应用中并不总是最好的建模技术，其中计算复杂度较低的线性模型和机器学习技术有时可能更可取 [Manibardo et al., 2021]。

Additional research surveys consider aspects other than model selection. In Pavlyuk [2019], spatiotemporal feature selection and extraction pre-processing methods, which may also be embedded as internal model processes, are reviewed. A meta-analysis of prediction accuracy when applying deep learning methods to transport studies is given in Varghese et al. [2020]. In this study, apart from the models themselves, additional factors including sample size and prediction time horizon are shown to have a significant influence on prediction accuracy.
其他研究调查考虑了模型选择以外的其他方面。 Pavlyuk [2019] 回顾了时空特征选择和提取预处理方法，这些方法也可以作为内部模型过程嵌入。 Varghese 等人给出了将深度学习方法应用于交通研究时预测准确性的荟萃分析。 [2020]。在这项研究中，除了模型本身之外，样本大小和预测时间范围等其他因素也被证明对预测精度有显着影响。

To the authors’ best knowledge, there are no existing surveys focusing on the application of GNNs for traffic forecasting. Graph-based deep learning architectures are reviewed in Ye et al. [2020a], for a series of traffic applications, namely, traffic congestion, travel demand, transportation safety, traffic surveillance, and autonomous driving. Specific and practical guidance for constructing graphs in these applications is provided. The advantages and disadvantages of both GNNs and other deep learning models ,e.g. recurrent neural network (RNN), temporal convolutional network (TCN), Seq2Seq, and generative adversarial network (GAN), are examined. While the focus is not limited to traffic prediction problems, the graph construction process is universal in the traffic domain when GNNs are involved.
据作者所知，目前还没有针对 GNN 在流量预测中的应用的调查。 Ye 等人对基于图的深度学习架构进行了综述。 [2020a]，针对交通拥堵、出行需求、交通安全、交通监控、自动驾驶等一系列交通应用。提供了在这些应用程序中构建图形的具体且实用的指导。 GNN 和其他深度学习模型的优缺点，例如研究了循环神经网络（RNN）、时间卷积网络（TCN）、Seq2Seq 和生成对抗网络（GAN）。虽然重点不限于流量预测问题，但当涉及 GNN 时，图构建过程在流量领域是通用的。

3 Problems 3问题

In this section, we discuss and categorize the different types of traffic forecasting problems considered in the literature. Problems are first categorized by the traffic state to be predicted. Traffic flow, speed, and demand problems are considered separately while the remaining types are grouped together under “other problems”. Then, the problem-types are further broken down into levels according to where the traffic states are defined. These include road-level, region-level, and station-level categories.
在本节中，我们对文献中考虑的不同类型的流量预测问题进行讨论和分类。首先根据要预测的交通状况对问题进行分类。交通流、速度和需求问题分别考虑，而其余类型则归为“其他问题”。然后，根据交通状态的定义，将问题类型进一步细分为多个级别。其中包括道路级、区域级和车站级类别。

Different problem types have different modelling requirements for representing spatial dependency. For the road-level problems, the traffic data are usually collected from sensors, which are associated with specific road segments, or GPS trajectory data, which are also mapped into the road network with map matching techniques. In this case, the road network topology can be seen as the graph to use, which may contain hundreds or thousands of road segments potentially. The spatial dependency may be described by the road network connectivity or spatial proximity. For the station-level problems, the metro or bus station topology can be taken as the graph to use, which may contain tens or hundreds of stations potentially. The spatial dependency may be described by the metro lines or bus routes. For the region-level problem, the regular or irregular regions are used as the nodes in a graph. The spatial dependency between different regions can be extracted from the land use purposes, e.g., from the points-of-interest data.
不同的问题类型对于表示空间依赖性有不同的建模要求。对于道路层面的问题，交通数据通常是从与特定路段相关的传感器收集的，或者是GPS轨迹数据，这些数据也通过地图匹配技术映射到道路网络中。在这种情况下，道路网络拓扑可以被视为要使用的图，其中可能包含数百或数千个路段。空间依赖性可以通过道路网络连通性或空间邻近性来描述。对于车站级问题，可以将地铁或公交车站拓扑作为图来使用，其中可能包含数十或数百个车站。空间依赖性可以通过地铁线路或公交路线来描述。对于区域级问题，规则或不规则区域被用作图中的节点。不同区域之间的空间依赖性可以从土地使用目的中提取，例如从兴趣点数据中提取。

A full list of the traffic forecasting problems considered in the surveyed studies is shown in Table LABEL:tab:problems. Instead of giving the whole picture of traffic forecasting research, only those problems with GNN-based solutions in the literature are listed in Table LABEL:tab:problems.
表 LABEL:tab:problems 显示了调查研究中考虑的交通预测问题的完整列表。表 LABEL:tab:problems 中仅列出了文献中基于 GNN 的解决方案的问题，而不是给出流量预测研究的全貌。

Table 1: Traffic forecasting problems in the surveyed studies.
表 1：调查研究中的交通预测问题。

Problem	Relevant Studies 相关研究
Road Traffic Flow 道路交通流量	Zhang et al. [2018b], Wei et al. [2019], Xu et al. [2020a], Guo et al. [2020a], Zheng et al. [2020b], Pan et al. [2020, 2019], Lu et al. [2019a], Mallick et al. [2020], Zhang et al. [2020j, l], Bai et al. [2020], Fang et al. [2019], Huang et al. [2020a], Wang et al. [2018b], Zhang et al. [2020e], Song et al. [2020a], Xu et al. [2020b], Wang et al. [2020g], Chen et al. [2020e], Lv et al. [2020], Kong et al. [2020], Fukuda et al. [2020], Zhang & Guo [2020], Boukerche & Wang [2020b], Tang et al. [2020b], Kang et al. [2019], Guo et al. [2019c], Li et al. [2019b], Xu et al. [2019], Zhang et al. [2019d], Wu et al. [2018a], Sun et al. [2020], Wei & Sheng [2020], Li et al. [2020f], Cao et al. [2020], Yu et al. [2018, 2019b], Li et al. [2020b], Yin et al. [2020], Chen et al. [2020g], Zhang et al. [2020a], Wang et al. [2020a], Xin et al. [2020], Qu et al. [2020], Wang et al. [2020b], Xie et al. [2020d], Huang et al. [2020b], Guo et al. [2020b], Zhang et al. [2020h], Fang et al. [2020a], Li & Zhu [2021], Tian et al. [2020], Xu et al. [2020c], Chen et al. [2020c 张等人 2018b，徐等人 2020a，郑等人 2020，2019，卢等人 2020，张等人 2020j，Bai 等人 2020，黄等人 2020a，Zhang 等人 2020a，Xu 等人 2020b， Wang 等人 2020g，Lv 等人 2020，Fukuda 等人 2020，Boukerche 等人 2020b，Kang 等人。 2019，Li 等人 2019b，Zhang 等人 2019d，Sun 等人 2020，Li 等人 2020f等人 2020，Yu 等人 2020b，Yin 等人 2020g，Wang 等人 2020a，Qu等人 2020，Xie 等人 2020b，Guo 等人 2020h，Fang 等人 2020a，Tian 等人。 2020，徐等人 2020c，陈等人 2020c]
Road OD Flow 道路外径流量	Xiong et al. [2020], Ramadan et al. [2020 熊等人。 2020 年，斋月等。 2020年]
Intersection Traffic Throughput 路口交通吞吐量	Sánchez et al. [2020 桑切斯等人。 2020年]
Regional Taxi Flow 区域出租车流量	Zhou et al. [2020d], Sun et al. [2020], Chen et al. [2020d], Wang et al. [2018a], Peng et al. [2020], Zhou et al. [2019], Wang et al. [2020e], Qiu et al. [2020] Zhou 等人 2020d，Chen 等人 2020d，Peng 等人 2020，Wang 等人 2020
Regional Bike Flow 区域自行车流量	Zhou et al. [2020d], Sun et al. [2020], Wang et al. [2018a, 2020e 周等人。 2020d，Sun 等人。 2020，王等人。 2018年a, 2020年e]
Regional Ride-hailing Flow 区域网约车流量	Zhou et al. [2019 周等人。 2019年]
Regional Dockless E-Scooter Flow 区域无桩电动滑板车流程	He & Shin [2020a 和信 2020a]
Regional OD Taxi Flow 区域 OD 出租车流量	Wang et al. [2020e], Yeghikyan et al. [2020 王等人。 2020e，Yeghikyan 等人。 2020年]
Regional OD Bike Flow 区域 OD 自行车流量	Wang et al. [2020e 王等人。 2020年预计]
Regional OD Ride-hailing Flow 区域OD网约车流量	Shi et al. [2020], Wang et al. [2020h, 2019 石等人。 2020，王等人。 2020h, 2019]
Station-level Subway Passenger Flow 车站级地铁客流量	Fang et al. [2019, 2020a], Peng et al. [2020], Ren & Xie [2019], Li et al. [2018a], Zhao et al. [2020a], Han et al. [2019], Zhang et al. [2020b, c], Li et al. [2020e], Liu et al. [2020b], Ye et al. [2020b], Ou et al. [2020 方等人。 2019、2020a，Peng 等人。 2020，Ren & Xie 2019，Li 等人。 2018a，赵等人。 2020a，Han 等人。 2019，张等人。 2020b，c，Li 等人。 2020e，刘等人。 2020b，叶等人。 2020b，Ou 等人。 2020年]
Station-level Bus Passenger Flow 车站级公交客流	Fang et al. [2019, 2020a], Peng et al. [2020 方等人。 2019、2020a，Peng 等人。 2020年]
Station-level Shared Vehicle Flow 车站级共享车流	Zhu et al. [2019 朱等人。 2019年]
Station-level Bike Flow 车站级自行车流量	He & Shin [2020b], Chai et al. [2018 He & Shin 2020b，Chai 等人。 2018年]
Station-level Railway Passenger Flow 车站级铁路客流	He et al. [2020 他等人。 2020年]
Road Traffic Speed 道路交通速度	Li et al. [2018b], Wu et al. [2019], Zhang et al. [2018b], Wei et al. [2019], Xu et al. [2020a], Guo et al. [2020a], Zheng et al. [2020b], Pan et al. [2020, 2019], Lu et al. [2019a], Mallick et al. [2020], Zhang et al. [2020j], Lv et al. [2020], Li et al. [2020f], Yin et al. [2020], Guo et al. [2020b], Li & Zhu [2021], Chen et al. [2020d], Zhao et al. [2020a], Bai et al. [2021], Tang et al. [2020a], James [2020], Shin & Yoon [2020], Liu et al. [2020a], Zhang et al. [2018a, 2019f], Yu & Gu [2019], Xie et al. [2019], Zhang et al. [2019a], Guo et al. [2019a], Diao et al. [2019], Cirstea et al. [2019], Lu et al. [2019b], Zhang et al. [2019c], James [2019], Ge et al. [2019a, b], Zhang et al. [2019b], Lee & Rhee [2022], Shleifer et al. [2019], Yu et al. [2020a], Ge et al. [2020], Lu et al. [2020b], Yang et al. [2020], Zhao et al. [2019], Cui et al. [2019], Chen et al. [2019], Zhang et al. [2019e], Yu et al. [2019a], Lee & Rhee [2019], Bogaerts et al. [2020], Wang et al. [2020f], Cui et al. [2020b, a], Guo et al. [2020c], Zhou et al. [2020a], Cai et al. [2020], Zhou et al. [2020b], Wu et al. [2020c], Chen et al. [2020f], Opolka et al. [2019], Mallick et al. [2021], Oreshkin et al. [2021], Jia et al. [2020], Sun et al. [2021], Guo & Yuan [2020], Xie et al. [2020b], Zhang et al. [2020i], Zhu et al. [2021], Feng et al. [2020], Zhu et al. [2020], Fu et al. [2020], Zhang et al. [2020d], Xie et al. [2020c], Park et al. [2020], Agafonov [2020], Chen et al. [2020a], Lu et al. [2020a], Jepsen et al. [2019, 2020], Bing et al. [2020], Lewenfus et al. [2020], Zhu et al. [2022], Liao et al. [2018], Maas & Bloem [2020], Li et al. [2020d], Song et al. [2020b], Zhao et al. [2020b], Guopeng et al. [2020], Kim et al. [2020 李等人。 2018b，吴等人。 2019，张等人。 2018b，Wei 等人。 2019，徐等人。 2020a，郭等人。 2020a，郑等人。 2020b，潘等人。 2020、2019，Lu 等人。 2019a，Mallick 等人。 2020，张等人。 2020j，Lv 等人。 2020，李等人。 2020f，尹等人。 2020，郭等人。 2020b，Li & Zhu 2021，Chen 等人。 2020d，赵等人。 2020a，Bai 等人。 2021，唐等人。 2020a，James 2020，Shin & Yoon 2020，Liu 等人。 2020a，张等人。 2018a，2019f，Yu & Gu 2019，Xie 等人。 2019，张等人。 2019a，郭等人。 2019a，Diao 等人。 2019，Cirstea 等人。 2019，卢等人。 2019b，Zhang 等人。 2019c，James 2019，Ge 等人。 2019a、b，Zhang 等人。 2019b，Lee & Rhee 2022，Shleifer 等人。 2019，Yu 等人。 2020a，Ge 等人。 2020，卢等人。 2020b，杨等人。 2020，赵等人。 2019，崔等人。 2019，陈等人。 2019，张等人。 2019e，Yu 等人。 2019a，Lee & Rhee 2019，Bogaerts 等人。 2020，王等人。 2020f，崔等人。 2020b，a，郭等人。 2020c，Zhou 等人。 2020a，蔡等人。 2020，Zhou 等人。 2020b，吴等人。 2020c，陈等人。 2020f，Opolka 等人。 2019，马利克等人。 2021，奥列什金等人。 2021，贾等人。 2020，孙等人。 2021，Guo & Yuan 2020，Xie 等人。 2020b，张等人。 2020i，朱等人。 2021，冯等人。 2020，朱等人。 2020，傅等人。 2020，张等人。 2020d，Xie 等人。 2020c，Park 等人。 2020，阿加福诺夫 2020，陈等人。 2020a，Lu 等人。 2020a，杰普森等人。 2019、2020，Bing 等人。 2020，Lewenfus 等人。 2020，朱等人。 2022，廖等人。 2018 年，Maas 和 Bloem 2020 年，Li 等人。 2020d，宋等人。 2020b，赵等人。 2020b，郭鹏等人。 2020，金等人。 2020年]
Road Travel Time 公路旅行时间	Guo et al. [2020a], Hasanzadeh et al. [2019], Fang et al. [2020b], Shao et al. [2020], Shen et al. [2020] 郭等人。 2020a，哈桑扎德等人。 2019，方等人。 2020b，Shao 等人。 2020，沉等人。 2020年
Traffic Congestion 交通拥堵	Dai et al. [2020], Mohanty & Pozdnukhov [2018], Mohanty et al. [2020], Qin et al. [2020a], Han et al. [2020 戴等人。 2020 年，Mohanty 和 Pozdnukhov 2018 年，Mohanty 等人。 2020，秦等人。 2020a，Han 等人。 2020年]
Time of Arrival 到达时间	Hong et al. [2020 洪等人。 2020年]
Regional OD Taxi Speed 区域 OD 出租车速度	Hu et al. [2018 胡等人。 2018年]
Ride-hailing Demand 网约车需求	Pian & Wu [2020], Jin et al. [2020b], Li & Axhausen [2020], Jin et al. [2020a], Geng et al. [2019b], Lee et al. [2019], Bai et al. [2019b], Geng et al. [2019a], Bai et al. [2019a], Ke et al. [2021a], Li et al. [2020c Pian & Wu 2020，Jin 等人。 2020b，Li 和 Axhausen 2020，Jin 等人。 2020a，耿等人。 2019b，李等人。 2019，白等人。 2019b，耿等人。 2019a，Bai 等人。 2019a，柯等人。 2021a，Li 等人。 2020c]
Taxi Demand 出租车需求	Lee et al. [2019], Bai et al. [2019b, a], Ke et al. [2021b], Hu et al. [2020], Zheng et al. [2020a], Xu & Li [2019], Davis et al. [2020], Chen et al. [2020h], Du et al. [2020], Li & Moura [2020], Wu et al. [2020a], Ye et al. [2021 李等人。 2019，白等人。 2019b，a，Ke 等人。 2021b，胡等人。 2020，郑等人。 2020a，Xu & Li 2019，Davis 等人。 2020，陈等人。 2020h，杜等人。 2020，Li & Moura 2020，Wu 等人。 2020a，叶等人。 2021年]
Shared Vehicle Demand 共享汽车需求	Luo et al. [2020 罗等人。 2020年]
Bike Demand 自行车需求	Lee et al. [2019], Bai et al. [2019b, a], Du et al. [2020], Ye et al. [2021], Chen et al. [2020b], Wang et al. [2020d], Qin et al. [2020b], Xiao et al. [2020], Yoshida et al. [2019], Guo et al. [2019b], Kim et al. [2019], Lin et al. [2018 Lee 等人 2019b，Du 等人 2021，Chen 等人 2020d，Qin 等人 2020吉田等人 2019，郭等人 2019b，金等人 2018]
Traffic Accident 交通意外	Zhou et al. [2020e], Yu et al. [2020b], Zhang et al. [2020k], Zhou et al. [2020f] 周等人。 2020e，Yu 等人。 2020b，张等人。 2020k，Zhou 等人。 2020年f
Traffic Anomaly 流量异常	Liu et al. [2020c 刘等人。 2020c]
Parking Availability 停车位	Zhang et al. [2020g], Yang et al. [2019], Zhang et al. [2020f 张等人。 2020g，杨等人。 2019，张等人。 2020年f]
Transportation Resilience 运输弹性	Wang et al. [2020c 王等人。 2020c]
Urban Vehicle Emission 城市车辆排放	Xu et al. [2020d 徐等人。 2020d]
Railway Delay 铁路延误	Heglund et al. [2020 赫格伦德等人。 2020年]
Lane Occupancy 车道占用率	Wright et al. [2019 赖特等人。 2019年]

Generally speaking, traffic forecasting problems are challenging, not only for the complex temporal dependency, but only for the complex spatial dependency. While many solutions have been proposed for dealing with the time dependency, e.g., recurrent neural networks and temporal convolutional networks, the problem to capture and model the spatial dependency has not been fully solved. The spatial dependency, which refers to the complex and nonlinear relationship between the traffic state in one particular location with other locations. This location could be a road intersection, a subway station, or a city region. The spatial dependency may not be local, e.g., the traffic state may not only be affected by nearby areas, but also those which are far away in the spatial range but connected by a fast transportation tool. The graphs are necessary to capture such kind of spatial information as we would discuss in the next section.
一般来说，交通预测问题不仅对于复杂的时间依赖性而且对于复杂的空间依赖性都具有挑战性。虽然已经提出了许多解决时间依赖性的解决方案，例如循环神经网络和时间卷积网络，但捕获和建模空间依赖性的问题尚未完全解决。空间依赖性，是指某一特定地点的交通状态与其他地点之间的复杂且非线性的关系。该位置可以是道路交叉口、地铁站或城市区域。空间依赖性可能不是局部的，例如，交通状态可能不仅受到附近区域的影响，而且还受到空间范围较远但通过快速交通工具连接的区域的影响。这些图表对于捕获我们将在下一节中讨论的此类空间信息是必要的。

Before the usage of graph theories and GNNs, the spatial information is usually extracted by multivariate time series models or CNNs. Within a multivariate time series model, e.g., vector autoregression, the traffic states collected in different locations or regions are combined together as multivariate time series. However, the multivariate time series models can only extract the linear relationship among different states, which is not enough for modeling the complex and nonlinear spatial dependency. CNNs take a step further by modeling the local spatial information, e.g., the whole spatial range is divided into regular grids as the two-dimensional image format and the convolution operation is performed in the neighbor grids. However, the CNN-based approach is bounded to the case of Euclidean structure data, which cannot model the topological structure of the subway network or the road network.
在使用图论和 GNN 之前，通常通过多元时间序列模型或 CNN 来提取空间信息。在多元时间序列模型（例如向量自回归）中，在不同位置或区域收集的交通状态被组合在一起作为多元时间序列。然而，多元时间序列模型只能提取不同状态之间的线性关系，不足以对复杂的非线性空间依赖性进行建模。 CNN 更进一步，对局部空间信息进行建模，例如，将整个空间范围划分为规则网格作为二维图像格式，并在相邻网格中执行卷积运算。然而，基于CNN的方法仅限于欧几里得结构数据的情况，无法对地铁网络或道路网络的拓扑结构进行建模。

Graph neural networks bring new opportunities for solving traffic forecasting problems, because of their strong learning ability to capture the spatial information hidden in the non-Euclidean structure data, which are frequently seen in the traffic domain. Based on graph theories, both nodes and edges have their own attributes, which can be used further in the convolution or aggregation operations. These attributes describe different traffic states, e.g., volume, speed, lane numbers, road level, etc. For the dynamic spatial dependency, dynamic graphs can be learned from the data automatically. For the case of hierarchical traffic problems, the concepts of super-graphs and sub-graphs can be defined and further used.
图神经网络具有强大的学习能力，能够捕获交通领域中常见的非欧几里得结构数据中隐藏的空间信息，为解决交通预测问题带来了新的机遇。基于图论，节点和边都有自己的属性，可以在卷积或聚合操作中进一步使用。这些属性描述了不同的交通状态，例如流量、速度、车道数量、道路等级等。对于动态空间依赖性，可以从数据中自动学习动态图。对于分层流量问题的情况，可以定义并进一步使用超图和子图的概念。

3.1 Traffic Flow

Traffic flow is defined as the number of vehicles passing through a spatial unit, such as a road segment or traffic sensor point, in a given time period. An accurate traffic flow prediction is beneficial for a variety of applications, e.g., traffic congestion control, traffic light control, vehicular cloud, etc [Boukerche & Wang, 2020a]. For example, traffic light control can reduce vehicle staying time at the road intersections, optimizing the traffic flow, and reducing traffic congestion and vehicle emission.
交通流量定义为在给定时间段内通过某个空间单元（例如路段或交通传感器点）的车辆数量。准确的交通流预测有利于各种应用，例如交通拥堵控制、交通灯控制、车辆云等[Boukerche & Wang，2020a]。例如，交通灯控制可以减少车辆在道路交叉口的停留时间，优化交通流量，减少交通拥堵和车辆排放。

We consider three levels of traffic flow problems in this survey, namely, road-level flow, region-level flow, and station-level flow.
本次调查考虑三个层面的交通流问题，即道路级流量、区域级流量和车站级流量。

Road-level flow problems are concerned with traffic volumes on a road and include road traffic flow, road origin-destination (OD) Flow, and intersection traffic throughput. In road traffic flow problems, the prediction target is the traffic volume that passes a road sensor or a specific location along the road within a certain time period (e.g. five minutes). In the road OD flow problem, the target is the volume between one location (the origin) and another (the destination) at a single point in time. The intersection traffic throughput problem considers the volume of traffic moving through an intersection.
道路级流量问题与道路上的交通量有关，包括道路交通流量、道路起点-目的地 (OD) 流量和交叉路口交通吞吐量。在道路交通流问题中，预测目标是在一定时间段（例如五分钟）内通过道路传感器或道路沿线特定位置的交通量。在道路 OD 流量问题中，目标是单个时间点一个位置（起点）和另一位置（目的地）之间的流量。交叉口交通吞吐量问题考虑通过交叉口的交通量。

Region-level flow problems consider traffic volume in a region. A city may be divided into regular regions (where the partitioning is grid-based) or irregular regions (e.g. road-based or zip-code-based partitions). These problems are classified by transport mode into regional taxi flow, regional bike flow, regional ride-hailing flow, regional dockless e-scooter flow, regional OD taxi flow, regional OD bike flow, and regional OD ride-hailing flow problems.
区域级流量问题考虑区域内的流量。一个城市可以分为规则区域（基于网格的分区）或不规则区域（例如基于道路或基于邮政编码的分区）。这些问题按交通方式分为区域出租车流量、区域自行车流量、区域网约车流量、区域无桩电动滑板车流量、区域OD出租车流量、区域OD自行车流量和区域OD网约车流量问题。

Station-level flow problems relate to the traffic volume measured at a physical station, for example, a subway or bus station. These problems are divided by station type into station-level subway passenger flow, station-level bus passenger flow, station-level shared vehicle flow, station-level bike flow, and station-level railway passenger flow problems.
车站级流量问题与在物理车站（例如地铁站或公交车站）测量的交通量有关。这些问题按车站类型分为车站级地铁客流、车站级公交客流、车站级共享车流、车站级自行车流和车站级铁路客流问题。

Road-level traffic flow problems are further divided into cases of unidirectional and bidirectional traffic flow, whereas region-level and station-level traffic flow problems are further divided into the cases of inflow and outflow, based on different problem formulations.
根据问题表述的不同，道路级交通流问题进一步分为单向交通流和双向交通流情况，而区域级和车站级交通流问题根据问题表述的不同又进一步分为流入和流出两种情况。

While traffic sensors have been successfully used, data collection for traffic flow information is still a challenge when considering the high costs in deployment and maintenance of traffic sensors. Another potential approach is using the pervasive mobile and IoT devices, which have a lower cost generally, e.g., GPS sensors. However, challenges still exist when considering the data quality problems frequently seen in GPS data, e.g., missing data caused by unstable communication links.
尽管交通传感器已被成功使用，但考虑到交通传感器的部署和维护成本高昂，交通流信息的数据收集仍然是一个挑战。另一种潜在的方法是使用普遍的移动和物联网设备，它们通常成本较低，例如 GPS 传感器。然而，考虑到GPS数据中常见的数据质量问题，例如由于通信链路不稳定导致的数据丢失，挑战仍然存在。

The traffic light is another source of challenges for various traffic prediction tasks. Short-term traffic flow fluctuation and the spatial relation change between two road segments can be caused by the traffic light. The way of controlling the traffic light may be different in different time periods, causing an inconsistent traffic flow pattern.
交通信号灯是各种交通预测任务的另一个挑战来源。交通灯可以引起短期交通流量波动以及两个路段之间的空间关系变化。不同时间段控制交通灯的方式可能不同，导致交通流模式不一致。

3.2 Traffic Speed 3.2交通速度

Traffic speed is another important indicator of traffic state with potential applications in ITS systems, which is defined as the average speed of vehicles passing through a spatial unit in a given time period. The speed value on the urban road can reflect the crowdedness level of road traffic. For example, Google Maps visualizes this crowdedness level from crowd-sourcing data collected from individual mobile devices and in-vehicle sensors. A better traffic speed prediction is also useful for route navigation and estimation-of-arrival applications.
交通速度是智能交通系统中具有潜在应用前景的另一重要交通状态指标，其定义为给定时间段内车辆通过某一空间单元的平均速度。城市道路上的速度值可以反映道路交通的拥挤程度。例如，谷歌地图通过从个人移动设备和车载传感器收集的众包数据来可视化这种拥挤程度。更好的交通速度预测对于路线导航和预计到达应用也很有用。

We consider two levels of traffic speed problems in this survey, namely, road-level and region-level problems. We also include travel time and congestion predictions in this category because they are closely correlated to traffic speed. Travel time prediction is useful for passengers to plan their commuting time and for drivers to select fast routes, respectively. Traffic congestion is one of the most important and urgent transportation problems in cities, which brings significant time loss, air pollution and energy waste. The congestion prediction results can be used to control the road conditions and optimize vehicle flow, e.g., with traffic signal control. In several studies, traffic congestion is judged by a threshold-based speed inference. The specific road-level speed problem categories considered are road traffic speed, road travel time, traffic congestion, and time of arrival problems; while the region-level speed problem considered is regional OD taxi speed.
本次调查我们考虑两个层面的交通速度问题，即道路层面和区域层面的问题。我们还将行程时间和拥堵预测纳入此类别，因为它们与交通速度密切相关。出行时间预测分别有助于乘客规划通勤时间和驾驶员选择快捷路线。交通拥堵是城市最重要、最紧迫的交通问题之一，它带来了巨大的时间损失、空气污染和能源浪费。拥堵预测结果可用于控制道路状况并优化车流，例如通过交通信号控制。在一些研究中，交通拥堵是通过基于阈值的速度推断来判断的。考虑的具体道路级速度问题类别有道路交通速度、道路行驶时间、交通拥堵和到达时间问题；而考虑的区域级速度问题是区域OD出租车速度。

Traffic speed is concerned in both urban roads and freeways. However, the challenges differ in these two different scenarios. Freeways have a few traffic signals or on/off-ramps, making the prediction easier than the urban case. And the challenge mainly comes from the complex temporal dependency. More complex traffic networks exist in urban roads with more complicated connection patterns and abrupt changes. For example, different road segments may have different speed limit values and the allowed vehicle types. Besides the complex temporal dependency, modeling the spatial dependency becomes a bigger challenge for urban traffic speed forecasting.
城市道路和高速公路都关注交通速度。然而，这两种不同场景所面临的挑战有所不同。高速公路有一些交通信号或入口/出口匝道，使得预测比城市情况更容易。挑战主要来自复杂的时间依赖性。城市道路交通网络更加复杂，连接方式更加复杂，变化突变。例如，不同的路段可能具有不同的速度限制值和允许的车辆类型。除了复杂的时间依赖性之外，对空间依赖性进行建模也成为城市交通速度预测的更大挑战。

3.3 Traffic Demand 3.3流量需求

Traffic demand prediction is a key component for taxi and ride-hailing services to be successful, which benefits these service providers to allocate limited available transportation resources to those urban areas with a higher demand. For passengers, traffic demand prediction encourages the consideration of various transportation forms, e.g., taking the public transit service when taxi or ride-hailing services are in short supply.
交通需求预测是出租车和叫车服务成功的关键组成部分，这有利于这些服务提供商将有限的可用交通资源分配给需求较高的城市地区。对于乘客来说，交通需求预测鼓励考虑各种交通方式，例如在出租车或网约车服务短缺时乘坐公共交通服务。

Traffic demand refers to the potential demand for travel, which may or may not be fulfilled completely. For example, on an online ride-hailing platform, the ride requests sent by passengers represent the demand, whereas only a subset of these requests may be served depending on the supply of drivers and vehicles, especially during rush hours. Accurate prediction of travel demand is a key element of vehicle scheduling systems (e.g. online ride-hailing or taxi dispatch platforms). However, in some cases, it is difficult to collect the potential travel demand from passengers and a compromise method using transaction records as an indication of the traffic demand is used. In such cases the real demand may be underestimated. Based on transport mode, the traffic demand problems considered include ride-hailing demand, taxi demand, shared vehicle demand, and bike demand.
交通需求是指潜在的出行需求，可能会也可能不会完全满足。例如，在在线乘车平台上，乘客发送的乘车请求代表了需求，而根据司机和车辆的供应情况，尤其是在高峰时段，可能只能满足这些请求的一部分。准确预测出行需求是车辆调度系统（例如网约车或出租车调度平台）的关键要素。然而，在某些情况下，很难收集乘客的潜在出行需求，因此采用了以交易记录作为交通需求指示的折衷方法。在这种情况下，实际需求可能会被低估。根据交通方式，考虑的交通需求问题包括网约车需求、出租车需求、共享车需求和自行车需求。

3.4 Other Problems 3.4其他问题

In addition to the above three categories of traffic forecasting problems, GNNs are also being applied to the following problems.
除了上述三类流量预测问题外，GNN 还被应用于以下问题。

Traffic accident and Traffic anomaly: the target is to predict the traffic accident number reported to the police system. Traffic anomaly is the major cause of traffic delay and a timely detection and prediction would help the administrators to identify the situation and turn the traffic situation back to normal as quickly as possible. A traffic accident is usually an accident in road traffic involving different vehicles, which may cause significant loss of life and property. The traffic anomaly has a broader definition that deviates from the normal traffic state, e.g., the traffic jam caused by a traffic accident or a public procession.
交通事故和交通异常：目标是预测向警察系统报告的交通事故数量。交通异常是造成交通延误的主要原因，及时的检测和预测有助于管理人员及时发现情况，尽快使交通状况恢复正常。交通事故通常是道路交通中涉及不同车辆的事故，可能造成重大生命和财产损失。交通异常的定义更广泛，偏离正常交通状态，例如交通事故或公众游行造成的交通拥堵。

Parking availability: the target is to predict the availability of vacant parking space for cars in the streets or in a car parking lot.
停车位可用性：目标是预测街道或停车场的空置停车位的可用性。

Urban vehicle emission: while not directly related to traffic states, the prediction of urban vehicle emission is considered in Xu et al. [2020d]. Urban vehicle emission refers to the emission produced by motor vehicles, e.g., those use internal combustion engines. Urban vehicle emission is a major source of air pollutants and its amount is affected by different traffic states, e.g., the excess emission would be created in traffic congestion situations.
城市车辆排放：虽然与交通状况没有直接关系，但 Xu 等人考虑了城市车辆排放的预测。 [2020d]。城市车辆排放是指机动车辆（例如使用内燃机的车辆）产生的排放。城市车辆排放是空气污染物的主要来源，其排放量受不同交通状态的影响，例如在交通拥堵的情况下会产生超标排放。

Railway delay: the delay time of specific routes in the railway system is considered in Heglund et al. [2020].
铁路延误：Heglund等人考虑了铁路系统中特定路线的延误时间。 [2020]。

Lane occupancy: With simulated traffic data, lane occupancy has been measured and predicted [Wright et al., 2019].
车道占用率：通过模拟交通数据，测量并预测了车道占用率 [Wright et al., 2019]。

4 Graphs and Graph Neural Networks
4图和图神经网络

In this section, we summarize the types of graphs and GNNs used in the surveyed studies, focusing on GNNs that are frequently used for traffic forecasting problems. The contributions of this section include an organized approach for classifying the different traffic graphs based on the domain knowledge, and a summary of the common ways for constructing adjacency matrices, which may not be encountered in other neural networks before and would be very helpful for those who would like to use graph neural networks. The different GNN structures already used for traffic forecasting problems are briefly introduced in this section too. For a wider and deeper discussion of GNNs, refer to Wu et al. [2020b], Zhou et al. [2020c], Zhang et al. [2020m].
在本节中，我们总结了调查研究中使用的图和 GNN 的类型，重点关注经常用于流量预测问题的 GNN。本节的贡献包括一种基于领域知识对不同流量图进行分类的有组织的方法，以及构建邻接矩阵的常用方法的总结，这些方法以前在其他神经网络中可能不会遇到，对于那些人来说非常有帮助谁想使用图神经网络。本节还简要介绍了已用于流量预测问题的不同 GNN 结构。有关 GNN 的更广泛、更深入的讨论，请参阅 Wu 等人。 [2020b]，Zhou 等人。 [2020c]，Zhang 等人。 [2020米]。

4.1 Traffic Graphs 4.1流量图

4.1.1 Graph Construction 4.1.1图的构建

A graph is the basic structure used in GNNs. It is defined as $G=(V,E,A)$ , where $V$ is the set of vertices or nodes, $E$ is the set of edges between the nodes, and $A$ is the adjacency matrix. Both nodes and edges can be associated with different attributes in different GNN problems. Element $a_{ij}$ of $A$ represents the “edge weight” between nodes $i$ and $j$ . For a binary connection matrix $A$ , $a_{ij}=1$ if there is an edge between nodes $i$ and $j$ in $E$ , and $a_{ij}=0$ otherwise. If $A$ is symmetric, the corresponding graph $G$ is defined as undirected. Otherwise, $G$ is directed, when the edge only exists in one direction between a node pair.
图是 GNN 中使用的基本结构。它定义为 $G=(V,E,A)$ ，其中 $V$ 是顶点或节点的集合， $E$ 是节点之间的边的集合， $A$ 的元素 $a_{ij}$ 表示节点 $i$ 和 $j$ 之间的“边权重”。对于二元连接矩阵 $A$ 、 $a_{ij}=1$ 如果 $E$ 中的节点 $i$ 和 $j$ 之间存在边，否则 $a_{ij}=0$ 。如果 $A$ 是对称的，则对应的图 $G$ 被定义为无向。否则，当边仅存在于节点对之间的一个方向上时， $G$ 是有向的。

For simplicity, we assume that the traffic state is associated with the nodes. The other case with edges can be derived similarly. In practice, the traffic state is collected or aggregated in discrete time steps, e.g. five minutes or one hour, depending on the specific scenario.
为了简单起见，我们假设流量状态与节点相关联。其他有边缘的情况也可以类似推导。在实践中，交通状态是在离散的时间步长中收集或聚合的，例如五分钟或一小时，根据具体情况而定。

For a single time step $t$ , we denote the node feature matrix as $\chi_{t}\in{R}^{N\times d}$ , where $N$ is the number of nodes and $d$ is the dimension of the node features, i.e., the number of traffic state variables. Now we are ready to give a formal definition of traffic graph.
对于单个时间步 $t$ ，我们将节点特征矩阵表示为 $\chi_{t}\in{R}^{N\times d}$ ，其中 $N$ 是节点数， $d$ 是节点特征的维度，即交通状态变量的数量。现在我们准备给出流量图的正式定义。

Definition 4.1 (Traffic Graph).

A traffic graph (with node features) is defined as a specific type of graph $G=(V,E,A)$ , where $V$ is the node set, $E$ is the edge set, and $A$ is the adjacency matrix. For a single time step $t$ , the node feature matrix $\chi_{t}\in{R}^{N\times d}$ for $G$ contains specific traffic states, where $N$ is the number of nodes and $d$ is the number of traffic state variables.

定义 4.1（流量图）。流量图（具有节点特征）被定义为特定类型的图

G=(V,E,A)

，其中

V

是节点集，

E

是边集，

A

是邻接矩阵。对于单个时间步

t

，

G

的节点特征矩阵

\chi_{t}\in{R}^{N\times d}

包含特定的流量状态，其中

N

是节点数量

d

是交通状态变量的数量。

Then we give a formal definition of graph-based traffic forecasting problem without leveraging external factors firstly.
然后我们在不首先利用外部因素的情况下给出基于图的流量预测问题的正式定义。

Definition 4.2 (Graph-based Traffic Forecasting).

A graph-based traffic forecasting (without external factors) is defined as follows: find a function $f$ which generates $y=f(\mathbf{\chi};G)$ , where $y$ is the traffic state to be predicted, $\mathbf{\chi}=\{\chi_{1},\chi_{2},...,\chi_{T}\}$ is the historical traffic state defined on graph $G$ , and $T$ is the number of time steps in the historical window size.

定义 4.2（基于图的流量预测）。基于图的流量预测（没有外部因素）定义如下：找到一个生成

y=f(\mathbf{\chi};G)

的函数

f

，其中

y

是要预测的流量状态预测，

\mathbf{\chi}=\{\chi_{1},\chi_{2},...,\chi_{T}\}

是图

G

上定义的历史流量状态，

T

是历史窗口大小中的时间步数。

In single step forecasting, the traffic state in the next time step only is predicted, whereas in multiple step forecasting the traffic state several time steps later is the prediction target. As mentioned in Section 1, traffic states can be highly affected by external factors, e.g. weather and holidays. The forecasting problem formulation, extended to incorporate these external factors, takes the form $y=f(\mathbf{\chi},\varepsilon;G)$ , where $\varepsilon$ represents the external factors. Figure 1 demonstrates the graph-based traffic forecasting problem, where different color patches represent different traffic variables.
在单步预测中，仅预测下一个时间步的交通状态，而在多步预测中，将几个时间步之后的交通状态作为预测目标。正如第 1 节中提到的，交通状态可能会受到外部因素的很大影响，例如。天气和假期。预测问题公式扩展为包含这些外部因素，采用 $y=f(\mathbf{\chi},\varepsilon;G)$ 形式，其中 $\varepsilon$ 代表外部因素。图 1 演示了基于图的流量预测问题，其中不同的色块代表不同的流量变量。

Refer to caption — Figure 1: The single-step graph-based traffic forecasting problem. Adapted from Ye et al. [2020a] with external factors added.
图 1：基于图的单步流量预测问题。改编自 Ye 等人。 [2020a] 添加了外部因素。

Various graph structures are used to model traffic forecasting problems depending on both the forecasting problem-type and the traffic datasets available. These graphs can be pre-defined static graphs, or dynamic graphs continuously learned from the data. The static graphs can be divided into two types, namely, natural graphs and similarity graphs. Natural graphs are based on a real-world transportation system, e.g. the road network or subway system; whereas similarity graphs are based solely on the similarity between different node attributes where nodes may be virtual stations or regions.
根据预测问题类型和可用的交通数据集，使用各种图结构对交通预测问题进行建模。这些图可以是预先定义的静态图，也可以是从数据中不断学习的动态图。静态图可以分为两类，即自然图和相似图。自然图基于现实世界的交通系统，例如道路网络或地铁系统；而相似性图仅基于不同节点属性之间的相似性，其中节点可以是虚拟站或区域。

We categorize the existing traffic graphs into the same three levels used in Section 3, namely, road-level, region-level and station-level graphs.
我们将现有的交通图分类为与第 3 节中使用的相同的三个级别，即道路级、区域级和车站级图。

Road-level graphs. These include sensor graphs, road segment graphs, road intersection graphs, and road lane graphs. Sensor graphs are based on traffic sensor data (e.g. the PeMS dataset) where each sensor is a node, and the edges are road connections. The other three graphs are based on road networks with the nodes formed by road segments, road intersections, and road lanes, respectively. The real-world case and example of road-level graphs are shown in Figure 2. In some cases, road-level graphs are the most suitable format, e.g., when vehicles can move only through pre-defined roads.
道路级别的图表。其中包括传感器图、路段图、道路交叉口图和道路车道图。传感器图基于交通传感器数据（例如 PeMS 数据集），其中每个传感器是一个节点，边缘是道路连接。其他三个图基于道路网络，其节点分别由路段、道路交叉口和道路车道形成。现实世界的情况和道路级别图的示例如图 2 所示。在某些情况下，道路级别图是最合适的格式，例如，当车辆只能通过预定义的道路移动时。

Region-level graphs. These include irregular region graphs, regular region graphs, and OD graphs. In both irregular and regular region graphs the nodes are regions of the city. Regular region graphs, which have grid-based partitioning, are listed separately because of their natural connection to previous widely used grid-based forecasting using CNNs, in which the grids may be seen as image pixels. Irregular region graphs include all other partitioning approaches, e.g. road based, or zip code based Ke et al. [2021b]. In the OD graph, the nodes are origin region - destination region pairs. In these graphs, the edges are usually defined with a spatial neighborhood or other similarities, e.g., functional similarity derived from point-of-interests (PoI) data. The real-world case and example of region-level graphs are shown in Figure 3.
区域级图表。其中包括不规则区域图、规则区域图和 OD 图。在不规则区域图中和规则区域图中，节点都是城市的区域。具有基于网格划分的常规区域图被单独列出，因为它们与之前广泛使用的使用 CNN 的基于网格的预测有天然的联系，其中网格可以被视为图像像素。不规则区域图包括所有其他划分方法，例如基于道路，或基于邮政编码 Ke 等人。 [2021b]。在OD图中，节点是起始区域-目的地区域对。在这些图中，边缘通常用空间邻域或其他相似性来定义，例如从兴趣点 (PoI) 数据导出的功能相似性。实际案例和区域级图示例如图 3 所示。

Station-level graphs. These include subway station graphs, bus station graphs, bike station graphs, railway station graphs, car-sharing station graphs, parking lot graphs, and parking block graphs. Usually, there are natural links between stations that are used to define the edges, e.g. subway or railway lines, or the road network. The real-world case and example of station-level graphs are shown in Figure 4.
站级图表。其中包括地铁站图、公交车站图、自行车站图、火车站图、汽车共享站图、停车场图和停车场图。通常，用于定义边缘的站点之间存在自然链接，例如地铁或铁路线，或公路网。实际情况和站级图示例如图 4 所示。

A full list of the traffic graphs used in the surveyed studies is shown in Table 2. Sensor graphs and road segment graphs are most frequently used because they are compatible with the available public datasets as discussed in Section 5. It is noted that in some studies multiple graphs are used as simultaneous inputs and then fused to improve the forecasting performance [Lv et al., 2020, Zhu et al., 2019].

Table 2: Traffic graphs in the surveyed studies.

Graph	Node	Edge	Relevant Studies
Sensor Graph	Traffic Sensors	Road Links	Li et al. [2018b], Wu et al. [2019], Xu et al. [2020a], Zheng et al. [2020b], Pan et al. [2020, 2019], Lu et al. [2019a], Mallick et al. [2020], Zhang et al. [2020j], Bai et al. [2020], Huang et al. [2020a], Zhang et al. [2020e], Song et al. [2020a], Xu et al. [2020b], Wang et al. [2020g], Chen et al. [2020e], Lv et al. [2020], Kong et al. [2020], Fukuda et al. [2020], Zhang & Guo [2020], Boukerche & Wang [2020b], Tang et al. [2020b], Kang et al. [2019], Guo et al. [2019c], Li et al. [2019b], Sun et al. [2020], Wei & Sheng [2020], Li et al. [2020f], Cao et al. [2020], Yu et al. [2018, 2019b], Li et al. [2020b], Yin et al. [2020], Chen et al. [2020g], Zhang et al. [2020a], Wang et al. [2020a], Xin et al. [2020], Xie et al. [2020d], Huang et al. [2020b], Li & Zhu [2021], Tian et al. [2020], Xu et al. [2020c], Chen et al. [2020c], Xiong et al. [2020], Chen et al. [2020d], Tang et al. [2020a], Zhang et al. [2018a, 2019a], Cirstea et al. [2019], Ge et al. [2019a, b], Shleifer et al. [2019], Ge et al. [2020], Yang et al. [2020], Zhao et al. [2019], Cui et al. [2019], Chen et al. [2019], Yu et al. [2019a], Wang et al. [2020f], Cui et al. [2020b, a], Zhou et al. [2020a], Cai et al. [2020], Zhou et al. [2020b], Wu et al. [2020c], Chen et al. [2020f], Opolka et al. [2019], Mallick et al. [2021], Oreshkin et al. [2021], Jia et al. [2020], Sun et al. [2021], Guo & Yuan [2020], Zhang et al. [2020i], Feng et al. [2020], Xie et al. [2020c], Park et al. [2020], Chen et al. [2020a], Lewenfus et al. [2020], Maas & Bloem [2020], Li et al. [2020d], Song et al. [2020b], Zhao et al. [2020b], Wang et al. [2020c 李等人。 2018b，吴等人。 2019，徐等人。 2020a，郑等人。 2020b，潘等人。 2020、2019，Lu 等人。 2019a，Mallick 等人。 2020，张等人。 2020j，白等人。 2020，黄等人。 2020a，张等人。 2020e，宋等人。 2020a，Xu 等人。 2020b，王等人。 2020g，陈等人。 2020e，Lv 等人。 2020，孔等人。 2020，福田等人。 2020，Zhang 和Guo 2020，Boukerche 和Wang 2020b，Tang 等人。 2020b，康等人。 2019，郭等人。 2019c，Li 等人。 2019b，Sun 等人。 2020，Wei & Shen 2020，Li 等人。 2020f，曹等人。 2020，Yu 等人。 2018、2019b，Li 等人。 2020b，尹等人。 2020，陈等人。 2020g，张等人。 2020a，王等人。 2020a，Xin 等人。 2020，谢等人。 2020d，黄等人。 2020b，Li & Zhu 2021，Tian 等人。 2020，徐等人。 2020c，陈等人。 2020c，Xiong 等人。 2020，陈等人。 2020d，唐等人。 2020a，张等人。 2018a、2019a，Cirstea 等人。 2019，葛等人。 2019a、b，Shleifer 等人。 2019，葛等人。 2020，杨等人。 2020，赵等人。 2019，崔等人。 2019，陈等人。 2019，Yu 等人。 2019a，王等人。 2020f，崔等人。 2020b，a，Zhou 等人。 2020a，蔡等人。 2020，Zhou 等人。 2020b，吴等人。 2020c，陈等人。 2020f，Opolka 等人。 2019，马利克等人。 2021，奥列什金等人。 2021，贾等人。 2020，孙等人。 2021，Guo & Yuan 2020，Zhang 等人。 2020i，冯等人。 2020，谢等人。 2020c，Park 等人。 2020，陈等人。 2020a，Lewenfus 等人。 2020，Maas 和 Bloem 2020，Li 等人。 2020d，宋等人。 2020b，赵等人。 2020b，王等人。 2020c]
Road Segment Graph 路段图	Road Segments 路段	Road Intersections 道路交叉口	Zhang et al. [2018b], Guo et al. [2020a], Pan et al. [2019], Zhang et al. [2020j, l], Wang et al. [2018b], Zhang et al. [2020e], Lv et al. [2020], Zhang et al. [2019d, 2020a], Qu et al. [2020], Guo et al. [2020b], Ramadan et al. [2020], Zhao et al. [2020a], Bai et al. [2021], Shin & Yoon [2020], Liu et al. [2020a], Yu & Gu [2019], Xie et al. [2019], Guo et al. [2019a], Diao et al. [2019], Lu et al. [2019b], Zhang et al. [2019c], James [2019], Zhang et al. [2019b], Lee & Rhee [2022], Yu et al. [2020a], Lu et al. [2020b], Zhao et al. [2019], Cui et al. [2019], Zhang et al. [2019e], Lee & Rhee [2019], Cui et al. [2020b, a], Guo et al. [2020c], Xie et al. [2020b], Zhu et al. [2021, 2020], Fu et al. [2020], Zhang et al. [2020d], Agafonov [2020], Lu et al. [2020a], Jepsen et al. [2019, 2020], Zhu et al. [2022], Liao et al. [2018], Guopeng et al. [2020], Kim et al. [2020], Hasanzadeh et al. [2019], Fang et al. [2020b], Dai et al. [2020], Han et al. [2020], Hong et al. [2020], Chen et al. [2020h], Yu et al. [2020b 张等人 2018b，郭等人 2019，张等人 2020e，张等人 2019d，2020a ，Qu 等人 2020，Ramadan 等人 2020，Bai 等人 2020，Liu 等人 2020a，Xie 等人。 2019，Guo 等人 2019a，Lu 等人 2019b，Zhang 等人 2019b，Lee 等人 2020a，Lu 等人 2020b ，Zhao 等人 2019，Zhang 等人 2019e，Cui 等人 2020b，Guo 等人 2020b，Zhu 等人 2021。 2020，Zhang 等人 2020d，Lu 等人 2020a，Jepsen 等人 2022，Liao 等人 2018，Kim 等人。等人 2020，Fang 等人 2020，Han 等人 2020，Yu 等人 2020b]
Road Intersection Graph 道路交叉口图	Road Intersections 道路交叉口	Road Segments 路段	Zhang et al. [2018b], Wei et al. [2019], Fang et al. [2019], Zhang et al. [2020e], Xu et al. [2019], Wu et al. [2018a], Sánchez et al. [2020], James [2020], Zhang et al. [2019f], Lu et al. [2019b], Zhang et al. [2019c], Bogaerts et al. [2020], Shao et al. [2020], Qin et al. [2020a 张等人。 2018b，Wei 等人。 2019，方等人。 2019，张等人。 2020e，徐等人。 2019，吴等人。 2018a，桑切斯等人。 2020，詹姆斯 2020，张等人。 2019f，Lu 等人。 2019b，Zhang 等人。 2019c，Bogaerts 等人。 2020，Shao 等人。 2020，秦等人。 2020年a]
Road Lane Graph 道路车道图	Road Lanes 道路车道	Road Line Adjacency 道路线邻接	Wright et al. [2019 赖特等人。 2019年]
Irregular Region Graph 不规则区域图	Irregular Regions 不规则区域	Regional Adjacency or Virtual Edges 区域邻接或虚拟边缘	Zhou et al. [2020d], Sun et al. [2020], Chen et al. [2020d], Bing et al. [2020], Mohanty & Pozdnukhov [2018], Mohanty et al. [2020], Hu et al. [2018], Li & Axhausen [2020], Bai et al. [2019b, a], Ke et al. [2021a], Hu et al. [2020], Zheng et al. [2020a], Davis et al. [2020], Du et al. [2020], Li & Moura [2020], Ye et al. [2021], Zhang et al. [2020k], Liu et al. [2020c 周等人。 2020d，Sun 等人。 2020，陈等人。 2020d，Bing 等人。 2020，Mohanty 和 Pozdnukhov 2018，Mohanty 等人。 2020，胡等人。 2018，Li & Axhausen 2020，Bai 等人。 2019b，a，Ke 等人。 2021a，胡等人。 2020，郑等人。 2020a，戴维斯等人。 2020，杜等人。 2020，Li & Moura 2020，Ye 等人。 2021，张等人。 2020k，刘等人。 2020年c]
Regular Region Graph 正则区域图	Regular Regions 常规地区	Regional Adjacency or Virtual Edges 区域邻接或虚拟边缘	Pan et al. [2020], Wang et al. [2020b], Zhang et al. [2020h], Wang et al. [2018a], Zhou et al. [2019], Wang et al. [2020e], Qiu et al. [2020], He & Shin [2020a], Yeghikyan et al. [2020], Shi et al. [2020], Wang et al. [2019], Shen et al. [2020], Pian & Wu [2020], Jin et al. [2020b, a], Geng et al. [2019b], Lee et al. [2019], Geng et al. [2019a], Li et al. [2020c], Xu & Li [2019], Davis et al. [2020], Wu et al. [2020a], Zhou et al. [2020e, f], Xu et al. [2020d 潘等人。 2020，王等人。 2020b，张等人。 2020h，王等人。 2018a，Zhou 等人。 2019，王等人。 2020e，Qiu 等人。 2020，He & Shin 2020a，Yeghikyan 等人。 2020，Shi 等人。 2020，王等人。 2019，沉等人。 2020，Pian & Wu 2020，Jin 等人。 2020b，a，耿等人。 2019b，李等人。 2019，耿等人。 2019a，Li 等人。 2020c，Xu & Li 2019，Davis 等人。 2020，吴等人。 2020a，Zhou 等人。 2020e, f, Xu 等人。 2020d]
OD Graph OD图	OD Pair 外径对	Virtual Edges 虚拟边缘	Wang et al. [2020h], Ke et al. [2021b 王等人。 2020h，Ke 等人。 2021b]
Subway Station Graph 地铁站图	Subway Stations 地铁站	Subway Lines 地铁线路	Fang et al. [2019, 2020a], Ren & Xie [2019], Li et al. [2018a], Zhao et al. [2020a], Han et al. [2019], Zhang et al. [2020b, c], Li et al. [2020e], Liu et al. [2020b], Ye et al. [2020b], Ou et al. [2020 方等人。 2019, 2020a，Ren & Xie 2019，Li 等人。 2018a，赵等人。 2020a，Han 等人。 2019，张等人。 2020b，c，Li 等人。 2020e，刘等人。 2020b，叶等人。 2020b，Ou 等人。 2020年]
Bus Station Graph 公交车站图	Bus Stations 巴士站	Bus Lines 公交线路	Fang et al. [2019, 2020a 方等人。 2019, 2020a]
Bike Station Graph 自行车站图	Bike Stations 自行车站	Road Links 道路链接	He & Shin [2020b], Chai et al. [2018], Du et al. [2020], Chen et al. [2020b], Wang et al. [2020d], Qin et al. [2020b], Xiao et al. [2020], Yoshida et al. [2019], Guo et al. [2019b], Kim et al. [2019], Lin et al. [2018 He & Shin 2020b，Chai 等人。 2018，杜等人。 2020，陈等人。 2020b，王等人。 2020d，Qin 等人。 2020b，肖等人。 2020，吉田等人。 2019，郭等人。 2019b，Kim 等人。 2019，林等人。 2018年]
Railway Station Graph 火车站图	Railway Stations 火车站	Railway Lines 铁路线	He et al. [2020], Heglund et al. [2020 他等人。 2020，赫格伦德等人。 2020年]
Car-sharing Station Graph 共享汽车站图	Car-sharing Stations 汽车共享站	Road Links 道路链接	Zhu et al. [2019], Luo et al. [2020 朱等人。 2019，罗等人。 2020年]
Parking Lot Graph 停车场图	Parking Lots 停车场	Road Links 道路链接	Zhang et al. [2020g, f 张等人。 2020克，f]
Parking Block Graph 停车位图	Parking Blocks 停车位	Road Links 道路链接	Yang et al. [2019 杨等人。 2019年]

4.1.2 Adjacency Matrix Construction
4.1.2邻接矩阵构造

Adjacency matrices are seen as the key to capturing spatial dependency in traffic forecasting [Ye et al., 2020a]. While nodes may be fixed by physical constraints, the user typically has control over the design of the adjacency matrix, which can even be dynamically trained from continuously evolving data. We extend the categories of adjacency matrices used in previous studies [Ye et al., 2020a] and divide them into four types, namely, road-based, distance-based, similarity-based, and dynamic matrices.
邻接矩阵被视为捕获流量预测中空间依赖性的关键 [Ye et al., 2020a]。虽然节点可能受到物理约束的固定，但用户通常可以控制邻接矩阵的设计，甚至可以根据不断发展的数据进行动态训练。我们扩展了之前研究中使用的邻接矩阵的类别[Ye et al., 2020a]，并将其分为四种类型，即基于道路的矩阵、基于距离的矩阵、基于相似性的矩阵和动态矩阵。

Road-based Matrix. This type of adjacency matrix relates to the road network and includes connection matrices, transportation connectivity matrices, and direction matrices. A connection matrix is a common way of representing the connectivity between nodes. It has a binary format, with an element value of 1 if connected and 0 otherwise. The transportation connectivity matrix is used where two regions are geographically distant but conveniently reachable by motorway, highway, or subway [Ye et al., 2020a]. It also includes cases where the connection is measured by travel time between different nodes, e.g. if a vehicle can travel between two intersections in less than 5 minutes then there is an edge between the two intersections [Wu et al., 2018a]. The less commonly used direction matrix takes the angle between road links into consideration.
基于道路的矩阵。此类邻接矩阵与道路网络相关，包括连接矩阵、交通连通性矩阵和方向矩阵。连接矩阵是表示节点之间连接性的常用方法。它具有二进制格式，如果已连接，则元素值为 1，否则为 0。交通连通性矩阵适用于地理上相距较远但可通过高速公路、高速公路或地铁方便到达的两个区域 [Ye et al., 2020a]。它还包括通过不同节点之间的旅行时间来衡量连接的情况，例如如果车辆可以在 5 分钟内在两个十字路口之间行驶，则两个十字路口之间存在边缘 [Wu et al., 2018a]。不太常用的方向矩阵考虑了道路连接之间的角度。

Distance-based Matrix. This widely used matrix-type represents the spatial closeness between nodes. It contains two sub-types, namely, neighbor and distance matrices. In neighbor matrices, the element values are determined by whether the two regions share a common boundary (if connected the value is set to 1, generally, or 1/4 for grids, and 0 otherwise). In distance-based matrices, the element values are a function of geometrical distance between nodes. This distance may be calculated in various ways, e.g. the driving distance between two sensors, the shortest path length along the road [Kang et al., 2019, Lee & Rhee, 2022], or the proximity between locations calculated by the random walk with restart (RWR) algorithm [Zhang et al., 2019e]. One flaw of distance-based matrices is that the fail to take into account the similarity of traffic states between long-distance nodes, and the constructed adjacency matrix is static in most cases.
基于距离的矩阵。这种广泛使用的矩阵类型表示节点之间的空间接近度。它包含两个子类型，即邻居矩阵和距离矩阵。在邻域矩阵中，元素值由两个区域是否共享公共边界来确定（如果连接，则该值通常设置为 1，对于网格，则设置为 1/4，否则设置为 0）。在基于距离的矩阵中，元素值是节点之间几何距离的函数。该距离可以通过多种方式计算，例如两个传感器之间的行驶距离、沿路的最短路径长度 [Kang et al., 2019, Lee & Rhee, 2022]，或通过重新启动随机游走 (RWR) 算法计算的位置之间的接近度 [Zhang et al., 2019, Lee & Rhee, 2022]。，2019e]。基于距离的矩阵的一个缺陷是没有考虑远距离节点之间交通状态的相似性，并且构造的邻接矩阵在大多数情况下是静态的。

Similarity-based Matrix. This type of matrix is divided into two sub-types, namely, traffic pattern and functional similarity matrices. Traffic pattern similarity matrices represent the correlations between traffic states, e.g. similarities of flow patterns, mutual dependencies between different locations, and traffic demand correlation in different regions. Functional similarity matrices represent, for example, the distribution of different types of PoIs in different regions.
基于相似性的矩阵。此类矩阵分为两个子类型，即流量模式矩阵和功能相似性矩阵。交通模式相似度矩阵表示交通状态之间的相关性，例如流量模式的相似性、不同地点之间的相互依赖关系以及不同区域的交通需求相关性。例如，功能相似性矩阵表示不同类型的 PoI 在不同区域的分布。

Dynamic Matrix. This type of matrix is used when no pre-defined static matrices are used. Many studies have demonstrated the advantages of using dynamic matrices, instead of a pre-defined adjacency matrix, for various traffic forecasting problems.
动态矩阵。当没有使用预定义的静态矩阵时，使用这种类型的矩阵。许多研究已经证明，对于各种交通预测问题，使用动态矩阵而不是预定义的邻接矩阵具有优势。

A full list of the adjacency matrices applied in the surveyed studies is shown in Table 3. Dynamic matrices are listed at the bottom of the table, with no further subdivisions. The connection and distance matrices are the most frequently used types, because of their simple definition and representation of spatial dependency.
表 3 显示了调查研究中应用的邻接矩阵的完整列表。动态矩阵列在表底部，没有进一步细分。连接矩阵和距离矩阵是最常用的类型，因为它们的定义和空间依赖性的表示很简单。

Table 3: Adjacency matrices in the surveyed studies.
表 3：调查研究中的邻接矩阵。

Adjacency Matrix 邻接矩阵	Formula	Relevant Studies 相关研究
Connection Matrix 连接矩阵	$a_{ij}=1$ when nodes $i$ and $j$ are connected and $a_{ij}=0$ otherwise $a_{ij}=1$ 当节点 $i$ 和 $j$ 连接时， $a_{ij}=0$ 否则	Zhang et al. [2018b], Wei et al. [2019], Xu et al. [2020a], Guo et al. [2020a], Zhang et al. [2020l], Wang et al. [2018b], Song et al. [2020a], Zhang & Guo [2020], Xu et al. [2019], Cao et al. [2020], Yu et al. [2019b], Chen et al. [2020g], Zhang et al. [2020a], Qu et al. [2020], Wang et al. [2020b], Huang et al. [2020b], Xiong et al. [2020], Sánchez et al. [2020], Wang et al. [2020h], Zhang et al. [2020c], Li et al. [2020e], Liu et al. [2020b], Ou et al. [2020], He et al. [2020], Bai et al. [2021], Liu et al. [2020a], Zhang et al. [2019f], Yu & Gu [2019], Xie et al. [2019], Guo et al. [2019a], Lu et al. [2019b], Zhang et al. [2019c], James [2019], Zhang et al. [2019b], Zhao et al. [2019], Cui et al. [2019, 2020b, 2020a], Wu et al. [2020c], Opolka et al. [2019], Sun et al. [2021], Guo & Yuan [2020], Xie et al. [2020b], Zhu et al. [2021, 2020], Zhang et al. [2020d], Agafonov [2020], Chen et al. [2020a], Lu et al. [2020a], Bing et al. [2020], Zhu et al. [2022], Fang et al. [2020b], Shao et al. [2020], Shen et al. [2020], Qin et al. [2020a], Hong et al. [2020], Xu & Li [2019], Davis et al. [2020], Chen et al. [2020h], Wang et al. [2020d], Zhou et al. [2020e], Yu et al. [2020b], Liu et al. [2020c], Zhang et al. [2020g, f], Heglund et al. [2020], Yin et al. [2020], Zhang et al. [2020b 张等人 2018b，徐等人 2020a，张等人 2020l，宋等人 2020a，徐等人。 . 2019，Yu 等人 2020g，Zhang 等人 2020b，Huang 等人 2020 ，Sánchez 等人 2020，Zhang 等人 2020e，Liu 等人 2020，He 等人 2021，Liu 等人 2020。等人 2020a，张等人 2019，Xie 等人 2019a，Lu 等人 2019c，James 2019，Zhang 等人 2019等人 2019，Cui 等人 2020c，Opolka 等人 2021，Guo 等人 2020，Zhu 等人 2021 2020，Agafonov 2020a，Lu 等人 2020，Zhu 等人 2022，Shao 等人 2020 2020，Qin 等人 2020a，Xu 等人 2020，Chen 等人 2020d，Zhou 等人 2020b，Liu 等人 2020。等人 2020c，张等人 2020g，赫格伦德等人 2020，张等人 2020b]
Transportation Connectivity Matrix 交通连接矩阵	$a_{ij}=1$ when one can travel from node $i$ to node $j$ and $a_{ij}=0$ otherwise $a_{ij}=1$ 当可以从节点 $i$ 移动到节点 $j$ 时，否则为 $a_{ij}=0$	Pan et al. [2020, 2019], Lv et al. [2020], Wu et al. [2018a], Ye et al. [2020b], Geng et al. [2019b, a], Luo et al. [2020], Wright et al. [2019 潘等人。 2020、2019，Lv 等人。 2020，吴等人。 2018a，叶等人。 2020b，耿等人。 2019b，a，罗等人。 2020，赖特等人。 2019年]
Direction Matrix 方向矩阵	$a_{ij}=$ the angle between two road segments $a_{ij}=$ 两条路段之间的角度	Shin & Yoon [2020], Lee & Rhee [2022, 2019 申&尹 2020, 李&李 2022, 2019]
Neighbor Matrix 邻域矩阵	$a_{ij}=1$ when nodes $i$ and $j$ are neighbors and $a_{ij}=0$ otherwise $a_{ij}=1$ 当节点 $i$ 和 $j$ 是邻居时， $a_{ij}=0$ 否则	Wang et al. [2018a], Yeghikyan et al. [2020], Shi et al. [2020], Wang et al. [2019], Hu et al. [2018], Geng et al. [2019b], Lee et al. [2019], Ke et al. [2021a, b], Hu et al. [2020], Zheng et al. [2020a], Yoshida et al. [2019 王等人。 2018a，Yeghikyan 等人。 2020，Shi 等人。 2020，王等人。 2019，胡等人。 2018，耿等人。 2019b，李等人。 2019，柯等人。 2021a，b，胡等人。 2020，郑等人。 2020a，吉田等人。 2019年]
Distance Matrix 距离矩阵	$a_{ij}=d_{ij}$ and $d_{ij}$ is some distance between nodes $i$ and $j$ $a_{ij}=d_{ij}$ 和 $d_{ij}$ 是节点 $i$ 和 $j$ 之间的一定距离	Li et al. [2018b], Zheng et al. [2020b], Pan et al. [2020, 2019], Lu et al. [2019a], Mallick et al. [2020], Huang et al. [2020a], Xu et al. [2020b], Wang et al. [2020g], Boukerche & Wang [2020b], Kang et al. [2019], Sun et al. [2020], Wei & Sheng [2020], Yu et al. [2018], Li et al. [2020b], Chen et al. [2020g], Wang et al. [2020a], Xin et al. [2020], Xie et al. [2020d], Li & Zhu [2021], Tian et al. [2020], Xu et al. [2020c], Chen et al. [2020c], Zhou et al. [2020d], Chen et al. [2020d], He & Shin [2020a], Ren & Xie [2019], Zhu et al. [2019], He & Shin [2020b], Chai et al. [2018], Shin & Yoon [2020], Zhang et al. [2018a], Ge et al. [2019a, b], Lee & Rhee [2022], Shleifer et al. [2019], Ge et al. [2020], Yang et al. [2020], Chen et al. [2019], Zhang et al. [2019e], Lee & Rhee [2019], Bogaerts et al. [2020], Wang et al. [2020f], Guo et al. [2020c], Zhou et al. [2020a], Cai et al. [2020], Zhou et al. [2020b], Chen et al. [2020f], Mallick et al. [2021], Jia et al. [2020], Zhang et al. [2020i], Feng et al. [2020], Xie et al. [2020c], Li et al. [2020d], Song et al. [2020b], Zhao et al. [2020b], Kim et al. [2020], Mohanty & Pozdnukhov [2018], Mohanty et al. [2020], Jin et al. [2020b], Li & Axhausen [2020], Jin et al. [2020a], Geng et al. [2019a], Ke et al. [2021a], Li et al. [2020c], Ke et al. [2021b], Luo et al. [2020], Chen et al. [2020b], Xiao et al. [2020], Guo et al. [2019b], Kim et al. [2019], Lin et al. [2018], Yang et al. [2019], Wang et al. [2020c], Xu et al. [2020d 李等人。 2018b，郑等人。 2020b，潘等人。 2020、2019，Lu 等人。 2019a，Mallick 等人。 2020，黄等人。 2020a，Xu 等人。 2020b，王等人。 2020g，Boukerche & Wang 2020b，Kang 等人。 2019，孙等人。 2020，Wei & Shen 2020，Yu 等人。 2018，李等人。 2020b，陈等人。 2020g，王等人。 2020a，Xin 等人。 2020，谢等人。 2020d，Li & Zhu 2021，Tian 等人。 2020，徐等人。 2020c，陈等人。 2020c，Zhou 等人。 2020d，陈等人。 2020d，He & Shin 2020a，Ren & Xie 2019，Zhu 等人。 2019，He & Shin 2020b，Chai 等人。 2018 年，Shin & Yoon 2020 年，Zhang 等人。 2018a，Ge 等人。 2019a、b，Lee & Rhee 2022，Shleifer 等人。 2019，葛等人。 2020，杨等人。 2020，陈等人。 2019，张等人。 2019e，Lee & Rhee 2019，Bogaerts 等人。 2020，王等人。 2020f，郭等人。 2020c，Zhou 等人。 2020a，蔡等人。 2020，Zhou 等人。 2020b，陈等人。 2020f，Mallick 等人。 2021，贾等人。 2020，张等人。 2020i，冯等人。 2020，谢等人。 2020c，Li 等人。 2020d，宋等人。 2020b，赵等人。 2020b，Kim 等人。 2020 年，Mohanty 和 Pozdnukhov 2018 年，Mohanty 等人。 2020，金等人。 2020b，Li 和 Axhausen 2020，Jin 等人。 2020a，耿等人。 2019a，柯等人。 2021a，Li 等人。 2020c，Ke 等人。 2021b，罗等人。 2020，陈等人。 2020b，肖等人。 2020，郭等人。 2019b，Kim 等人。 2019，林等人。 2018，杨等人。 2019，王等人。 2020c，Xu 等人。 2020d]
Traffic Pattern Similarity Matrix 流量模式相似度矩阵	$a_{ij}=$ the correlation coefficient of historical traffic states of nodes $i$ and $j$ $a_{ij}=$ 节点 $i$ 和 $j$ 历史流量状态的相关系数	Lv et al. [2020], Li & Zhu [2021], Xu et al. [2020c], Zhou et al. [2020d], Sun et al. [2020], Wang et al. [2020e], He & Shin [2020a], Ren & Xie [2019], Han et al. [2019], Liu et al. [2020b], He & Shin [2020b], Chai et al. [2018], Lu et al. [2020a], Lewenfus et al. [2020], Dai et al. [2020], Han et al. [2020], Jin et al. [2020b], Li & Axhausen [2020], Jin et al. [2020a], Bai et al. [2019b, a], Li et al. [2020c], Ke et al. [2021b], Chen et al. [2020b], Wang et al. [2020d], Yoshida et al. [2019], Kim et al. [2019], Lin et al. [2018], Zhou et al. [2020f Lv 等人 2020，Li 和 Zhu 2021，Zhou 等人 2020d，Wang 等人 2020e，He 和 Shin 2020a，Ren 和 Xie 2019 ，Liu 等人 2020b，Chai 等人 2020a，Lewenfus 等人 2020，Han 等人 2020b，Li 等人。 Axhausen 2020a，Bai 等人 2020c，Ke 等人 2020b，Wang 等人 2020d，Kim 等人。 2019，林等人，2018，周等人，2020f]
Functional Similarity Matrix 功能相似矩阵	$a_{ij}=$ the correlation coefficient of POI distributions in regions $i$ and $j$ $a_{ij}=$ $i$ 和 $j$ 区域POI分布的相关系数	Lv et al. [2020], He & Shin [2020a], Shi et al. [2020], Zhu et al. [2019], Ge et al. [2019a, b, 2020], Jin et al. [2020b], Geng et al. [2019b, a], Ke et al. [2021b], Luo et al. [2020], Zhang et al. [2020k Lv 等人。 2020，He & Shin 2020a，Shi 等人。 2020，朱等人。 2019，葛等人。 2019a，b，2020，Jin 等人。 2020b，耿等人。 2019b，a，Ke 等人。 2021b，罗等人。 2020，张等人。 2020k]
Dynamic Matrix 动态矩阵	N/A	Wu et al. [2019], Bai et al. [2020], Fang et al. [2019], Zhang et al. [2020e], Chen et al. [2020e], Kong et al. [2020], Tang et al. [2020b], Guo et al. [2019c], Li et al. [2019b], Zhang et al. [2019d], Li et al. [2020f], Guo et al. [2020b], Zhang et al. [2020h], Peng et al. [2020], Zhou et al. [2019], Shi et al. [2020], Li et al. [2018a], Tang et al. [2020a], Zhang et al. [2019a], Diao et al. [2019], Yu et al. [2020a], Fu et al. [2020], Maas & Bloem [2020], Li & Axhausen [2020], Du et al. [2020], Li & Moura [2020], Wu et al. [2020a], Ye et al. [2021 吴等人。 2019，白等人。 2020，方等人。 2019，张等人。 2020e，陈等人。 2020e，Kong 等人。 2020，唐等人。 2020b，郭等人。 2019c，Li 等人。 2019b，Zhang 等人。 2019d，Li 等人。 2020f，郭等人。 2020b，张等人。 2020h，Peng 等人。 2020，Zhou 等人。 2019，Shi 等人。 2020，李等人。 2018a，唐等人。 2020a，张等人。 2019a，Diao 等人。 2019，Yu 等人。 2020a，Fu 等人。 2020，Maas 和 Bloem 2020，Li 和 Axhausen 2020，Du 等人。 2020，Li & Moura 2020，Wu 等人。 2020a，叶等人。 2021年]

4.2 Graph Neural Networks 4.2图神经网络

Previous neural networks, e.g. fully-connected neural networks (FNNs), CNNs, and RNNs, could only be applied to Euclidean data (i.e. images, text, and videos). As a type of neural network which directly operates on a graph structure, GNNs have the ability to capture complex relationships between objects and make inferences based on data described by graphs. GNNs have been proven effective in various node-level, edge-level, and graph-level prediction tasks [Jiang, 2022]. As mentioned in Section 2, GNNs are currently considered the state-of-the-art techniques for traffic forecasting problems. GNNs can be roughly divided into four types, namely, recurrent GNNs, convolutional GNNs, graph autoencoders, and spatiotemporal GNNs [Wu et al., 2020b]. Because traffic forecasting is a spatiotemporal problem, the GNNs used in this field can all be categorized as the spatiotemporal GNNs. However, certain components of the other types of GNNs have also been applied in the surveyed traffic forecasting studies.
以前的神经网络，例如全连接神经网络 (FNN)、CNN 和 RNN 只能应用于欧几里德数据（即图像、文本和视频）。作为一种直接在图结构上运行的神经网络，GNN 能够捕获对象之间的复杂关系，并根据图描述的数据进行推理。 GNN 已被证明在各种节点级、边缘级和图级预测任务中有效[Jiang，2022]。正如第 2 节中提到的，GNN 目前被认为是解决交通预测问题的最先进技术。 GNN 大致可以分为四种类型，即循环 GNN、卷积 GNN、图自编码器和时空 GNN [Wu et al., 2020b]。由于流量预测是一个时空问题，因此该领域使用的 GNN 都可以归类为时空 GNN。然而，其他类型 GNN 的某些组件也已应用于调查的交通预测研究中。

To give the mathematical formulation of GCN, we further introduce some notations. Give a graph $G=(V,E,A)$ , $\mathcal{N}(v_{i})$ is defined as the neighbor node set of a single node $v_{i}$ . $\mathbf{D}$ is defined as the degree matrix, of which each element is $\mathbf{D}_{ii}=\|\mathcal{N}(v_{i})\|$ . $\mathbf{L}=\mathbf{D}-\mathbf{A}$ is defined as the Laplacian matrix of an undirected graph and $\tilde{\mathbf{L}}=\mathbf{I}_{N}-\mathbf{D}^{-\frac{1}{2}}\mathbf{A}\mathbf{D}^{-\frac{1}{2}}$ is defined as the normalized Laplacian matrix, where $\mathbf{I}_{N}$ is the identity matrix with size $N$ . Without considering the time step index, the node feature matrix of a graph is simplified as $\mathbf{X}\in{R}^{N\times d}$ , where $N$ is the node number and $d$ is the dimension of the node feature vector as before. The basic notations used in this survey is summarized in Table 4.
为了给出 GCN 的数学公式，我们进一步引入一些符号。给定一个图 $G=(V,E,A)$ ，将 $\mathcal{N}(v_{i})$ 定义为单个节点 $v_{i}$ 的邻居节点集合。 $\mathbf{D}$ 定义为度矩阵，其中每个元素为 $\mathbf{D}_{ii}=\|\mathcal{N}(v_{i})\|$ 。 $\mathbf{L}=\mathbf{D}-\mathbf{A}$ 定义为无向图的拉普拉斯矩阵， $\tilde{\mathbf{L}}=\mathbf{I}_{N}-\mathbf{D}^{-\frac{1}{2}}\mathbf{A}\mathbf{D}^{-\frac{1}{2}}$ 定义为归一化拉普拉斯矩阵，其中 $\mathbf{I}_{N}$ 是大小为 $N$ 。在不考虑时间步索引的情况下，图的节点特征矩阵简化为 $\mathbf{X}\in{R}^{N\times d}$ ，其中 $N$ 是节点编号， $d$ 是节点的维度像以前一样的节点特征向量。表 4 总结了本次调查中使用的基本符号。

Table 4: Basic notations used in this study.
表 4：本研究中使用的基本符号。

Symbol	Description
$G$	Graph
$V$	Node set 节点集
$E$	Edge set 边缘设置
$A$	Adjacency matrix 邻接矩阵
$\chi_{t}$ or $\mathbf{X}$ $\chi_{t}$ 或 $\mathbf{X}$	Node feature matrix w/o time step index $t$ 不带时间步长索引的节点特征矩阵 $t$
$N$	Node number 节点数
$d$	Node feature dimension 节点特征维度
$\mathcal{N}(v_{i})$	Neighbor node set of a single node $v_{i}$ 单个节点的邻居节点集 $v_{i}$
$\mathbf{D}$	Degree matrix 度矩阵
$\mathbf{L}$	Laplacian matrix 拉普拉斯矩阵
$\tilde{\mathbf{L}}$	Normalized Laplacian matrix 归一化拉普拉斯矩阵
$\mathbf{I}_{N}$	Identity matrix with size $N$ 大小为 $N$ 的单位矩阵

When extending the convolution operation from Euclidean data to non-Euclidean data, the basic idea of GNNs is to learn a function mapping for a node to aggregate its own features and the features of its neighbors to generate a new representation. GCNs are spectral-based convolutional GNNs, in which the graph convolutions are defined by introducing filters from graph signal processing in the spectral domain, e.g., the Fourier domain. The graph Fourier transform is firstly used to transform the graph signal to the spectral domain and the inverse graph Fourier transform is further used to transform the result after the convolution operation back. Several spectral-based GCNs are introduced in the literature. Spectral convoluted neural networking [Bruna et al., 2014] assumes that the filter is a set of learnable parameters and considers graph signals with multiple channels. GNN [Henaff et al., 2015] introduces a parameterization with smooth coefficients and makes the spectral filters spatially localized. Chebyshev’s spectral CNN (ChebNet) [Defferrard et al., 2016] leverages a truncated expansion in terms of Chebyshev polynomials up to $K$ th order to approximate the diagonal matrix.
当将卷积运算从欧几里德数据扩展到非欧几里德数据时，GNN 的基本思想是学习节点的函数映射，以聚合其自身特征和邻居特征以生成新的表示。 GCN 是基于谱的卷积 GNN，其中图卷积是通过引入谱域（例如傅里叶域）中图信号处理的滤波器来定义的。图傅立叶变换首先用于将图信号变换到谱域，然后使用图傅立叶逆变换将卷积运算后的结果变换回来。文献中介绍了几种基于谱的 GCN。谱卷积神经网络 [Bruna et al., 2014] 假设滤波器是一组可学习的参数，并考虑具有多个通道的图信号。 GNN [Henaff et al., 2015] 引入了具有平滑系数的参数化，并使光谱滤波器在空间上局部化。切比雪夫的谱 CNN (ChebNet) [Defferrard et al., 2016] 利用高达 $K$ 阶的切比雪夫多项式的截断展开来近似对角矩阵。

GCN [Kipf & Welling, 2017] is a first-order approximation of ChebNet, which approximates the filter using the Chebyshev polynomials of the diagonal matrix of eigenvalues. To avoid overfitting, $K=1$ is used in GCN. Formally, the graph convolution operation $*G$ in GCN is defined as follows:
GCN [Kipf & Welling, 2017] 是 ChebNet 的一阶近似，它使用特征值对角矩阵的切比雪夫多项式来近似滤波器。为了避免过拟合，GCN中使用了 $K=1$ 。形式上，GCN中的图卷积运算 $*G$ 定义如下：

\mathbf{X}_{*G}=\mathbf{W}(\mathbf{I}_{N}+\mathbf{D}^{-\frac{1}{2}}\mathbf{A}\mathbf{D}^{-\frac{1}{2}})\mathbf{X}

(1)

where $\mathbf{W}$ is a learnable weight matrix, i.e., the model parameters. While in practice, the graph convolution operation is further developed in order to alleviate the potential gradient explosion problem as follows:
其中 $\mathbf{W}$ 是可学习的权重矩阵，即模型参数。而在实践中，为了缓解潜在的梯度爆炸问题，图卷积操作被进一步发展如下：

\mathbf{X}_{*G}=\mathbf{W}(\tilde{\mathbf{D}}^{-\frac{1}{2}}\tilde{\mathbf{A}}\tilde{\mathbf{D}}^{-\frac{1}{2}})\mathbf{X}

(2)

where $\tilde{\mathbf{A}}=\mathbf{A}+\mathbf{I}_{N}$ and $\tilde{\mathbf{D}}_{ii}=\sum_{j}{\tilde{\mathbf{A}}_{ij}}$ .
其中 $\tilde{\mathbf{A}}=\mathbf{A}+\mathbf{I}_{N}$ 和 $\tilde{\mathbf{D}}_{ii}=\sum_{j}{\tilde{\mathbf{A}}_{ij}}$ 。

The alternative approach is spatial-based convolutional GNNs, in which the graph convolutions are defined by information propagation. Diffusion graph convolution (DGC) [Atwood & Towsley, 2016], message passing neural network (MPNN) [Gilmer et al., 2017], GraphSAGE [Hamilton et al., 2017], and graph attention network (GAT) [Veličković et al., 2018] all follow this approach. The graph convolution is modeled as a diffusion process with a transition probability from one node to a neighboring node in DGC. An equilibrium is expected to be obtained after several rounds of information transition. The general framework followed is a message passing network, which models the graph convolutions as an information-passing process from one node to another connected node directly. To alleviate the computation problems caused by a large number of neighbors, sampling is used to obtain a fixed number of neighbors in GraphSAGE. Lastly, without using a predetermined adjacency matrix, the attention mechanism is used to learn the relative weights between two connected nodes in GAT.
另一种方法是基于空间的卷积 GNN，其中图卷积由信息传播定义。扩散图卷积 (DGC) [Atwood & Towsley, 2016]、消息传递神经网络 (MPNN) [Gilmer et al., 2017]、GraphSAGE [Hamilton et al., 2017] 和图注意力网络 (GAT) [Veličković et al., 2017] al., 2018] 都遵循这种方法。图卷积被建模为一种扩散过程，具有从 DGC 中一个节点到相邻节点的转移概率。经过几轮信息传递预计会达到均衡。接下来的总体框架是消息传递网络，它将图卷积建模为从一个节点直接到另一个连接节点的信息传递过程。为了缓解大量邻居带来的计算问题，GraphSAGE 中使用采样来获取固定数量的邻居。最后，在不使用预定邻接矩阵的情况下，使用注意力机制来学习 GAT 中两个连接节点之间的相对权重。

MPNN uses message passing functions to unify different spatial-based variants. MPNN operates in two stages, namely, a message passing phase and a readout phase. The message passing phase is defined as follows:
MPNN 使用消息传递函数来统一不同的基于空间的变体。 MPNN 分两个阶段运行，即消息传递阶段和读出阶段。消息传递阶段定义如下：

\mathbf{m}_{v_{i}}^{(t)}=\sum_{v_{j}\in\mathcal{N}{(v_{i})}}\mathcal{M}^{(t)}(\mathbf{X}_{i}^{(t-1)},\mathbf{X}_{j}^{(t-1)},\mathbf{e}_{ij})

(3)

where $\mathbf{m}_{v_{i}}^{(t)}$ is the message aggregated from the neighbors of node $v_{i}$ , $\mathcal{M}^{(t)}(\cdot)$ is the aggregation function in the $t$ -th iteration, $\mathbf{X}_{i}^{(t)}$ is the hidden state of node $v_{i}$ in the $t$ -th iteration, and $\mathbf{e}_{ij}$ is the edge feature vector between node $v_{i}$ and node $v_{j}$ .
其中 $\mathbf{m}_{v_{i}}^{(t)}$ 是从节点 $v_{i}$ 的邻居聚合的消息， $\mathcal{M}^{(t)}(\cdot)$ 是第 $t$ 次迭代中的聚合函数，< b4>是节点 $v_{i}$ 在第 $t$ 次迭代中的隐藏状态， $\mathbf{e}_{ij}$ 是节点 $v_{i}$ 和节点 $v_{j}$ 。

The readout phase is defined as follows:
读出阶段定义如下：

\mathbf{X}_{i}^{(t)}=\mathcal{U}^{(t)}(\mathbf{X}_{i}^{(t-1)},\mathbf{m}_{v_{i}}^{(t)})

(4)

where $\mathcal{U}^{(t)}(\cdot)$ is the readout function in the $t$ -th iteration.
其中 $\mathcal{U}^{(t)}(\cdot)$ 是第 $t$ 次迭代中的读出函数。

In GAT [Veličković et al., 2018], the attention mechanism [Vaswani et al., 2017] is incorporated into the propagation step and the multi-head attention mechanism is further utilized with the aim of stabilizing the learning process. The specific operation is defined as follows:
在 GAT [Veličković et al., 2018] 中，注意力机制 [Vaswani et al., 2017] 被纳入传播步骤，并进一步利用多头注意力机制，以稳定学习过程。具体操作定义如下：

\mathbf{X}_{i}^{(t)}=\|_{k}\sigma(\sum_{j\in\mathcal{N}{(v_{i})}}\alpha^{k}(\mathbf{X}_{i}^{(t-1)},\mathbf{X}_{j}^{(t-1)})\mathbf{W}^{(t-1)}\mathbf{X}_{j}^{(t-1)})

(5)

where $\|$ is the concatenation operation, $\sigma$ is the activation method, $\alpha^{k}(\cdot)$ is the $k$ -th attention mechanism.
其中 $\|$ 是串联操作， $\sigma$ 是激活方法， $\alpha^{k}(\cdot)$ 是第 $k$ 注意力机制。

A general spatiotemporal GNN structure is shown in Figure 5, in which GCN is used to capture the spatial dependency and 1D-CNN is used to capture the temporal dependency. Both GCN and 1D-CNN components can be replaced with other structures for other spatiotemporal GNNs. A multilayer perceptron (MLP) component is used to generate the desired output. As for comparison, a two-layer GCN is also shown in Figure 5, in which only the spatial dependency is concerned.
通用的时空 GNN 结构如图 5 所示，其中 GCN 用于捕获空间依赖性，1D-CNN 用于捕获时间依赖性。 GCN 和 1D-CNN 组件都可以替换为其他时空 GNN 的其他结构。多层感知器 (MLP) 组件用于生成所需的输出。作为比较，图 5 还显示了两层 GCN，其中仅涉及空间依赖性。

Spatiotemporal GNNs can be further categorized based on the approach used to capture the temporal dependency in particular. Most of the relevant studies in the literature can be split into two types, namely, RNN-based and CNN-based spatiotemporal GNNs [Wu et al., 2020b]. The RNN-based approach is used in Li et al. [2018b], Guo et al. [2020a], Pan et al. [2020, 2019], Lu et al. [2019a], Mallick et al. [2020], Zhang et al. [2020j, l], Bai et al. [2020], Huang et al. [2020a], Wang et al. [2018b, 2020g], Lv et al. [2020], Fukuda et al. [2020], Zhang & Guo [2020], Boukerche & Wang [2020b], Kang et al. [2019], Li et al. [2019b], Xu et al. [2019], Wu et al. [2018a], Wei & Sheng [2020], Li et al. [2020f], Yu et al. [2019b], Yin et al. [2020], Xin et al. [2020], Qu et al. [2020], Huang et al. [2020b], Guo et al. [2020b], Fang et al. [2020a], Li & Zhu [2021], Chen et al. [2020c], Ramadan et al. [2020], Zhou et al. [2020d], Wang et al. [2018a], Peng et al. [2020], Zhou et al. [2019], Wang et al. [2020e], Qiu et al. [2020], Shi et al. [2020], Wang et al. [2020h, 2019], Zhang et al. [2020b], Liu et al. [2020b], Ye et al. [2020b], Zhu et al. [2019], Chai et al. [2018], He et al. [2020], Bai et al. [2021], Zhang et al. [2018a, 2019f], Xie et al. [2019], Zhang et al. [2019a], Guo et al. [2019a], Cirstea et al. [2019], Lu et al. [2019b], Zhang et al. [2019b], Lu et al. [2020b], Zhao et al. [2019], Cui et al. [2019], Chen et al. [2019], Zhang et al. [2019e], Bogaerts et al. [2020], Cui et al. [2020a], Zhou et al. [2020a], Mallick et al. [2021], Sun et al. [2021], Xie et al. [2020b], Zhu et al. [2021, 2020], Fu et al. [2020], Chen et al. [2020a], Lewenfus et al. [2020], Zhu et al. [2022], Liao et al. [2018], Zhao et al. [2020b], Guopeng et al. [2020], Shao et al. [2020], Shen et al. [2020], Mohanty & Pozdnukhov [2018], Mohanty et al. [2020], Hu et al. [2018], Pian & Wu [2020], Jin et al. [2020a], Geng et al. [2019a], Bai et al. [2019a], Li et al. [2020c], Ke et al. [2021b], Hu et al. [2020], Xu & Li [2019], Davis et al. [2020], Chen et al. [2020h], Du et al. [2020], Wu et al. [2020a], Ye et al. [2021], Luo et al. [2020], Chen et al. [2020b], Wang et al. [2020d], Xiao et al. [2020], Guo et al. [2019b], Lin et al. [2018], Zhou et al. [2020f], Liu et al. [2020c], Zhang et al. [2020g], Yang et al. [2019], Zhang et al. [2020f], Wang et al. [2020c], Wright et al. [2019]; while the CNN-based approach is used in Wu et al. [2019], Fang et al. [2019], Zhang et al. [2020e], Xu et al. [2020b], Chen et al. [2020e], Kong et al. [2020], Tang et al. [2020b], Guo et al. [2019c], Sun et al. [2020], Yu et al. [2018], Li et al. [2020b], Wang et al. [2020a], Tian et al. [2020], Chen et al. [2020d], Zhao et al. [2020a], Zhang et al. [2020c], Ou et al. [2020], Tang et al. [2020a], Diao et al. [2019], Lee & Rhee [2022, 2019], Wang et al. [2020f], Wu et al. [2020c], Guo & Yuan [2020], Zhang et al. [2020i], Feng et al. [2020], Zhang et al. [2020d], Xie et al. [2020c], Lu et al. [2020a], Maas & Bloem [2020], Li et al. [2020d], Song et al. [2020b], Dai et al. [2020], Hong et al. [2020], Zheng et al. [2020a], Zhou et al. [2020e], Yu et al. [2020b], Xu et al. [2020d], Heglund et al. [2020].
时空 GNN 可以根据用于捕获特定时间依赖性的方法进一步分类。文献中的大多数相关研究可以分为两种类型，即基于 RNN 的时空 GNN 和基于 CNN 的时空 GNN [Wu et al., 2020b]。 Li 等人使用了基于 RNN 的方法。 [2018b]，郭等人。 [2020a]，潘等人。 [2020，2019]，Lu 等人。 [2019a]，Mallick 等人。 [2020]，张等人。 [2020j，l]，白等人。 [2020]，黄等人。 [2020a]，王等人。 [2018b，2020g]，Lv 等人。 [2020]，福田等人。 [ 2020]，Zhang 和Guo [2020]，Boukerche 和Wang [2020b]，Kang 等人。 [2019]，李等人。 [2019b]，徐等人。 [2019]，吴等人。 [2018a]，Wei & Shen [2020]，Li 等人。 [2020f]，Yu 等人。 [2019b]，尹等人。 [2020]，Xin 等人。 [2020]，Qu 等人。 [2020]，黄等人。 [2020b]，郭等人。 [2020b]，方等人。 [2020a]，Li & Zhu [2021]，Chen 等人。 [2020c]，Ramadan 等人。 [2020]，Zhou 等人。 [2020d]，王等人。 [2018a]，彭等人。 [2020]，Zhou 等人。 [2019]，王等人。 [2020e]，Qiu 等人。 [2020]，Shi 等人。 [2020]，王等人。 [2020h，2019]，Zhang 等人。 [2020b]，刘等人。 [2020b]，Ye 等人。 [2020b]，朱等人。 [2019]，柴等人。 [2018]，何等人。 [2020]，白等人。 [2021]，张等人。 [2018a，2019f]，Xie 等人。 [2019]，张等人。 [2019a]，郭等人。 [2019a]，Cirstea 等人。 [2019]，卢等人。 [2019b]，张等人。 [2019b]，Lu 等人。 [2020b]，赵等人。 [2019]，崔等人。 [2019]，陈等人。 [2019]，张等人。 [2019e]，Bogaerts 等人。 [2020]，崔等人。 [2020a]，Zhou 等人。 [2020a]，Mallick 等人。 [2021]，Sun 等人。 [2021]，Xie 等人。 [2020b]，朱等人。 [2021, 2020]，Fu 等人。 [2020]，陈等人。 [2020a]，Lewenfus 等人。 [2020]，朱等人。 [2022]，廖等人。 [2018]，赵等人。 [2020b]，国鹏等。 [2020]，Shao 等人。 [2020]，沉等人。 [2020]，Mohanty 和 Pozdnukhov [2018]，Mohanty 等人。 [2020]，胡等人。 [2018]，Pian & Wu [2020]，Jin 等人。 [2020a]，耿等人。 [2019a]，白等人。 [2019a]，Li 等人。 [2020c]，Ke 等人。 [2021b]，胡等人。 [2020]，Xu & Li [2019]，Davis 等人。 [2020]，陈等人。 [2020h]，杜等人。 [2020]，吴等人。 [2020a]，叶等人。 [2021]，罗等人。 [2020]，陈等人。 [2020b]，王等人。 [2020d]，Xiao 等人。 [2020]，郭等人。 [2019b]，林等人。 [2018]，周等人。 [2020f]，刘等人。 [2020c]，Zhang 等人。 [2020g]，杨等人。 [2019]，张等人。 [2020f]，王等人。 [2020c]，赖特等人。 [2019]; Wu 等人使用了基于 CNN 的方法。 [2019]，方等人。 [2019]，张等人。 [2020e]，Xu 等人。 [2020b]，陈等人。 [2020e]，Kong 等人。 [2020]，唐等人。 [2020b]，郭等人。 [2019c]，Sun 等人。 [2020]，Yu 等人。 [2018]，李等人。 [2020b]，Wang 等人。 [2020a]，Tian 等人。 [2020]，陈等人。 [2020d]，赵等人。 [2020a]，Zhang 等人。 [2020c]，Ou 等人。 [2020]，唐等人。 [2020a]，Diao 等人。 [ 2019]，Lee & Rhee [2022，2019]，Wang 等人。 [2020f]，吴等人。 [2020c]，Guo & Yuan [2020]，Zhang 等人。 [2020i]，冯等人。 [2020]，张等人。 [2020d]，Xie 等人。 [2020c]，Lu 等人。 [2020a]，Maas 和 Bloem [2020]，Li 等人。 [2020d]，宋等人。 [2020b]，戴等人。 [2020]，洪等人。 [2020]，郑等人。 [2020a]，Zhou 等人。 [2020e]，Yu 等人。 [2020b]，Xu 等人。 [2020d]，赫格伦德等人。 [2020]。

With the recent expansion of relevant studies, we add two sub-types of spatiotemporal GNNs in this survey, namely, attention-based and FNN-based. Attention mechanism is firstly proposed to memorize long source sentences in neural machine translation [Vaswani et al., 2017]. Then it is used for temporal forecasting problems. As a special case, Transformer is built entirely upon attention mechanisms, which makes it possible to access any part of a sequence regardless of its distance to the target [Xie et al., 2020d, Cai et al., 2020, Jin et al., 2020b, Li & Moura, 2020]. The attention-based approaches are used in Zheng et al. [2020b], Zhang et al. [2020a], Wang et al. [2020b], Xie et al. [2020d], Cai et al. [2020], Zhou et al. [2020b], Chen et al. [2020f], Park et al. [2020], Fang et al. [2020b], Jin et al. [2020b], Bai et al. [2019b], Li & Moura [2020], Zhang et al. [2020k], while the simpler FNN-based approach is used in Zhang et al. [2018b], Wei et al. [2019], Song et al. [2020a], Cao et al. [2020], Chen et al. [2020g], Zhang et al. [2020h], Sun et al. [2020], He & Shin [2020a], Yeghikyan et al. [2020], Ren & Xie [2019], Li et al. [2018a], Han et al. [2019], He & Shin [2020b], Zhang et al. [2019c], Ge et al. [2019a, b], Yu et al. [2020a], Ge et al. [2020], Yu et al. [2019a], Guo et al. [2020c], Agafonov [2020], Geng et al. [2019b], Qin et al. [2020b], Kim et al. [2019]. Apart from using neural networks to capture temporal dependency, other techniques that have also been combined with GNNs include autoregression [Lee et al., 2019], Markov processes [Cui et al., 2020b], and Kalman filters [Xiong et al., 2020].
随着最近相关研究的扩展，我们在本次调查中添加了两种时空 GNN 子类型，即基于注意力的和基于 FNN 的。注意力机制首先被提出来记忆神经机器翻译中的长源句子 [Vaswani et al., 2017]。然后将其用于时间预测问题。作为一个特例，Transformer 完全建立在注意力机制的基础上，这使得访问序列的任何部分成为可能，无论其与目标的距离如何[Xie et al., 2020d, Cai et al., 2020, Jin et al., 2020] ，2020b，Li 和 Moura，2020]。 Cheng 等人使用了基于注意力的方法。 [2020b]，Zhang 等人。 [2020a]，王等人。 [2020b]，Xie 等人。 [2020d]，蔡等人。 [2020]，Zhou 等人。 [2020b]，陈等人。 [2020f]，Park 等人。 [2020]，方等人。 [2020b]，金等人。 [2020b]，白等人。 [2019b]，Li 和 Moura [2020]，Zhang 等人。 [2020k]，而Zhang等人使用了更简单的基于FNN的方法。 [2018b]，Wei 等人。 [2019]，宋等人。 [2020a]，曹等人。 [2020]，陈等人。 [2020g]，张等人。 [2020h]，Sun 等人。 [2020]，He & Shin [2020a]，Yeghikyan 等人。 [2020]，Ren & Xie [2019]，Li 等人。 [2018a]，韩等人。 [ 2019]，He & Shin [2020b]，Zhang 等人。 [2019c]，Ge 等人。 [2019a，b]，Yu 等人。 [2020a]，Ge 等人。 [2020]，Yu 等人。 [2019a]，郭等人。 [2020c]，阿加福诺夫[2020]，耿等人。 [2019b]，秦等人。 [2020b]，Kim 等人。 [2019]。除了使用神经网络来捕获时间依赖性之外，还与 GNN 相结合的其他技术包括自回归 [Lee et al., 2019]、马尔可夫过程 [Cui et al., 2020b] 和卡尔曼滤波器 [Xiong et al., 2019]。 2020]。

Among different approaches for temporal modeling, RNNs suffer from time-consuming iterations and gradient vanishing or explosion problem with long sequences. CNNs demonstrate their superiority in terms of simple structure, parallel computing and stable gradients. As for the traffic problems, the spatial and temporal dependencies are closely intertwined in reality. For example, it is argued that the historical observations in different locations at different times have varying impacts on central region in the future [Guo et al., 2019c]. Some efforts are put to jointly modeling the potential interaction between spatial and temporal features and one promising direction is the incorporate of the graph convolution operations into RNNs to capture spatial-temporal correlations [Yu et al., 2019b, Zhou et al., 2019, Chen et al., 2019, Liu et al., 2020b, Chen et al., 2020f, Guo et al., 2020a]. For example, the localized spatio-temporal correlation information is extracted simultaneously with the adjacency matrix of localized spatio-temporal graph in Song et al. [2020a], in which a localized spatio-temporal graph that includes both temporal and spatial attributes is constructed first and a spatial-based GCN method is applied then.
在不同的时间建模方法中，RNN 面临着耗时的迭代以及长序列的梯度消失或爆炸问题。 CNN 在结构简单、并行计算和稳定梯度方面表现出其优越性。至于交通问题，空间和时间依赖性在现实中是紧密交织在一起的。例如，有人认为不同地点、不同时间的历史观测对未来中部地区的影响不同[Guo et al., 2019c]。人们付出了一些努力来联合建模空间和时间特征之间的潜在相互作用，一个有前途的方向是将图卷积运算合并到 RNN 中以捕获时空相关性 [Yu et al., 2019b, Zhou et al., 2019, Chen 等人，2019；Liu 等人，2020b；Chen 等人，2020f；Guo 等人，2020a]。例如，Song等人在提取局部时空相关信息的同时，还提取了局部时空图的邻接矩阵。 [2020a]，其中首先构建包括时间和空间属性的局部时空图，然后应用基于空间的GCN方法。

Of the additional GNN components adopted in the surveyed studies, convolutional GNNs are the most popular, while recurrent GNN [Scarselli et al., 2008] and Graph Auto-Encoder (GAE) [Kipf & Welling, 2016] are used less frequently. We further categorize convolutional GNNs into the following five types: (1) GCN [Kipf & Welling, 2017], (2) DGC [Atwood & Towsley, 2016], (3) MPNN [Gilmer et al., 2017], (4) GraphSAGE [Hamilton et al., 2017], and (5) GAT [Veličković et al., 2018]. These relevant graph neural networks are listed chronologically in Figure 6. While different GNNs can be used for traffic forecasting, a general design pipeline is proposed in [Zhou et al., 2020c] and suggested for future studies as follows:
在调查研究中采用的其他 GNN 组件中，卷积 GNN 是最受欢迎的，而循环 GNN [Scarselli et al., 2008] 和图自动编码器 (GAE) [Kipf & Welling, 2016] 的使用频率较低。我们进一步将卷积 GNN 分为以下五种类型：(1) GCN [Kipf & Welling, 2017]，(2) DGC [Atwood & Towsley, 2016]，(3) MPNN [Gilmer et al., 2017]，(4 ) GraphSAGE [Hamilton 等人，2017]，以及 (5) GAT [Veličković 等人，2018]。这些相关的图神经网络按时间顺序在图 6 中列出。虽然不同的 GNN 可用于流量预测，但 [Zhou et al., 2020c] 中提出了通用设计流程，并建议未来的研究如下：

1.

Find graph structure. As discussed in Section IV, different traffic graphs are available.

1. 查找图结构。正如第四节中所讨论的，可以使用不同的流量图。
2.

Specify graph type and scale. The graphs can be further classified into different types if needed, e.g., directed/undirected graphs, homogeneous/heterogeneous graphs, static/dynamic graphs. For most cases in traffic forecasting, the graphs of the same type are used in a single study. As for the graph scale, the graphs in the traffic domain are not as large as those for the social networks or academic networks with millions of nodes and edges.

2. 指定图表类型和比例。如果需要，图可以进一步分为不同类型，例如有向/无向图、同构/异构图、静态/动态图。对于流量预测的大多数情况，同一类型的图表用于单个研究。就图规模而言，流量领域的图不像社交网络或学术网络那样大，具有数百万个节点和边。
3.

Design loss function. The training setting usually follows the supervised approach, which means the GNN-based models are firstly trained on a training set with labels and then evaluated on a test set. The forecasting task is usually designed as the node-level regression problem. Based on these considerations, the proper loss function and evaluation metrics can be chosen, e.g., root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE).

3.设计损失函数。训练设置通常遵循监督方法，这意味着基于 GNN 的模型首先在带有标签的训练集上进行训练，然后在测试集上进行评估。预测任务通常被设计为节点级回归问题。基于这些考虑，可以选择适当的损失函数和评估指标，例如均方根误差（RMSE）、平均绝对误差（MAE）和平均绝对百分比误差（MAPE）。
4.

Build model using computational modules. The GNNs discussed in this section are exactly those which have already been used as computational modules to build forecasting models in the surveyed studies.

4. 使用计算模块构建模型。本节讨论的 GNN 正是那些在调查研究中已被用作构建预测模型的计算模块的 GNN。

A full list of the GNN components used in the surveyed studies is shown in Table 5. Currently, the most widely used GNN is the GCN. However, we also notice a growing trend in the use of GAT in traffic forecasting.
表 5 显示了调查研究中使用的 GNN 组件的完整列表。目前，使用最广泛的 GNN 是 GCN。然而，我们也注意到 GAT 在流量预测中的使用呈增长趋势。

Table 5: GNNs in the surveyed studies.
表 5：调查研究中的 GNN。

GNN	Relevant Studies 相关研究
Recurrent GNN 循环神经网络	Wang et al. [2018b, a], Lu et al. [2019b, 2020b 王等人。 2018b，a，Lu 等人。 2019b, 2020b]
GAE	Xu et al. [2020a, 2019], Opolka et al. [2019], Shen et al. [2020 徐等人。 2020a，2019，Opolka 等人。 2019，沉等人。 2020年]
GCN	Wu et al. [2019], Zhang et al. [2018b], Guo et al. [2020a], Lu et al. [2019a], Zhang et al. [2020j, l], Bai et al. [2020], Fang et al. [2019], Zhang et al. [2020e], Song et al. [2020a], Xu et al. [2020b], Wang et al. [2020g], Lv et al. [2020], Boukerche & Wang [2020b], Tang et al. [2020b], Guo et al. [2019c], Li et al. [2019b], Zhang et al. [2019d], Sun et al. [2020], Li et al. [2020f], Cao et al. [2020], Yu et al. [2018, 2019b], Li et al. [2020b], Chen et al. [2020g], Zhang et al. [2020a], Wang et al. [2020a], Xin et al. [2020], Qu et al. [2020], Wang et al. [2020b], Huang et al. [2020b], Guo et al. [2020b], Fang et al. [2020a], Li & Zhu [2021], Xu et al. [2020c], Chen et al. [2020c], Xiong et al. [2020], Ramadan et al. [2020], Zhou et al. [2020d], Sun et al. [2020], Peng et al. [2020], Zhou et al. [2019], Wang et al. [2020e], Qiu et al. [2020], He & Shin [2020a], Yeghikyan et al. [2020], Shi et al. [2020], Wang et al. [2020h], Ren & Xie [2019], Li et al. [2018a], Zhao et al. [2020a], Han et al. [2019], Zhang et al. [2020b, c], Liu et al. [2020b], Ye et al. [2020b], Zhu et al. [2019], Chai et al. [2018], He et al. [2020], Bai et al. [2021], Tang et al. [2020a], James [2020], Zhang et al. [2018a, 2019f], Yu & Gu [2019], Guo et al. [2019a], Diao et al. [2019], Zhang et al. [2019c], James [2019], Ge et al. [2019a, b], Zhang et al. [2019b], Lee & Rhee [2022], Yu et al. [2020a], Ge et al. [2020], Zhao et al. [2019], Cui et al. [2019], Zhang et al. [2019e], Yu et al. [2019a], Lee & Rhee [2019], Bogaerts et al. [2020], Cui et al. [2020b, a], Guo et al. [2020c], Cai et al. [2020], Wu et al. [2020c], Chen et al. [2020f], Jia et al. [2020], Sun et al. [2021], Xie et al. [2020b], Zhu et al. [2021], Feng et al. [2020], Zhu et al. [2020], Fu et al. [2020], Agafonov [2020], Chen et al. [2020a], Lu et al. [2020a], Jepsen et al. [2019, 2020], Bing et al. [2020], Lewenfus et al. [2020], Zhu et al. [2022], Liao et al. [2018], Maas & Bloem [2020], Li et al. [2020d], Song et al. [2020b], Zhao et al. [2020b], Guopeng et al. [2020], Shao et al. [2020], Dai et al. [2020], Mohanty & Pozdnukhov [2018], Mohanty et al. [2020], Qin et al. [2020a], Han et al. [2020], Hong et al. [2020], Hu et al. [2018], Li & Axhausen [2020], Jin et al. [2020a], Geng et al. [2019b], Bai et al. [2019b], Geng et al. [2019a], Bai et al. [2019a], Ke et al. [2021a], Li et al. [2020c], Ke et al. [2021b], Hu et al. [2020], Zheng et al. [2020a], Davis et al. [2020], Chen et al. [2020h], Du et al. [2020], Li & Moura [2020], Ye et al. [2021], Luo et al. [2020], Chen et al. [2020b], Wang et al. [2020d], Qin et al. [2020b], Xiao et al. [2020], Yoshida et al. [2019], Guo et al. [2019b], Kim et al. [2019], Lin et al. [2018], Zhou et al. [2020e], Yu et al. [2020b], Zhang et al. [2020k], Zhou et al. [2020f], Liu et al. [2020c], Zhang et al. [2020g], Yang et al. [2019], Zhang et al. [2020f], Xu et al. [2020d], Heglund et al. [2020 Wu 等人 2019，Guo 等人 2020a，Zhang 等人 2020，Fang 等人 2020e等人 2020a，Xu 等人 2020g，Lv 等人 2020b，Tang 等人 2019c，Li 等人 2019b 2019d，Sun 等人 2020f，Cao 等人 2018，2019b，Li 等人 2020g，Zhang 等人 2020a。 2020a，Qu 等人 2020，Huang 等人 2020b，Fang 等人 2020a，Xu 等人 2020c等人 2020c，Xiong 等人 2020，Zhou 等人 2020，Peng 等人 2020，Wang 等人 2020e 2020，He 和 Shin 2020a，Shi 等人 2020，Ren 和 Xie 2018a，Zhao 等人 2020a，Zhang 等人。等人 2020b，c，刘等人 2020b，朱等人 2018，何等人 2021，唐等人 2020 ，Zhang 等人 2018a，2019f，Guo 等人 2019a，Diao 等人 2019c，James 等人 2019a，b，Zhang 等人 2019b。 & Rhee 2022，Ge 等人 2020，Cui 等人 2019e，Yu 等人 2019a，Bogaerts 等人 2020 ，Cui 等人 2020b，Guo 等人 2020，Wu 等人 2020f，Sun 等人 2020b。，Zhu 等人 2021，Feng 等人 2020，Fu 等人 2020，Chen 等人 2020a，Jepsen 等人 2019，2020等人 2020，Lewenfus 等人 2022，Liao 等人 2020，Li 等人 2020d。 2020b，Guopeng 等人 2020，Dai 等人 2020，Mohanty 等人 2020，Han 等人 2020等人 2020，Li 等人 2020a，Geng 等人 2019b，Geng 等人 2019a，Ke 等人。 2021a，Li 等人 2021b，Hu 等人 2020，Davis 等人 2020h，Du 等人 2020，Ye等人 2021，陈等人 2020b，秦等人 2020，吉田等人 2019b . 2019，Zhou 等人 2020e，Zhang 等人 2020f，Liu 等人 2020g，Yang 等人 2019 ，Zhang 等人 2020f，Xu 等人 2020d，Heglund 等人。 2020]
DGC	Li et al. [2018b], Mallick et al. [2020], Chen et al. [2020e], Fukuda et al. [2020], Ou et al. [2020], Chen et al. [2019], Wang et al. [2020f], Zhou et al. [2020a, b], Mallick et al. [2021], Xie et al. [2020c], Kim et al. [2020], Wang et al. [2020c 李等人。 2018b，Mallick 等人。 2020，陈等人。 2020e，福田等人。 2020，欧等人。 2020，陈等人。 2019，王等人。 2020f，Zhou 等人。 2020a、b，Mallick 等人。 2021，谢等人。 2020c，Kim 等人。 2020，王等人。 2020年c]
MPNN	Wei et al. [2019], Xu et al. [2020b], Wang et al. [2019 魏等人。 2019，徐等人。 2020b，王等人。 2019年]
GraphSAGE	Liu et al. [2020a 刘等人。 2020年a]
GAT	Zheng et al. [2020b], Pan et al. [2020, 2019], Huang et al. [2020a], Kong et al. [2020], Zhang & Guo [2020], Tang et al. [2020b], Kang et al. [2019], Wu et al. [2018a], Wei & Sheng [2020], Yin et al. [2020], Xie et al. [2020d], Zhang et al. [2020h], Tian et al. [2020], He & Shin [2020b], Tang et al. [2020a], Zhang et al. [2019a], Cirstea et al. [2019], Yang et al. [2020], Guo & Yuan [2020], Zhang et al. [2020i, d], Park et al. [2020], Song et al. [2020b], Fang et al. [2020b], Pian & Wu [2020], Jin et al. [2020b], Xu & Li [2019], Wu et al. [2020a], Wright et al. [2019 郑等人。 2020b，潘等人。 2020、2019，黄等人。 2020a，Kong 等人。 2020，Zhang 和Guo 2020，Tang 等人。 2020b，康等人。 2019，吴等人。 2018a，Wei & Shen 2020，Yin 等人。 2020，谢等人。 2020d，张等人。 2020h，Tian 等人。 2020，He & Shin 2020b，Tang 等人。 2020a，张等人。 2019a，Cirstea 等人。 2019，杨等人。 2020，Guo & Yuan 2020，Zhang 等人。 2020i、d、Park 等人。 2020，宋等人。 2020b，方等人。 2020b，Pian & Wu 2020，Jin 等人。 2020b，Xu & Li 2019，Wu 等人。 2020a，赖特等人。 2019年]

During the process of customizing GNNs for traffic forecasting, some classical models stand out in the literature. The most famous one is diffusion convolutional recurrent neural network (DCRNN) [Li et al., 2018b], which uses diffusion graph convolutional networks and RNN to learn the representations of spatial dependencies and temporal relations. DCRNN was originally proposed for traffic speed forecasting and is now widely used as a baseline. To create the traffic graph, the adjacency matrix is defined as the thresholded pairwise road network distances. Compared with other graph convolutional models that can only operate on undirected graphs, e.g., ChebNet, DCRNN introduces the diffusion convolution (DC) operation for directed graph and is more suitable for transportation scenarios, which is defined as follows:
在定制 GNN 用于流量预测的过程中，一些经典模型在文献中脱颖而出。最著名的是扩散卷积循环神经网络（DCRNN）[Li et al., 2018b]，它使用扩散图卷积网络和 RNN 来学习空间依赖性和时间关系的表示。 DCRNN 最初被提出用于交通速度预测，现在被广泛用作基线。为了创建交通图，邻接矩阵被定义为阈值成对道路网络距离。与其他只能在无向图上操作的图卷积模型（例如ChebNet）相比，DCRNN引入了有向图的扩散卷积（DC）操作，更适合交通场景，其定义如下：

\mathbf{X}_{*DC}=\sum_{k=0}^{K-1}(\theta_{k,1}(D_{O}^{-1}A)^{k})+\theta_{k,2}(D_{I}^{-1}A^{T})^{k})\mathbf{X}

(6)

where $\mathbf{X}\in{R}^{N\times d}$ is the node feature matrix, $A$ is the adjacency matrix, $D_{O}$ and $D_{I}$ are diagonal out-degree and in-degree matrices, $\theta_{k,1}$ and $\theta_{k,2}$ are model parameters, $K$ is the number of diffusion steps. By defining and using out-degree and in-degree matrices, DCRNN models the bidirectional diffusion process to capture the influence of both upstream and downstream traffic. While DCRNN is a strong baseline, it is not suitable or desirable for the undirected graph cases. Then DCRNN is extended with a stronger learning ability in graph GRU in Zhang et al. [2018a], in which a unified method for constructing an RNN based on an arbitrary graph convolution operator is proposed, instead of the single RNN model used in DCRNN.
其中 $\mathbf{X}\in{R}^{N\times d}$ 是节点特征矩阵， $A$ 是邻接矩阵， $D_{O}$ 和 $D_{I}$ 是对角线出度和入度矩阵， $\theta_{k,1}$ 和 $\theta_{k,2}$ 是模型参数， $K$ 是扩散步数。通过定义和使用出度和入度矩阵，DCRNN 对双向扩散过程进行建模，以捕获上游和下游流量的影响。虽然 DCRNN 是一个强大的基线，但它不适合或不适合无向图情况。然后，Zhang 等人在图 GRU 中对 DCRNN 进行了扩展，使其具有更强的学习能力。 [2018a]，其中提出了一种基于任意图卷积算子构建 RNN 的统一方法，而不是 DCRNN 中使用的单一 RNN 模型。

Spatio-temporal graph convolutional network (STGCN) [Yu et al., 2018] stacks multiple spatio-temporal convolution blocks and each block concatenate two temporal convolution and one graph convolution layer. ChebNet is chosen as the graph convolution operator in STGCN, after a comparison with its first-order approximation. The usage of temporal convolution layers instead of RNNs for temporal modeling accelerates the training phase of STGCN. Attention based Spatio-temporal graph convolutional network (ASTGCN) [Guo et al., 2019c] further introduces two attention layers in STGCN to capture the dynamic correlations in spatial dimension and temporal dimension, respectively.
时空图卷积网络（STGCN）[Yu et al., 2018]堆叠多个时空卷积块，每个块连接两个时间卷积和一个图卷积层。在与其一阶近似值进行比较后，选择 ChebNet 作为 STGCN 中的图卷积算子。使用时间卷积层而不是 RNN 进行时间建模加速了 STGCN 的训练阶段。基于注意力的时空图卷积网络（ASTGCN）[Guo et al., 2019c]进一步在 STGCN 中引入两个注意力层，分别捕获空间维度和时间维度的动态相关性。

Graph WaveNet [Wu et al., 2019] constructs a self-adaptive matrix to uncover unseen graph structures automatically from the data and WaveNet, which is based on causal convolutions, is used to learn temporal relations. However, the self-adaptive matrix in Graph WaveNet is fixed after training, which is unable to be adjusted dynamically with the data characteristics.
Graph WaveNet [Wu et al., 2019] 构造一个自适应矩阵，从数据中自动发现看不见的图结构，并且基于因果卷积的 WaveNet 用于学习时间关系。然而Graph WaveNet中的自适应矩阵在训练后是固定的，无法随数据特征动态调整。

5 Open Data and Source Codes
5开放数据和源代码

In this section, we summarize the open data and source code used in the surveyed papers. These open data are suitable for GNN-related studies with graph structures discussed in Section IV, which can be used to formulate different forecasting problems in Section III. We also list the GNN-related code resources for those who want to replicate the previous GNN-based solutions as baselines in the follow-up studies.
在本节中，我们总结了调查论文中使用的开放数据和源代码。这些开放数据适用于第四节中讨论的具有图结构的 GNN 相关研究，可用于制定第三节中的不同预测问题。我们还列出了 GNN 相关的代码资源，供那些想要复制之前基于 GNN 的解决方案的人作为后续研究的基线。

5.1 Open Data 5.1开放数据

We categorize the data used in the surveyed studies into three major types, namely, graph-related data, historical traffic data, and external data. Graph-related data refer to those data which exhibit a graph structure in the traffic domain, i.e., transportation network data. Historical traffic data refer to those data which record the historical traffic states, usually in different locations and time points. We further categorize the historical traffic data into sub-types as follows. External data refer to the factors that would affect the traffic states, i.e., weather data and calendar data. Some of these data can be used in the graph-based modeling directly, while the others may require some pre-processing steps before being Incorporated into GNN-based models.
我们将调查研究中使用的数据分为三大类，即图形相关数据、历史流量数据和外部数据。图相关数据是指在交通领域呈现出图结构的数据，即交通网络数据。历史交通数据是指记录历史交通状况的数据，通常是不同地点和时间点的交通状况。我们将历史流量数据进一步分类为以下子类型。外部数据是指影响交通状况的因素，例如天气数据和日历数据。其中一些数据可以直接用于基于图的建模，而其他数据可能需要一些预处理步骤才能合并到基于 GNN 的模型中。

Transportation Network Data. These data represent the underlying transportation infrastructure, e.g., road, subway, and bus networks. They can be obtained from government transportation departments or extracted from online map services, e.g., OpenStreetMap. Based on their topology structure, these data can be used to build the graphs directly, e.g., the road segments or the stations are nodes and the road intersections or subway links are the edges. While this modeling approach is straightforward, the disadvantage is that only static graphs can be built from transportation network data.
交通网络数据。这些数据代表了底层的交通基础设施，例如道路、地铁和公交网络。它们可以从政府交通部门获得或从在线地图服务（例如 OpenStreetMap）中提取。基于它们的拓扑结构，这些数据可以直接用来构建图，例如，路段或车站是节点，道路交叉口或地铁线路是边。虽然这种建模方法很简单，但缺点是只能根据交通网络数据构建静态图。

Traffic Sensor Data. Traffic sensors, e.g. loop detectors, are installed on roads to collect traffic information, e.g., traffic volume or speed. This type of data is widely used for traffic prediction, especially road traffic flow and speed prediction problems. For graph-based modeling, each sensor can be used as a node, with road connections as the edges. One advantage of using traffic sensor data for graph-based modeling is that the captured traffic information can be used directly as the node attributes, with little pre-processing overhead. One exception is that the sensors are prone to hardware faults, which causes the missing data or data noise problems and requires corresponding pre-processing techniques, e.g., data imputation and denoising methods. Another disadvantage of using traffic sensor data for graph-based modeling is that the traffic sensors can only be installed in a limited number of locations for a series of reasons, e.g., installation cost. With this constraint, only the part of the road networks with traffic sensors can be incorporated into a graph, while the uncovered areas are neglected.
交通传感器数据。交通传感器，例如环路探测器安装在道路上以收集交通信息，例如交通量或速度。此类数据广泛用于交通预测，特别是道路交通流量和速度预测问题。对于基于图的建模，每个传感器都可以用作节点，道路连接作为边缘。使用交通传感器数据进行基于图的建模的优点之一是捕获的交通信息可以直接用作节点属性，而预处理开销很小。一种例外是传感器容易出现硬件故障，从而导致数据丢失或数据噪声问题，需要相应的预处理技术，例如数据插补和去噪方法。使用交通传感器数据进行基于图的建模的另一个缺点是，由于安装成本等一系列原因，交通传感器只能安装在有限数量的位置。在这种限制下，只有带有交通传感器的道路网络部分可以纳入图表中，而未覆盖的区域将被忽略。

GPS Trajectory Data. Different types of vehicles (e.g. taxis, buses, online ride-hailing vehicles, and shared bikes) can be equipped with GPS receivers, which record GPS coordinates in 2-60 second intervals. The trajectory data calculated from these GPS coordinate samples can be matched to road networks and further used to derive traffic flow or speed. The advantage of using GPS trajectory data for graph-based modeling is both the low expense to collect GPS data with smartphones and the wider coverage with the massive number of vehicles, compared with traffic sensor data. However, GPS trajectory data contain no direct traffic information, which can be derived with corresponding definitions though. The data quality problems also remain with GPS trajectory data and more pre-processing steps are required, e.g., map matching.
GPS 轨迹数据。不同类型的车辆（例如出租车、公交车、网约车、共享单车）可以配备GPS接收器，以2-60秒的间隔记录GPS坐标。根据这些 GPS 坐标样本计算出的轨迹数据可以与道路网络相匹配，并进一步用于推导出交通流量或速度。与交通传感器数据相比，使用 GPS 轨迹数据进行基于图形的建模的优势在于，通过智能手机收集 GPS 数据的费用较低，而且覆盖范围更广，可以覆盖大量车辆。然而，GPS轨迹数据不包含直接的交通信息，但可以通过相应的定义导出。 GPS轨迹数据也存在数据质量问题，需要更多的预处理步骤，例如地图匹配。

Location-based Service Data. GPS function is also embedded in smartphones, which can be used to collect various types of location-related data, e.g., check-in data, point-of-interest data, and route navigation application data. The pros and cons of using location-based service data are similar with GPS trajectory data. And the difference is that location-based service data are often collected in a crowd-sourced approach, with more data providers but potentially a lower data quality.
基于位置的服务数据。智能手机中还嵌入了GPS功能，可用于收集各种类型的位置相关数据，例如签到数据、兴趣点数据和路线导航应用数据。使用基于位置的服务数据的优点和缺点与 GPS 轨迹数据类似。不同之处在于，基于位置的服务数据通常以众包方式收集，数据提供者更多，但数据质量可能较低。

Trip Record Data. These include departure and arrival dates/times, departure and arrival locations, and other trip information. Traffic speed and demand can derived from trip record data from various sources, e.g., taxis, ride-hailing services, buses, bikes, or even dock-less e-scooters used in He & Shin [2020a]. These data can be collected in public transportation systems with mature methods, for example, by AFC (Automatic Fare Collection) in the subway and bus systems. Trip record data have the advantage of being capable of constructing multiple graph-based problems, e.g., station-level traffic flow and demand problems. They are also easier to collect in existing public transportation systems.
行程记录数据。其中包括出发和到达日期/时间、出发和到达地点以及其他旅行信息。交通速度和需求可以从各种来源的行程记录数据中得出，例如出租车、叫车服务、公共汽车、自行车，甚至 He & Shin [2020a] 中使用的无桩电动滑板车。这些数据可以通过成熟的方法在公共交通系统中收集，例如地铁和公交系统中的AFC（自动售检票）。行程记录数据的优点是能够构建多个基于图的问题，例如车站级交通流和需求问题。它们也更容易在现有的公共交通系统中收集。

Traffic Report Data. This type of data is often used for abnormal cases, e.g., anomaly report data used in Liu et al. [2020c] and traffic accident report data used in Zhou et al. [2020e], Zhang et al. [2020k], Zhou et al. [2020f]. Traffic report data are less used in graph-based modeling because of their sparsity in both spatial and temporal dimensions, compared with trip record data.
交通报告数据。此类数据通常用于异常情况，例如 Liu 等人使用的异常报告数据。 [2020c] 以及 Zhou 等人使用的交通事故报告数据。 [2020e]，Zhang 等人。 [2020k]，Zhou 等人。 [2020f]。与行程记录数据相比，交通报告数据由于在空间和时间维度上的稀疏性而较少用于基于图的建模。

Multimedia Data. This type of data can be used as an additional input to deep learning models or for verifying the traffic status indicated by other data sources. Multimedia data used in the surveyed studies include the Baidu street-view images used in Qin et al. [2020a] for traffic congestion, as well as satellite imagery data [Zhang et al., 2020k], and video surveillance data [Shao et al., 2020]. Multimedia data are also less seen in graph-based modeling because of their higher requirement for data collection, transmission and storage, compared with traffic sensor data with similar functionalities. It is also more difficult to extract precise traffic information, e.g., vehicle counts, from images or videos through image processing and object detection techniques.
多媒体数据。此类数据可用作深度学习模型的附加输入或用于验证其他数据源指示的流量状态。调查研究中使用的多媒体数据包括Qin等人使用的百度街景图像。 [2020a] 交通拥堵情况，以及卫星图像数据 [Zhang et al., 2020k] 和视频监控数据 [Shao et al., 2020]。多媒体数据在基于图的建模中也较少出现，因为与具有类似功能的交通传感器数据相比，多媒体数据对数据收集、传输和存储的要求更高。通过图像处理和目标检测技术从图像或视频中提取精确的交通信息（例如车辆数量）也更加困难。

Simulated Traffic Data. In addition to observed real-world datasets, microscopic traffic simulators are also used to build virtual training and testing datasets for deep learning models. Examples in the surveyed studies include the MATES Simulator used in Fukuda et al. [2020] and INTEGRATION software used in Ramadan et al. [2020]. With many real-world datasets available, simulated traffic data are rarely used in GNN-based and more broader ML-based traffic forecasting studies. Traffic simulations have the potential of modeling unseen graphs though, e.g., evaluating a planned road topology.
模拟交通数据。除了观察到的现实世界数据集之外，微观交通模拟器还用于为深度学习模型构建虚拟训练和测试数据集。调查研究中的例子包括 Fukuda 等人使用的 MATES Simulator。 [ 2020] 和 Ramadan 等人使用的 INTEGRATION 软件。 [2020]。由于有许多现实世界的数据集可用，模拟交通数据很少用于基于 GNN 和更广泛的基于 ML 的交通预测研究。不过，交通模拟具有对看不见的图形进行建模的潜力，例如评估规划的道路拓扑。

Weather Data. Traffic states are highly affected by the meteorological factors including temperature, humidity, precipitation, barometer pressure, and wind strength.
天气数据。交通状况受温度、湿度、降水、气压、风力等气象因素影响较大。

Calendar Data. This includes the information on weekends and holidays. Because traffic patterns vary significantly between weekdays and weekends/holidays, some studies consider these two cases separately. Both weather and calendar data have been proven useful for traffic forecasting in the literature and should not be neglected in graph-based modeling as external factors.
日历数据。这包括周末和节假日的信息。由于工作日和周末/节假日之间的流量模式差异很大，因此一些研究分别考虑这两种情况。文献中已证明天气和日历数据对于交通预测有用，并且在基于图形的建模中不应作为外部因素而被忽视。

While present road network and weather data can be easily found on the Internet, it is much more difficult to source historical traffic data, both due to data privacy concerns and the transmission and storage requirements of large data volumes. In Table 6 we present a list of the open data resources used in the surveyed studies. Most of these open data are already cleaned or preprocessed and can be readily used for benchmarking and comparing the performance of different models in future work.
虽然当前的路网和天气数据可以很容易地在互联网上找到，但由于数据隐私问题以及大数据量的传输和存储要求，获取历史交通数据要困难得多。在表 6 中，我们列出了调查研究中使用的开放数据资源。大多数开放数据已经过清理或预处理，可以在未来的工作中轻松用于基准测试和比较不同模型的性能。

Table 6: Open data for traffic prediction problems.
表 6：交通预测问题的开放数据。

Dataset Name 数据集名称	Relevant Studies 相关研究
METR-LA	Li et al. [2018b], Wu et al. [2019], Xu et al. [2020a], Pan et al. [2020, 2019], Lu et al. [2019a], Zhang et al. [2020e], Wang et al. [2020g], Zhang & Guo [2020], Boukerche & Wang [2020b], Cao et al. [2020], Yu et al. [2019b], Li & Zhu [2021], Tian et al. [2020], Chen et al. [2020d], Bai et al. [2021], Zhang et al. [2018a], Cirstea et al. [2019], Shleifer et al. [2019], Yang et al. [2020], Chen et al. [2019], Wang et al. [2020f], Cui et al. [2020b], Zhou et al. [2020a], Cai et al. [2020], Zhou et al. [2020b], Wu et al. [2020c], Chen et al. [2020f], Opolka et al. [2019], Oreshkin et al. [2021], Jia et al. [2020], Zhang et al. [2020i], Feng et al. [2020], Xie et al. [2020c], Park et al. [2020], Song et al. [2020b] 李等人。 2018b，吴等人。 2019，徐等人。 2020a，潘等人。 2020、2019，Lu 等人。 2019a，张等人。 2020e，Wang 等人。 2020g，Zhang 和Guo 2020，Boukerche 和Wang 2020b，Cao 等人。 2020，Yu 等人。 2019b，Li & Zhu 2021，Tian 等人。 2020，陈等人。 2020d，Bai 等人。 2021，张等人。 2018a，Cirstea 等人。 2019，Shleifer 等人。 2019，杨等人。 2020，陈等人。 2019，王等人。 2020f，崔等人。 2020b，Zhou 等人。 2020a，蔡等人。 2020，Zhou 等人。 2020b，吴等人。 2020c，陈等人。 2020f，Opolka 等人。 2019，奥列什金等人。 2021，贾等人。 2020，张等人。 2020i，冯等人。 2020，谢等人。 2020c，Park 等人。 2020，宋等人。 2020b
PeMS all 全部PEMS	Mallick et al. [2020, 2021 马利克等人。 2020, 2021]
PeMS-BAY	Li et al. [2018b], Wu et al. [2019], Zheng et al. [2020b], Pan et al. [2020, 2019], Xu et al. [2020b], Wang et al. [2020g], Zhang & Guo [2020], Boukerche & Wang [2020b], Li et al. [2020f], Cao et al. [2020], Xie et al. [2020d], Li & Zhu [2021], Tian et al. [2020], Shleifer et al. [2019], Chen et al. [2019], Yu et al. [2019a], Wang et al. [2020f], Cui et al. [2020b], Zhou et al. [2020a], Cai et al. [2020], Zhou et al. [2020b], Wu et al. [2020c], Chen et al. [2020f], Oreshkin et al. [2021], Guo & Yuan [2020], Zhang et al. [2020i], Feng et al. [2020], Xie et al. [2020c], Park et al. [2020], Song et al. [2020b 李等人。 2018b，吴等人。 2019，郑等人。 2020b，潘等人。 2020、2019，Xu 等人。 2020b，王等人。 2020g，Zhang 和Guo 2020，Boukerche 和Wang 2020b，Li 等人。 2020f，曹等人。 2020，谢等人。 2020d，Li & Zhu 2021，Tian 等人。 2020，Shleifer 等人。 2019，陈等人。 2019，Yu 等人。 2019a，王等人。 2020f，崔等人。 2020b，Zhou 等人。 2020a，蔡等人。 2020，Zhou 等人。 2020b，吴等人。 2020c，陈等人。 2020f，奥列什金等人。 2021，Guo & Yuan 2020，Zhang 等人。 2020i，冯等人。 2020，谢等人。 2020c，Park 等人。 2020，宋等人。 2020b]
PeMSD3	Song et al. [2020a], Cao et al. [2020], Chen et al. [2020g], Wang et al. [2020a], Li & Zhu [2021 宋等人。 2020a，曹等人。 2020，陈等人。 2020g，王等人。 2020a，李朱2021]
PeMSD4	Bai et al. [2020], Huang et al. [2020a], Zhang et al. [2020e], Song et al. [2020a], Chen et al. [2020e], Tang et al. [2020b], Guo et al. [2019c], Li et al. [2019b], Wei & Sheng [2020], Cao et al. [2020], Li et al. [2020b], Yin et al. [2020], Zhang et al. [2020a], Wang et al. [2020a], Xin et al. [2020], Huang et al. [2020b], Guo et al. [2020b], Li & Zhu [2021], Xu et al. [2020c], Chen et al. [2020c], Ge et al. [2019a, b, 2020], Zhao et al. [2020b 白等人。 2020，黄等人。 2020a，张等人。 2020e，宋等人。 2020a，陈等人。 2020e，唐等人。 2020b，郭等人。 2019c，Li 等人。 2019b，Wei & Shen 2020，Cao 等人。 2020，李等人。 2020b，尹等人。 2020，张等人。 2020a，王等人。 2020a，Xin 等人。 2020，黄等人。 2020b，郭等人。 2020b，Li & Zhu 2021，Xu 等人。 2020c，陈等人。 2020c，Ge 等人。 2019a、b、2020，Zhao 等人。 2020b]
PeMSD7	Zhang et al. [2020j], Huang et al. [2020a], Song et al. [2020a], Xu et al. [2020b], Tang et al. [2020b], Sun et al. [2020], Cao et al. [2020], Yu et al. [2018, 2019b], Chen et al. [2020g], Wang et al. [2020a], Xin et al. [2020], Xie et al. [2020d], Li & Zhu [2021], Zhang et al. [2019a], Ge et al. [2019a, b, 2020], Yu et al. [2019a], Zhao et al. [2020b 张等人。 2020j，黄等人。 2020a，宋等人。 2020a，Xu 等人。 2020b，唐等人。 2020b，Sun 等人。 2020，曹等人。 2020，Yu 等人。 2018、2019b，陈等人。 2020g，王等人。 2020a，Xin 等人。 2020，谢等人。 2020d，Li & Zhu 2021，Zhang 等人。 2019a，Ge 等人。 2019a、b、2020，Yu 等人。 2019a，赵等人。 2020b]
PeMSD8	Bai et al. [2020], Huang et al. [2020a], Song et al. [2020a], Chen et al. [2020e], Guo et al. [2019c], Wei & Sheng [2020], Cao et al. [2020], Li et al. [2020b], Yin et al. [2020], Zhang et al. [2020a], Wang et al. [2020a], Guo et al. [2020b], Li & Zhu [2021 白等人。 2020，黄等人。 2020a，宋等人。 2020a，陈等人。 2020e，郭等人。 2019c，Wei & Shen 2020，Cao 等人。 2020，李等人。 2020b，尹等人。 2020，张等人。 2020a，王等人。 2020a，郭等人。 2020b，李朱 2021]
Seattle Loop 西雅图环线	Cui et al. [2019, 2020a], Sun et al. [2021], Lewenfus et al. [2020 崔等人。 2019、2020a，Sun 等人。 2021，Lewenfus 等人。 2020年]
T-Drive	Pan et al. [2020, 2019 潘等人。 2020, 2019]
SHSpeed	Zhang et al. [2020j], Wang et al. [2018b], Guo et al. [2019a 张等人。 2020j，王等人。 2018b，郭等人。 2019a]
TaxiBJ	Zhang et al. [2020h], Wang et al. [2018a], Bai et al. [2019b 张等人。 2020h，王等人。 2018a，Bai 等人。 2019b]
TaxiSZ	Bai et al. [2021], Zhao et al. [2019 白等人。 2021，赵等人。 2019年]
TaxiCD	Hu et al. [2018, 2020 胡等人。 2018, 2020]
TaxiNYC	Zhang et al. [2020h], Sun et al. [2020], Zhou et al. [2019], Hu et al. [2018], Jin et al. [2020b], Li & Axhausen [2020], Zheng et al. [2020a], Xu & Li [2019], Davis et al. [2020], Du et al. [2020], Li & Moura [2020], Ye et al. [2021], Zhou et al. [2020f 张等人。 2020h，Sun 等人。 2020，Zhou 等人。 2019，胡等人。 2018，金等人。 2020b，Li & Axhausen 2020，Zheng 等人。 2020a，Xu & Li 2019，Davis 等人。 2020，杜等人。 2020，Li & Moura 2020，Ye 等人。 2021，Zhou 等人。 2020年f]
UberNYC	Jin et al. [2020b], Ke et al. [2021a 金等人。 2020b，Ke 等人。 2021a]
DiDiChengdu	Zhang et al. [2019d], Qu et al. [2020], Wang et al. [2020b], Zhou et al. [2019], Wang et al. [2020h], Bogaerts et al. [2020], Li et al. [2020c 张等人。 2019d，Qu 等人。 2020，王等人。 2020b，Zhou 等人。 2019，王等人。 2020h，Bogaerts 等人。 2020，李等人。 2020c]
DiDiTTIChengdu	Lu et al. [2020a 卢等人。 2020年a]
DiDiXi’an 滴滴西安	Qu et al. [2020], Bogaerts et al. [2020 曲等人。 2020，博加茨等人。 2020年]
DiDiHaikou	Pian & Wu [2020], Jin et al. [2020a Pian & Wu 2020，Jin 等人。 2020年a]
BikeDC	Sun et al. [2020], Wang et al. [2020d 孙等人。 2020，王等人。 2020d]
BikeNYC	Zhang et al. [2020h], Sun et al. [2020], Wang et al. [2018a], He & Shin [2020b], Chai et al. [2018], Lee et al. [2019], Bai et al. [2019b], Du et al. [2020], Ye et al. [2021], Wang et al. [2020d], Guo et al. [2019b], Lin et al. [2018 张等人 2020h，王等人 2018a，He 等人 2018，李等人 2019b，杜等人 2020 .2021，Wang 等人 2020d，Guo 等人 2019b，Lin 等人 2018]
BikeChicago	Chai et al. [2018 柴等人。 2018年]
SHMetro	Liu et al. [2020b 刘等人。 2020b]
HZMetro	Liu et al. [2020b 刘等人。 2020b]

5.1.1 Traffic Sensor Data 5.1.1交通传感器数据

The relevant open traffic sensor data are listed as follows.
相关开放交通传感器数据如下。

METR-LA ²²2Download link: https://github.com/liyaguang/DCRNN: This dataset contains traffic speed and volume collected from the highway of the Los Angeles County road network, with 207 loop detectors. The samples are aggregated in 5-minute intervals. The most frequently referenced time period for this dataset is from March 1st to June 30th, 2012.
METR-LA ² ：该数据集包含从洛杉矶县公路网的高速公路收集的交通速度和流量，有 207 个环路检测器。样本每隔 5 分钟聚合一次。该数据集最常被引用的时间段是2012年3月1日至6月30日。

Performance Measurement System (PeMS) Data ³³3http://pems.dot.ca.gov/: This dataset contains raw detector data from over 18,000 vehicle detector stations on the freeway system spanning all major metropolitan areas of California from 2001 to 2019, collected with various sensors including inductive loops, side-fire radar, and magnetometers. The samples are captured every 30 seconds and aggregated in 5-minute intervals. Each data sample contains a timestamp, station ID, district, freeway ID, direction of travel, total flow, and average speed. Different subsets of PeMS data have been used in previous studies, for example:
性能测量系统 (PeMS) 数据 ³ ：该数据集包含 2001 年至 2019 年跨越加州所有主要大都市区的高速公路系统上 18,000 多个车辆检测站的原始检测器数据，通过包括感应环路在内的各种传感器收集、侧射雷达和磁力计。每 30 秒捕获一次样本，并以 5 分钟的间隔进行聚合。每个数据样本包含时间戳、站点 ID、区域、高速公路 ID、行驶方向、总流量和平均速度。之前的研究中已经使用了 PeMS 数据的不同子集，例如：

1.

PeMS-BAY ⁴⁴4Download link: https://github.com/liyaguang/DCRNN: This subset contains data from 325 sensors in the Bay Area from January 1st to June 30th, 2017.

1. PeMS-BAY ⁴ ：该子集包含2017年1月1日至6月30日湾区325个传感器的数据。
2.

PeMSD3: This subset uses 358 sensors in the North Central Area. The frequently referenced time period for this dataset is September 1st to November 30th, 2018.

2. PeMSD3：该子集在中北部区域使用 358 个传感器。该数据集经常引用的时间段是2018年9月1日至11月30日。
3.

PeMSD4: This subset uses 307 sensors in the San Francisco Bay Area. The frequently referenced time period for this dataset is January 1st to February 28th, 2018.

3. PeMSD4：该子集使用旧金山湾区的 307 个传感器。该数据集经常引用的时间段是2018年1月1日至2月28日。
4.

PeMSD7: This subset uses 883 sensors in the Los Angeles Area. The frequently referenced time period for this dataset is May to June, 2012.

4. PeMSD7：该子集在洛杉矶地区使用 883 个传感器。该数据集经常被引用的时间段是 2012 年 5 月至 6 月。
5.

PeMSD8: This subset uses 170 sensors in the San Bernardino Area. The frequently referenced time period for this dataset is July to August, 2016.

5. PeMSD8：该子集在圣贝纳迪诺地区使用 170 个传感器。该数据集经常被引用的时间段是 2016 年 7 月至 8 月。

Seattle Loop ⁵⁵5Download link: https://github.com/zhiyongc/Seattle-Loop-Data: This dataset was collected by inductive loop detectors deployed on four connected freeways (I-5, I-405, I-90, and SR-520) in the Seattle area, from January 1st to 31st, 2015. It contains the traffic speed data from 323 detectors. The samples are aggregated in 5-minute intervals.
西雅图环路 ⁵ ：该数据集由部署在西雅图地区四条相连高速公路（I-5、I-405、I-90 和 SR-520）上的感应环路检测器收集，时间为 1 月 1 日至2015年3月31日。它包含来自323个探测器的交通速度数据。样本每隔 5 分钟聚合一次。

5.1.2 Taxi Data 5.1.2出租车数据

The open taxi datasets used in the surveyed studies are listed as follows.
调查研究中使用的开放出租车数据集如下。

T-drive [Yuan et al., 2010]: This dataset contains a large number of taxicab trajectories collected by 30,000 taxis in Beijing from February 1st to June 2nd, 2015.
T-drive [Yuan et al., 2010]：该数据集包含 2015 年 2 月 1 日至 6 月 2 日期间北京 30,000 辆出租车收集的大量出租车轨迹。

SHSpeed (Shanghai Traffic Speed) [Wang et al., 2018b] ⁶⁶6Download link: https://github.com/xxArbiter/grnn: This dataset contains 10-minute traffic speed data, derived from raw taxi trajectory data, collected from 1 to 30 April 2015, for 156 urban road segments in the central area of Shanghai, China.
SHSpeed（上海交通速度）[Wang et al., 2018b] ⁶ ：该数据集包含 10 分钟交通速度数据，源自原始出租车轨迹数据，收集时间为 2015 年 4 月 1 日至 30 日，涉及 156 个城市中国上海市中心区的路段。

TaxiBJ [Zhang et al., 2017]: This dataset contains inflow and outflow data derived from GPS data in more than 34,000 taxicabs in Beijing from four time intervals: (1) July 1st to October 30th, 2013; (2) March 1st to June 30th, 2014; (3) March 1st to June 30th, 2015; and (4) November 1st, 2015 to April 10th, 2016. The Beijing city map is divided into $32\times 32$ grids and the time interval of the flow data is 30 minutes.
TaxiBJ [Zhang et al., 2017]：该数据集包含从四个时间间隔北京 34,000 多辆出租车的 GPS 数据得出的流入和流出数据：(1) 2013 年 7 月 1 日至 10 月 30 日；（二）2014年3月1日至6月30日；（三）2015年3月1日至6月30日； (4)2015年11月1日至2016年4月10日。北京市地图分为 $32\times 32$ 个网格，流量数据的时间间隔为30分钟。

TaxiSZ [Zhao et al., 2019] ⁷⁷7Download link: https://github.com/lehaifeng/T-GCN: This dataset is derived from taxi trajectories in Shenzhen from January 1st to 31st, 2015. It contains the traffic speed on 156 major roads of the Luohu District every 15 minutes.
TaxiSZ [Zhao et al., 2019] ⁷ ：该数据集来源于2015年1月1日至31日深圳的出租车轨迹。它包含罗湖区156条主要道路每15分钟的交通速度。

TaxiCD ⁸⁸8 https://js.dclab.run/v2/cmptDetail.html?id=175: This dataset contains 1.4 billion GPS records from 14,864 taxis collected from August 3rd to 30th, 2014 in Chengdu, China. Each GPS record consists of a taxi ID, latitude, longitude, an indicator of whether the taxi is occupied, and a timestamp.
TaxiCD ⁸ ：该数据集包含 2014 年 8 月 3 日至 30 日在中国成都收集的 14,864 辆出租车的 14 亿条 GPS 记录。每个 GPS 记录由出租车 ID、纬度、经度、出租车是否被占用的指示符以及时间戳组成。

TaxiNYC⁹⁹9http://www.nyc.gov/html/tlc/html/about/trip_record_data.shtml: The taxi trip records in New York starting from 2009, in both yellow and green taxis. Each trip record contains pick-up and drop-off dates/times, pick-up and drop-off locations, trip distances, itemized fares, rate types, payment types, and driver-reported passenger counts.
TaxiNYC ⁹ ：从 2009 年开始的纽约出租车行程记录，包括黄色和绿色出租车。每条行程记录包含接送日期/时间、接送地点、行程距离、明细票价、费率类型、付款类型以及司机报告的乘客数量。

5.1.3 Ride-hailing Data 5.1.3网约车数据

The open ride-hailing data used in the surveyed studies are listed as follows.
调查研究中使用的开放网约车数据如下。

UberNYC ¹⁰¹⁰10https://github.com/fivethirtyeight/uber-tlc-foil-response: This dataset comes from Uber, which is one of the largest online ride-hailing companies in the USA, and is provided by the NYC Taxi & Limousine Commission (TLC). It contains data from over 4.5 million Uber pickups in New York City from April to September 2014, and 14.3 million more Uber pickups from January to June 2015.
UberNYC ¹⁰ ：该数据集来自 Uber（美国最大的在线叫车公司之一），由纽约市出租车和豪华轿车委员会 (TLC) 提供。它包含 2014 年 4 月至 9 月纽约市超过 450 万次 Uber 接载数据，以及 2015 年 1 月至 6 月另外 1,430 万次 Uber 接载数据。

Didi GAIA Open Data ¹¹¹¹11https://outreach.didichuxing.com/research/opendata/: This open data plan is supported by Didi Chuxing, which is one of the largest online ride-hailing companies in China.
滴滴 GAIA 开放数据 ¹¹ ：该开放数据计划由滴滴出行支持，滴滴出行是中国最大的在线叫车公司之一。

1.

DiDiChengdu: This dataset contains the trajectories of DiDi Express and DiDi Premier drivers within Chengdu, China. The data contains trips from October to November 2016.

1. 滴滴成都：该数据集包含滴滴快车和滴滴优享司机在中国成都境内的轨迹。该数据包含 2016 年 10 月至 11 月的行程。
2.

DiDiTTIChengdu: This dataset represents the DiDi Travel Time Index Data in Chengdu, China in the year of 2018, which contains the average speed of major roads every 10 minutes.

2.滴滴出行时间指数数据：该数据集代表2018年中国成都滴滴出行时间指数数据，包含主要道路每10分钟的平均速度。
3.

DiDiXi’an: This dataset contains the trajectories of DiDi Express and DiDi Premier drivers within Xi’an, China. The data contains trips from October to November 2016.

3.滴滴西安：该数据集包含滴滴快车和滴滴优享司机在中国西安市内的轨迹。该数据包含 2016 年 10 月至 11 月的行程。
4.

DiDiHaikou: The dataset contains DiDi Express and DiDi Premier orders from May 1st to October 31st, 2017 in the city of Haikou, China, including the coordinates of origins and destinations, pickup and drop-off timestamps, as well as other information.

4. 滴滴海口：该数据集包含2017年5月1日至10月31日在中国海口市的滴滴快车和滴滴优选订单，包括始发地和目的地坐标、接送时间戳等信息。

5.1.4 Bike Data 5.1.4自行车数据

The open bike data used in the surveyed studies are listed as follows.
调查研究中使用的开放式自行车数据如下。

BikeNYC ¹²¹²12 https://www.citibikenyc.com/system-data: This dataset is from the NYC Bike System, which contains 416 stations. The frequently referenced time period for this dataset is from 1st July, 2013 to 31th December, 2016.
BikeNYC ¹² ：此数据集来自 NYC Bike System，其中包含 416 个站点。该数据集经常被引用的时间段为2013年7月1日至2016年12月31日。

BikeDC ¹³¹³13 https://www.capitalbikeshare.com/system-data: This dataset is from the Washington D.C. Bike System, which contains 472 stations. Each record contains trip duration, start and end station IDs, and start and end times.
BikeDC ¹³ ：此数据集来自华盛顿特区自行车系统，其中包含 472 个站点。每条记录包含行程持续时间、起点和终点站 ID 以及起点和终点时间。

BikeChicago ¹⁴¹⁴14https://www.divvybikes.com/system-data: This dataset is from the Divvy System Data in Chicago, from 2015 to 2020.
BikeChicago ¹⁴ ：该数据集来自芝加哥的 Divvy 系统数据，时间为 2015 年至 2020 年。

5.1.5 Subway Data 5.1.5地铁数据

The subway data referenced in the surveyed studies are listed as follows.
调查研究引用的地铁数据如下。

SHMetro [Liu et al., 2020b] ¹⁵¹⁵15Download link: https://github.com/ivechan/PVCGN: This dataset is derived from 811.8 million transaction records of the Shanghai metro system collected from July 1st to September 30th, 2016. It contains 288 metro stations and 958 physical edges. The inflow and outflow of each station are provided in 15 minute intervals.
SHMetro [Liu et al., 2020b] ¹⁵ ：该数据集源自2016年7月1日至9月30日收集的上海地铁系统的8.118亿条交易记录。它包含288个地铁站和958条物理边。每个站的流入和流出每隔15分钟提供一次。

HZMetro [Liu et al., 2020b] ¹⁶¹⁶16Download link: https://github.com/ivechan/PVCGN: This dataset is similar to SHMetro, from the metro system in Hangzhou, China, in January 2019. It contains 80 metro stations and 248 physical edges, and the aggregation time length is also 15 minutes.
HZMetro [Liu et al., 2020b] ¹⁶ ：该数据集与 2019 年 1 月中国杭州地铁系统的 SHMetro 类似。它包含 80 个地铁站和 248 个物理边，并且聚合时间长度也是15分钟。

5.2 Open Source Codes 5.2开源代码

Several open source frameworks for implementing general deep learning models, most of which are built with the Python programming language, can be accessed online, e.g. TensorFlow ¹⁷¹⁷17https://www.tensorflow.org/, Keras ¹⁸¹⁸18https://keras.io/, PyTorch ¹⁹¹⁹19https://pytorch.org/, and MXNet ²⁰²⁰20https://mxnet.apache.org/. Additional Python libraries designed for implementing GNNs are available. These include DGL ²¹²¹21https://www.dgl.ai/, pytorch_geometric ²²²²22https://pytorch-geometric.readthedocs.io/, and Graph Nets ²³²³23https://github.com/deepmind/graph_nets.
可以在线访问几个用于实现通用深度学习模型的开源框架，其中大多数是使用 Python 编程语言构建的，例如TensorFlow ¹⁷ 、Keras ¹⁸ 、PyTorch ¹⁹ 和 MXNet ²⁰ 。还提供了专为实现 GNN 而设计的其他 Python 库。其中包括 DGL ²¹ 、 pytorch_geometric ²² 和 Graph Nets ²³ 。

Many authors have also released open-source implementations of their proposed models. The open source projects for traffic flow, traffic speed, traffic demand, and other problems are summarized in Tables 7, 8, 9, and 10, respectively. In these open source projects, TensorFlow and PyTorch are the two frameworks that are used most frequently.
许多作者还发布了他们提出的模型的开源实现。针对交通流量、交通速度、交通需求等问题的开源项目分别总结在表7、表8、表9、表10中。在这些开源项目中，TensorFlow和PyTorch是使用频率最高的两个框架。

Table 7: Open source projects for traffic flow related problems.
表 7：交通流相关问题的开源项目。

Article	Year	Framework	Problem	Link
Zheng et al. [2020b 郑等人。 2020b]	2020	TensorFlow	Road Traffic Flow, Road Traffic Speed 道路交通流量、道路交通速度	https://github.com/zhengchuanpan/GMAN
Bai et al. [2020 白等人。 2020年]	2020	PyTorch	Road Traffic Flow 道路交通流量	https://github.com/LeiBAI/AGCRN
Song et al. [2020a 宋等人。 2020年a]	2020	MXNet	Road Traffic Flow 道路交通流量	https://github.com/wanhuaiyu/STSGCN
Tang et al. [2020b 唐等人。 2020b]	2020	TensorFlow	Road Traffic Flow 道路交通流量	https://github.com/sam101340/GAGCN-BC-20200720
Wang et al. [2020a 王等人。 2020年a]	2020	MXNet, PyTorch MXNet、PyTorch	Road Traffic Flow 道路交通流量	https://github.com/zkx741481546/Auto-STGCN
Guo et al. [2020b 郭等人。 2020b]	2020	PyTorch	Road Traffic Flow, Road Traffic Speed 道路交通流量、道路交通速度	https://github.com/guokan987/DGCN
Li & Zhu [2021 李朱2021]	2020	MXNet	Road Traffic Flow, Road Traffic Speed 道路交通流量、道路交通速度	https://github.com/MengzhangLI/STFGNN
Tian et al. [2020 田等人。 2020年]	2020	PyTorch, DGL PyTorch、DGL	Road Traffic Flow 道路交通流量	https://github.com/Kelang-Tian/ST-MGAT
Xiong et al. [2020 熊等人。 2020年]	2020	TensorFlow	Road OD Flow 道路外径流量	https://github.com/alzmxx/OD_Prediction
Peng et al. [2020 彭等人。 2020年]	2020	Keras	Road Station-level Subway Passenger Flow, Station-level Bus Passenger Flow, Regional Taxi Flow 路站级地铁客流、站级公交客流、区域出租车流量	https://github.com/RingBDStack/GCNN-In-Traffic
Qiu et al. [2020 邱等人。 2020年]	2020	Pytorch	Regional Taxi Flow 区域出租车流量	https://github.com/Stanislas0/ToGCN-V2X
Yeghikyan et al. [2020 叶吉基安等人。 2020年]	2020	PyTorch	Regional OD Taxi Flow 区域 OD 出租车流量	https://github.com/FelixOpolka/Mobility-Flows-Neural-Networks
Zhang et al. [2020b 张等人。 2020b]	2020	Keras	Station-level Subway Passenger Flow 车站级地铁客流量	https://github.com/JinleiZhangBJTU/ResNet-LSTM-GCN
Zhang et al. [2020c 张等人。 2020c]	2020	Keras	Station-level Subway Passenger Flow 车站级地铁客流量	https://github.com/JinleiZhangBJTU/Conv-GCN
Liu et al. [2020b 刘等人。 2020b]	2020	PyTorch	Station-level Subway Passenger Flow 车站级地铁客流量	https://github.com/ivechan/PVCGN
Ye et al. [2020b 叶等人。 2020b]	2020	Keras	Station-level Subway Passenger Flow 车站级地铁客流量	https://github.com/start2020/Multi-STGCnet
Pan et al. [2019 潘等人。 2019年]	2019	MXNet, DGL MXNet、DGL	Road Traffic Flow, Road Traffic Speed 道路交通流量、道路交通速度	https://github.com/panzheyi/ST-MetaNet
Guo et al. [2019c 郭等人。 2019c]	2019	MXNet	Road Traffic Flow 道路交通流量	https://github.com/wanhuaiyu/ASTGCN
Guo et al. [2019c 郭等人。 2019c]	2019	PyTorch	Road Traffic Flow 道路交通流量	https://github.com/wanhuaiyu/ASTGCN-r-pytorch
Wang et al. [2018b 王等人。 2018b]	2018	PyTorch	Road Traffic Flow 道路交通流量	https://github.com/xxArbiter/grnn
Yu et al. [2018 于等人。 2018年]	2018	TensorFlow	Road Traffic Flow 道路交通流量	https://github.com/VeritasYin/STGCN_IJCAI-18
Li et al. [2018a 李等人。 2018年a]	2018	Keras	Station-level Subway Passenger Flow 车站级地铁客流量	https://github.com/RingBDStack/GCNN-In-Traffic
Chai et al. [2018 柴等人。 2018年]	2018	TensorFlow	Bike Flow 自行车流	https://github.com/Di-Chai/GraphCNN-Bike

Table 8: Open source projects for traffic speed related problems.
表 8：交通速度相关问题的开源项目。

Article	Year	Framework	Problem	Link
Zhang et al. [2020h 张等人。 2020小时]	2020	Keras	Road Traffic Speed 道路交通速度	https://github.com/jillbetty001/ST-CGA
Bai et al. [2021 白等人。 2021年]	2020	TensorFlow	Road Traffic Speed 道路交通速度	https://github.com/lehaifeng/T-GCN/tree/master/A3T
Yang et al. [2020 杨等人。 2020年]	2020	TensorFlow	Road Traffic Speed 道路交通速度	https://github.com/fanyang01/relational-ssm
Wu et al. [2020c 吴等人。 2020c]	2020	PyTorch	Road Traffic Speed 道路交通速度	https://github.com/nnzhan/MTGNN
Mallick et al. [2021 马利克等人。 2021年]	2020	TensorFlow	Road Traffic Speed 道路交通速度	https://github.com/tanwimallick/TL-DCRNN
Chen et al. [2020a 陈等人。 2020年a]	2020	PyTorch	Road Traffic Speed 道路交通速度	https://github.com/Fanglanc/DKFN
Lu et al. [2020a 卢等人。 2020年a]	2020	PyTorch	Road Traffic Speed 道路交通速度	https://github.com/RobinLu1209/STAG-GCN
Guopeng et al. [2020 郭鹏等. 2020年]	2020	TensorFlow, Keras TensorFlow、Keras	Road Traffic Speed 道路交通速度	https://github.com/RomainLITUD/DGCN_traffic_forecasting
Shen et al. [2020 沉等人。 2020年]	2020	PyTorch	Road Travel Time 公路旅行时间	https://github.com/YibinShen/TTPNet
Hong et al. [2020 洪等人。 2020年]	2020	TensorFlow	Time of Arrival 到达时间	https://github.com/didi/heteta
Wu et al. [2019 吴等人。 2019年]	2019	PyTorch	Road Traffic Speed 道路交通速度	https://github.com/nnzhan/Graph-WaveNet
Shleifer et al. [2019 施莱弗等人。 2019年]	2019	PyTorch	Road Traffic Speed 道路交通速度	https://github.com/sshleifer/Graph-WaveNet
Zhao et al. [2019 赵等人。 2019年]	2019	TensorFlow	Road Traffic Speed 道路交通速度	https://github.com/lehaifeng/T-GCN
Cui et al. [2019 崔等人。 2019年]	2019	TensorFlow	Road Traffic Speed 道路交通速度	https://github.com/zhiyongc/Graph_Convolutional_LSTM
Jepsen et al. [2019, 2020 杰普森等人。 2019, 2020]	2019	MXNet	Road Traffic Speed 道路交通速度	https://github.com/TobiasSkovgaardJepsen/relational-fusion-networks
Li et al. [2018b 李等人。 2018b]	2018	TensorFlow	Road Traffic Speed 道路交通速度	https://github.com/liyaguang/DCRNN
Li et al. [2018b 李等人。 2018b]	2018	PyTorch	Road Traffic Speed 道路交通速度	https://github.com/chnsh/DCRNN_PyTorch
Zhang et al. [2018a 张等人。 2018年a]	2018	MXNet	Road Traffic Speed 道路交通速度	https://github.com/jennyzhang0215/GaAN
Liao et al. [2018 廖等人。 2018年]	2018	TensorFlow	Road Traffic Speed 道路交通速度	https://github.com/JingqingZ/BaiduTraffic
Mohanty & Pozdnukhov [2018], Mohanty et al. [2020] Mohanty 和 Pozdnukhov 2018，Mohanty 等人。 2020年	2018	TensorFlow	Traffic Congestion 交通拥堵	https://github.com/sudatta0993/Dynamic-Congestion-Prediction

Table 9: Open source projects for traffic demand related problems.
表 9：流量需求相关问题的开源项目。

Article	Year	Framework	Problem	Link
Hu et al. [2020 胡等人。 2020年]	2020	TensorFlow	Taxi Demand 出租车需求	https://github.com/hujilin1229/od-pred
Davis et al. [2020 戴维斯等人。 2020年]	2020	TensorFlow, PyTorch TensorFlow、PyTorch	Taxi Demand 出租车需求	https://github.com/NDavisK/Grids-versus-Graphs
Ye et al. [2021 叶等人。 2021年]	2020	PyTorch	Taxi Demand, Bike Demand 出租车需求、自行车需求	https://github.com/Essaim/CGCDemandPrediction
Lee et al. [2019 李等人。 2019年]	2019	TensorFlow, Keras TensorFlow、Keras	Ride-hailing Demand, Bike Demand, Taxi Demand 网约车需求、自行车需求、出租车需求	https://github.com/LeeDoYup/TGGNet-keras
Ke et al. [2021b 柯等人。 2021b]	2019	Keras	Taxi Demand 出租车需求	https://github.com/kejintao/ST-ED-RMGC

Table 10: Open source projects for other problems.
表 10：其他问题的开源项目。

Article	Year	Framework	Problem	Link
Zhou et al. [2020e 周等人。 2020年预计]	2020	TensorFlow	Traffic Accident 交通意外	https://github.com/zzyy0929/AAAI2020-RiskOracle/
Yu et al. [2020b 于等人。 2020b]	2020	PyTorch, DGL PyTorch、DGL	Traffic Accident 交通意外	https://github.com/yule-BUAA/DSTGCN
Zhang et al. [2020f 张等人。 2020年f]	2020	PyTorch, DGL PyTorch、DGL	Parking Availability 停车位	https://github.com/Vvrep/SHARE-parking_availability_prediction-Pytorch
Wang et al. [2020c 王等人。 2020c]	2020	TensorFlow	Transportation Resilience 运输弹性	https://github.com/Charles117/resilience_shenzhen
Wright et al. [2019 赖特等人。 2019年]	2019	TensorFlow, Keras TensorFlow、Keras	Lane Occupancy 车道占用率	https://github.com/mawright/trafficgraphnn

5.3 State-of-the-art Performance
5.3最先进的性能

It is known that different works use different datasets and it is very hard to assess the relative performance of different state-of-the-art models [Tedjopurnomo et al., 2020]. Even for those studies using the same dataset, different subsets may be used. Different preprocessing techniques, e.g., the missing data imputation method, and different evaluation settings, e.g., the training/validation/test subset split ratio, also cause incomparable results. Considering these difficulties, we only summarize those comparable results for the most frequently used datasets from the surveyed studies in this part.
众所周知，不同的作品使用不同的数据集，并且很难评估不同最先进模型的相对性能 [Tedjopurnomo et al., 2020]。即使对于那些使用相同数据集的研究，也可能使用不同的子集。不同的预处理技术，例如缺失数据插补方法，以及不同的评估设置，例如训练/验证/测试子集分割比，也会导致无法比较的结果。考虑到这些困难，我们仅总结本部分调查研究中最常用数据集的可比结果。

Some commonly used evaluation metrics, namely, RMSE, MAE and MAPE, are defined as follows:
一些常用的评价指标，即RMSE、MAE和MAPE，定义如下：

1.

$\text{RMSE}(\mathbf{y},\mathbf{\hat{y}})=\sqrt{\frac{1}{M}\sum_{i=1}^{M}{(y_{i}-\hat{y}_{i})^{2}}}$ ;
2.

$\text{MAE}(\mathbf{y},\mathbf{\hat{y}})=\frac{1}{M}\sum_{i=1}^{M}|y_{i}-\hat{y}_{i}|$ ;
3.

$\text{MAPE}(\mathbf{y},\mathbf{\hat{y}})=\frac{1}{M}\sum_{i=1}^{M}\frac{|y_{i}-\hat{y}_{i}|}{y_{i}}$ ;

3. $\text{MAPE}(\mathbf{y},\mathbf{\hat{y}})=\frac{1}{M}\sum_{i=1}^{M}\frac{|y_{i}-\hat{y}_{i}|}{y_{i}}$ ；

where $\mathbf{y}$ denotes the true values, $\mathbf{\hat{y}}$ denotes the predicted values, and $M$ is the number of values to predict. A lower RMSE or MAE value indicates a better prediction performance. The summary for the state-of-the-art performance is shown in Table 11, with all or some of the above evaluation metrics and best values in bold. The default prediction time period is 60 minutes in Table 11 unless otherwise specified. Some classical baselines are also listed for comparison if available, e.g., DCRNN [Li et al., 2018b], STGCN [Yu et al., 2018] and Graph WaveNet [Wu et al., 2019]. Interested readers are recommended to check the experimental details in relevant studies.
其中 $\mathbf{y}$ 表示真实值， $\mathbf{\hat{y}}$ 表示预测值， $M$ 是要预测的值的数量。 RMSE 或 MAE 值越低表示预测性能越好。表 11 显示了最新性能的摘要，其中全部或部分上述评估指标和最佳值以粗体显示。除非另有说明，表 11 中的默认预测时间段为 60 分钟。如果有的话，还列出了一些经典基线进行比较，例如 DCRNN [Li et al., 2018b]、STGCN [Yu et al., 2018] 和 Graph WaveNet [Wu et al., 2019]。有兴趣的读者建议查看相关研究中的实验细节。

Table 11: State-of-the-art performance for traffic prediction problems.
表 11：交通预测问题的最先进性能。

Dataset	RMSE	MAE	MAPE	Relevant Studies 相关研究
METR-LA	7.59	3.60	10.5%	DCRNN
	7.40	3.55	10.0%	ST-UNet [Yu et al., 2019b] ST-UNet Yu 等人，2019b
	7.37	3.53	10.0%	Graph WaveNet 图波网
	7.20	3.30	9.7%	SLCNN [Zhang et al., 2020e] SLCNN 张等人，2020e
	6.68	3.28	9.08%	Traffic Transformer [Cai et al., 2020] 交通变压器蔡等人，2020
	6.40	3.18	8.81%	STFGNN [Li & Zhu, 2021] STFGNN 李和朱，2021
PeMS-BAY	4.74	2.07	4.9%	DCRNN
	4.53	2.03	4.8%	SLCNN [Zhang et al., 2020e] SLCNN 张等人，2020e
	4.52	1.95	4.63%	Graph WaveNet 图波网
	4.32	1.86	4.31%	GMAN [Zheng et al., 2020b] GMAN 郑等人，2020b
	4.36	1.77	4.29%	Traffic Transformer [Cai et al., 2020] 交通变压器蔡等人，2020
	3.74	1.66	3.77%	STFGNN [Li & Zhu, 2021] STFGNN 李和朱，2021
PeMSD3	30.31	18.18	18.91%	DCRNN
	30.12	17.49	17.15%	STGCN
	32.94	17.48	16.78%	Graph WaveNet 图波网
	28.34	16.77	16.30%	STFGNN [Li & Zhu, 2021] STFGNN 李和朱，2021
PeMSD4	39.70	25.45	17.29%	Graph WaveNet 图波网
	34.89	21.16	13.83%	STGCN
	33.44	21.22	14.17%	DCRNN
	32.26	19.83	12.97%	AGCRN [Bai et al., 2020] AGCRN Bai 等人，2020
	31.88	19.83	13.02%	STFGNN [Li & Zhu, 2021] STFGNN 李和朱，2021
PeMSD7	42.78	26.85	12.12%	Graph WaveNet 图波网
	38.78	25.38	11.08%	STGCN
	38.58	25.30	11.66%	DCRNN
	35.80	22.07	9.21%	STFGNN [Li & Zhu, 2021] STFGNN 李和朱，2021
PeMSD8	31.05	19.13	12.68%	Graph WaveNet 图波网
	27.09	17.50	11.29%	STGCN
	26.36	16.82	10.92%	DCRNN
	26.22	16.64	10.60%	STFGNN [Li & Zhu, 2021] STFGNN 李和朱，2021
	25.22	15.95	10.09%	AGCRN [Bai et al., 2020] AGCRN Bai 等人，2020
Seattle Loop 西雅图环线	8.22	4.64	11.18%	DCRNN
Seattle Loop 西雅图环线	3.59	2.45	5.90%	GLT-GCRNN [Sun et al., 2021] GLT-GCRNN Sun 等人，2021
TaxiSZ	4.76	3.38	N/A	Graph WaveNet 图波网
	4.64	3.31	N/A	DCRNN
	4.13	2.79	N/A	T-GCN [Zhao et al., 2019] T-GCN 赵等人，2019
	4.13	2.76	N/A	STGCN
	4.10	2.77	N/A	AST-GCN [Zhu et al., 2021] AST-GCN Zhu 等人，2021
	3.97	2.74	N/A	A3T-GCN [Bai et al., 2021] A3T-GCN Bai 等人，2021
TaxiNYC (30 min) 纽约出租车（30 分钟）	22.65	18.46	N/A	STGCN
	14.79	8.43	N/A	DCRNN
	13.07	8.10	N/A	Graph WaveNet 图波网
	9.56	5.50	N/A	CCRNN [Ye et al., 2021] CCRNN Ye 等人，2021
BikeNYC (30 min) 纽约自行车（30 分钟）	3.60	2.76	N/A	STGCN
	3.29	1.99	N/A	Graph WaveNet 图波网
	3.21	1.90	N/A	DCRNN
	2.84	1.74	N/A	CCRNN [Ye et al., 2021] CCRNN Ye 等人，2021

Since the relevant studies of applying GNNs for traffic forecasting are growing everyday, the results listed in this part are not guaranteed to be the latest ones and the readers are recommended to follow our Github repository to track latest results.
由于应用 GNN 进行流量预测的相关研究日益增多，本部分列出的结果不能保证是最新的，建议读者关注我们的 Github 存储库来跟踪最新结果。

6 Challenges and Future Directions
6挑战和未来方向

In this section, we discuss general challenges for traffic prediction problems as well as specific new challenges when GNNs are involved. While GNNs achieve a better forecasting performance, they are not the panacea. Some existing challenges from the border topic of traffic forecasting remain unsolved in current graph-based studies. Based on these challenges, we discuss possible future directions as well as early attempts in these directions. Some of these future directions are inspired from the border traffic forecasting research and remain insightful for the graph-based modeling approach. We would also highlight the special opportunities with GNNs.
在本节中，我们讨论流量预测问题的一般挑战以及涉及 GNN 时的具体新挑战。虽然 GNN 实现了更好的预测性能，但它们并不是万能药。在当前基于图的研究中，交通预测边界主题的一些现有挑战仍未得到解决。基于这些挑战，我们讨论未来可能的方向以及这些方向的早期尝试。其中一些未来方向受到边境交通预测研究的启发，并且对基于图的建模方法仍然具有洞察力。我们还将强调 GNN 的特殊机会。

6.1 Challenges 6.1挑战

6.1.1 Heterogeneous Data 6.1.1异构数据

Traffic prediction problems involve both spatiotemporal data and external factors, e.g., weather and calendar information. Heterogeneous data fusion is a challenge that is not limited to the traffic domain. GNNs have enabled significant progress by taking the underlying graph structures into consideration. However, some challenges remain; for example, geographically close nodes may not be the most influential, both for CNN-based and GNN-based approaches. Another special challenge for GNNs is that the underlying graph information may not be correct or up to date. For example, the road topology data of OpenStreetMap, an online map services, are collected in a crowd-sourced approach, which may be inaccurate or lagged behind the real road network. The spatial dependency relationship extracted by GNNs with these inaccurate data may decrease the forecasting accuracy.
交通预测问题既涉及时空数据，也涉及外部因素，例如天气和日历信息。异构数据融合是一个不仅限于流量领域的挑战。通过考虑底层图结构，GNN 取得了重大进展。然而，一些挑战仍然存在；例如，对于基于 CNN 和基于 GNN 的方法来说，地理位置接近的节点可能不是最具影响力的。 GNN 面临的另一个特殊挑战是底层图信息可能不正确或不是最新的。例如，在线地图服务OpenStreetMap的道路拓扑数据是通过众包方式收集的，这些数据可能不准确或滞后于真实的道路网络。 GNN 使用这些不准确的数据提取的空间依赖关系可能会降低预测精度。

Data quality concerns present an additional challenge with problems such as missing data, sparse data and noise potentially compromising forecasting results. Most of the surveyed models are only evaluated with processed high-quality datasets. A few studies do, however, take data quality related problems into consideration, e.g., using the Kalman filter to deal with the sensor data bias and noise [Chen et al., 2020a], infilling missing data with moving average filters [Hasanzadeh et al., 2019] or linear interpolation [Agafonov, 2020, Chen et al., 2020a]. Missing data problem could be more common in GNNs, with the potential missing phenomena happening with historical traffic data or underlying graph information, e.g., GCNs are proposed to fill data gaps in missing OD flow problems [Yao et al., 2020].
数据质量问题带来了额外的挑战，例如数据丢失、数据稀疏和噪声可能会影响预测结果。大多数调查模型仅使用经过处理的高质量数据集进行评估。然而，一些研究确实考虑了数据质量相关问题，例如，使用卡尔曼滤波器处理传感器数据偏差和噪声[Chen et al., 2020a]、用移动平均滤波器填充缺失数据[Hasanzadeh et al. ., 2019] 或线性插值 [Agafonov, 2020, Chen et al., 2020a]。丢失数据问题在 GNN 中可能更常见，历史流量数据或底层图信息可能会发生潜在的丢失现象，例如，GCN 被提出来填补丢失 OD 流问题中的数据空白 [Yao et al., 2020]。

Traffic anomalies (e.g., congestion) are an important external factor that may affect prediction accuracy and it has been proven that under congested traffic conditions a deep neural network may not perform as well as under normal traffic conditions [Mena-Oreja & Gozalvez, 2020]. However, it remains a challenge to collect enough anomaly data to train deep learning models (including GNNs) in both normal and anomalous situations. The same concern applies for social events, public holidays, etc.
交通异常（例如拥堵）是可能影响预测准确性的重要外部因素，事实证明，在拥堵交通条件下，深度神经网络的表现可能不如正常交通条件下 [Mena-Oreja & Gozalvez，2020] 。然而，收集足够的异常数据来训练正常和异常情况下的深度学习模型（包括 GNN）仍然是一个挑战。同样的担忧也适用于社交活动、公共假期等。

Challenges also exist for data privacy in the transportation domain. As discussed in Section 5.1, many open data are collected from individual mobile devices in a crowd sourcing approach. The data administrator must guarantee the privacy of individuals who contribute their personal traffic data, as the basis for encouraging a further contribution. Different techniques may be used, e.g., privacy-preserving data publishing techniques and privacy-aware data structures without personal identities.
交通领域的数据隐私也存在挑战。正如第 5.1 节中所讨论的，许多开放数据是通过众包方法从各个移动设备收集的。数据管理员必须保证贡献个人流量数据的个人的隐私，作为鼓励进一步贡献的基础。可以使用不同的技术，例如，隐私保护数据发布技术和没有个人身份的隐私感知数据结构。

6.1.2 Multi-task Performance
6.1.2 多任务性能

For the public service operation of ITSs, a multi-task framework is necessary to incorporate all the traffic information and predict the demand of multiple transportation modes simultaneously. For example, knowledge adaption is proposed to adapt the relevant knowledge from an information-intensive source to information-sparse sources for demand prediction [Li et al., 2020a]. Related challenges lie in data format incompatibilities as well as the inherent differences in spatial or temporal patterns. While some of the surveyed models can be used for multiple tasks, e.g., traffic flow and traffic speed prediction on the same road segment, most can only be trained for a single task at one time.
对于智能交通系统的公共服务运营，需要一个多任务框架来整合所有交通信息并同时预测多种交通方式的需求。例如，提出知识适应，将相关知识从信息密集型源调整到信息稀疏型源，以进行需求预测[Li et al., 2020a]。相关挑战在于数据格式不兼容以及空间或时间模式的固有差异。虽然一些调查模型可以用于多项任务，例如同一路段上的交通流量和交通速度预测，但大多数模型只能一次针对一项任务进行训练。

Multi-task forecasting is a bigger challenge in graph-based modeling because different tasks may use different graph structures, e.g., road-level and station-level problems use different graphs and thus are difficult to be solved with a single GNN model. Some efforts that have been made in GNN-based models for multi-task prediction include taxi departure flow and arrival flow [Chen et al., 2020h], region-flow and transition-flow [Wang et al., 2020b], crowd flows, and OD of the flows [Wang et al., 2020e]. However, most of the existing attempts are based on the same graph with multiple outputs generated by feed forward layers. Nonetheless, GNN-based multi-task prediction for different types of traffic forecasting problems is a research direction requiring significant further development, especially those requiring multiple graph structures.
多任务预测是基于图的建模中的一个更大的挑战，因为不同的任务可能使用不同的图结构，例如道路级和车站级问题使用不同的图，因此很难用单个 GNN 模型来解决。基于 GNN 的多任务预测模型已经做出了一些努力，包括出租车出发流和到达流 [Chen et al., 2020h]、区域流和转换流 [Wang et al., 2020b]、人群流和流量的 OD [Wang et al., 2020e]。然而，大多数现有的尝试都是基于同一个图，并具有由前馈层生成的多个输出。尽管如此，针对不同类型的交通预测问题的基于 GNN 的多任务预测是一个需要进一步发展的研究方向，特别是那些需要多个图结构的问题。

6.1.3 Practical Implementation
6.1.3实际实施

A number of challenges prevent the practical implementation of the models developed in the surveyed studies in city-scale ITSs.
许多挑战阻碍了城市规模智能交通系统中调查研究中开发的模型的实际实施。

First, there is significant bias introduced by the small amount of data considered in the existing GNN-based studies which, in most cases, spans less than one year. The proposed solutions are therefore not necessarily applicable to different time periods or different places. If longer traffic data are to be used in GNNs, the corresponding change of the underlying traffic infrastructures should be recorded and updated, which increases both the expense and difficulty of the associated data collection process in practice.
首先，现有的基于 GNN 的研究中考虑的数据量较少，因此存在显着的偏差，这些研究在大多数情况下持续时间不到一年。因此，所提出的解决方案不一定适用于不同时间段或不同地点。如果要在 GNN 中使用更长的交通数据，则需要记录和更新底层交通基础设施的相应变化，这在实践中增加了相关数据收集过程的费用和难度。

A second challenge is the computation scalability of GNNs. To avoid the huge computation requirements of the large-scale real-world traffic network graphs, only a subset of the nodes and edges are typically considered. For example, most studies only use a subset of the PeMS dataset when considering the road traffic flow or speed problems. Their results can therefore only be applied to the selected subsets. Graph partitioning and parallel computing infrastructures have been proposed for solving this problem. The traffic speed and flow of the entire PeMS dataset with 11,160 traffic sensor locations are predicted simultaneously in Mallick et al. [2020], using a graph-partitioning method that decomposes a large highway network into smaller networks and trains a single DCRNN model on a cluster with graphics processing units (GPUs). However, increased modeling power can only improve the state-of-the-art results with narrow performance margins, compared to statistical and machine learning models with less complex structures and computational requirements.
第二个挑战是 GNN 的计算可扩展性。为了避免大规模现实世界交通网络图的巨大计算需求，通常仅考虑节点和边的子集。例如，大多数研究在考虑道路交通流量或速度问题时仅使用 PeMS 数据集的子集。因此，他们的结果只能应用于选定的子集。图划分和并行计算基础设施已经被提出来解决这个问题。 Mallick 等人同时预测了具有 11,160 个交通传感器位置的整个 PeMS 数据集的交通速度和流量。 [2020]，使用图分区方法将大型高速公路网络分解为较小的网络，并在具有图形处理单元（GPU）的集群上训练单个 DCRNN 模型。然而，与结构和计算要求不太复杂的统计和机器学习模型相比，增强的建模能力只能提高最先进的结果，但性能差距较小。

A third challenge is presented by changes in the transportation networks and infrastructure, which are essential to build the graphs in GNNs. The real-world network graphs change when road segments or bus lines are added or removed. Points-of-interest in a city also change when new facilities are built. Static graph formulations are not enough for handling these situations. Some efforts have been made to solve this problem with promising results. For example, a dynamic Laplacian matrix estimator is proposed to find the change of Laplacian matrix, according to changes in spatial dependencies hidden in the traffic data [Diao et al., 2019], and a Data Adaptive Graph Generation (DAGG) module is proposed to infer the inter-dependencies between different traffic series automatically, without using pre-defined graphs based on spatial connections [Bai et al., 2020].
第三个挑战是交通网络和基础设施的变化，这对于在 GNN 中构建图至关重要。当添加或删除路段或公交线路时，现实世界的网络图会发生变化。当新设施建成时，城市的兴趣点也会发生变化。静态图公式不足以处理这些情况。为了解决这个问题已经做出了一些努力并取得了可喜的结果。例如，提出了一种动态拉普拉斯矩阵估计器，根据隐藏在交通数据中的空间依赖性的变化来查找拉普拉斯矩阵的变化[Diao et al., 2019]，并提出了数据自适应图生成（DAGG）模块自动推断不同流量序列之间的相互依赖关系，无需使用基于空间连接的预定义图表 [Bai et al., 2020]。

6.1.4 Model Interpretation
6.1.4模型解释

The challenge of model interpretation is a point of criticism for all “black-box” machine learning or deep learning models, and traffic forecasting tasks are no exception [Wu et al., 2018b, Barredo-Arrieta et al., 2019]. While there have been remarkable progresses for visualizing and explaining other deep neural network structures, e.g., CNNs, the development of post-processing techniques to explain the predictions made by GNNs is still in an early phase [Baldassarre & Azizpour, 2019, Pope et al., 2019, Ying et al., 2019] and the application of these techniques to the traffic forecasting domain has not yet been addressed.
模型解释的挑战是所有“黑盒”机器学习或深度学习模型的批评点，流量预测任务也不例外 [Wu et al., 2018b, Barredo-Arrieta et al., 2019]。尽管在可视化和解释其他深度神经网络结构（例如 CNN）方面取得了显着进展，但用于解释 GNN 预测的后处理技术的开发仍处于早期阶段 [Baldassarre & Azizpour，2019，Pope 等人., 2019, Ying et al., 2019] 并且这些技术在流量预测领域的应用尚未得到解决。

Compared with other similar forecasting problems in other domains, lack of model interpretation may be a more severe problem in the transportation domain, when complex data types and representations of heterogeneous traffic data make it more challenging to design an interpretable deep learning model, compared with other data formats, e.g., images and text. While some efforts have been made to incorporate the state space model to increase the model interpretation for traffic forecasting [Li et al., 2019a], this problem has not fully solved, especially for GNN-based models.
与其他领域的其他类似预测问题相比，交通领域缺乏模型解释可能是一个更严重的问题，因为与其他领域相比，复杂的数据类型和异构交通数据的表示使得设计可解释的深度学习模型更具挑战性。数据格式，例如图像和文本。尽管已经做出了一些努力来合并状态空间模型以增加流量预测的模型解释[Li et al., 2019a]，但这个问题尚未完全解决，特别是对于基于 GNN 的模型。

6.2 Future Directions 6.2未来方向

6.2.1 Centralized Data Repository
6.2.1集中数据存储库

A centralized data repository for GNN-based traffic forecasting resources would facilitate objective comparison of the performance of different models and be an invaluable contribution to the field. This future direction is proposed for the challenge of heterogeneous data as well as the data quality problem. Another unique feature of this repository could be the inclusion of graph-related data, which have not be provided directly in previous traffic forecasting studies.
基于 GNN 的交通预测资源的集中式数据存储库将有助于客观比较不同模型的性能，并对该领域做出宝贵贡献。这一未来方向是针对异构数据的挑战以及数据质量问题而提出的。该存储库的另一个独特功能可能是包含与图形相关的数据，这些数据在以前的流量预测研究中尚未直接提供。

Some criteria for building such data repositories, e.g. a unified data format, tracking of dataset versions, public code and ranked results, and sufficient record lengths (longer than a year ideally), have been discussed in previous surveys [Manibardo et al., 2021]. Compiling a centralized and standardized data repository is particularly challenging for GNN-based models where natural graphs are collected and stored in a variety of data formats (e.g. Esri Shapefile and OSM XML used by Openstreetmap are used for digital maps in the GIS community) and various different similarity graphs can be constructed from the same traffic data in different models.
构建此类数据存储库的一些标准，例如统一的数据格式、数据集版本跟踪、公共代码和排名结果以及足够的记录长度（理想情况下超过一年）已在之前的调查中讨论过 [Manibardo 等人，2021]。对于基于 GNN 的模型来说，编译集中式标准化数据存储库尤其具有挑战性，其中自然图以各种数据格式收集和存储（例如，Openstreetmap 使用的 Esri Shapefile 和 OSM XML 用于 GIS 社区中的数字地图）和各种不同模型中的相同流量数据可以构建不同的相似度图。

Some previous attempts in this direction have been made in the machine learning community, e.g. setting benchmarks for several traffic prediction tasks in Papers With Code ²⁴²⁴24https://paperswithcode.com/task/traffic-prediction, and in data science competitions, e.g., the Traffic4cast competition series ²⁵²⁵25https://www.iarai.ac.at/traffic4cast/. However, the realization of a centralized data repository remains an open challenge.
机器学习社区之前已经在这个方向进行了一些尝试，例如为 Papers With Code ²⁴ 和数据科学竞赛（例如 Traffic4cast 竞赛系列 ²⁵ ）中的多个流量预测任务设置基准。然而，实现集中式数据存储库仍然是一个开放的挑战。

A centralized data repository is also the basis for benchmarking traffic prediction, which is previously discussed in Section 5.3. With more and more GNN-based models being proposed, it becomes even more difficult to compare different models and validate the effectiveness of new traffic forecasting methods without a considerable effort, when a standardized benchmark dataset and consistent experimental settings have not been established yet. The most close one is the PeMS dataset, but it covers the road-level case only and more efforts are still needed, especially for the remaining cases.
集中式数据存储库也是流量预测基准测试的基础，这已在 5.3 节中讨论过。随着越来越多的基于 GNN 的模型被提出，在标准化的基准数据集和一致的实验设置尚未建立的情况下，比较不同的模型并验证新的流量预测方法的有效性变得更加困难，而不需要付出相当大的努力。最接近的一个是 PeMS 数据集，但它仅涵盖道路级别的情况，仍然需要更多的努力，特别是对于其余的情况。

6.2.2 Traffic Graph Design
6.2.2流量图设计

While various graphs have been constructed in the surveyed studies as discussed in Section 4.1 and have been proven successful to some extent, most of them are natural graphs based on a real-world transportation system, e.g. the road network or subway system, as the current development status. And most of the graphs used are static, instead of dynamic ones. One specific direction that is not fully considered before is the design of transportation knowledge graph. As an important tool for knowledge integration, knowledge graph is a complex relational network that consists of concepts, entities, entity relations and attributes [Yin et al., 2021]. The transportation knowledge graph helps to leverage the traffic semantic information to improve the forecasting performance. And the challenge is to extract the hidden transportation domain knowledge from multi-source and heterogeneous traffic data.
虽然在 4.1 节中讨论的调查研究中构建了各种图，并且在一定程度上被证明是成功的，但其中大多数是基于现实世界交通系统的自然图，例如道路网或者地铁系统，作为目前的发展现状。而且大多数使用的图表都是静态的，而不是动态的。之前没有充分考虑的一个具体方向是交通知识图谱的设计。作为知识集成的重要工具，知识图谱是一个由概念、实体、实体关系和属性组成的复杂关系网络[Yin et al., 2021]。交通知识图谱有助于利用交通语义信息来提高预测性能。挑战在于从多源异构交通数据中提取隐藏的交通领域知识。

6.2.3 Combination with Other Techniques
6.2.3与其他技术的结合

GNNs may be combined with other advanced techniques to overcome some of their inherent challenges and achieve better performance.
GNN 可以与其他先进技术相结合，以克服一些固有的挑战并实现更好的性能。

Data Augmentation. Data augmentation has been proven effective for boosting the performance of deep learning models, e.g. in image classification tasks and time series prediction tasks. Data augmentation is proposed for the challenge of the possible forecasting bias introduced by the small amount of available data. However, due to the complex structure of graphs, it is more challenging to apply data augmentation techniques to GNNs. Recently, data augmentation for GNNs has proven helpful in semi-supervised node classification tasks [Zhao et al., 2021]. However, it remains a question whether data augmentation may be effective in traffic forecasting GNN applications.
数据增强。数据增强已被证明可以有效提高深度学习模型的性能，例如在图像分类任务和时间序列预测任务中。数据增强的提出是为了应对少量可用数据可能带来的预测偏差的挑战。然而，由于图的复杂结构，将数据增强技术应用于 GNN 更具挑战性。最近，GNN 的数据增强已被证明在半监督节点分类任务中很有帮助 [Zhao et al., 2021]。然而，数据增强在流量预测 GNN 应用中是否有效仍然是一个问题。

Transfer Learning. Transfer learning utilizes knowledge or models trained for one task to solve related tasks, especially those with limited data. In the image classification field, pre-trained deep learning models from the ImageNet or MS COCO datasets are widely used in other problems. In traffic prediction problems, where a lack of historical data is a frequent problem, transfer learning is a possible solution. For GNNs, transfer learning can be used from a graph with more historical traffic data for the model training process to another graph with less available data. Transfer learning can also be used for the challenge caused by the changes in the transportation networks and infrastructure, when new stations or regions have not accumulated enough historical traffic data to train a GNN model. A novel transfer learning approach for DCRNN is proposed in Mallick et al. [2021], so that a model trained on data-rich regions of highway network can be used to predict traffic on unseen regions of the highway network. The authors demonstrated the efficacy of model transferability between the San Francisco and Los Angeles regions using different parts of the California road network from the PeMS.
迁移学习。迁移学习利用针对一项任务训练的知识或模型来解决相关任务，尤其是那些数据有限的任务。在图像分类领域，来自 ImageNet 或 MS COCO 数据集的预训练深度学习模型广泛用于其他问题。在交通预测问题中，缺乏历史数据是一个常见问题，迁移学习是一种可能的解决方案。对于 GNN，可以使用迁移学习从具有更多历史流量数据的图（用于模型训练过程）到另一个具有较少可用数据的图。当新的车站或地区没有积累足够的历史交通数据来训练 GNN 模型时，迁移学习还可以用于应对交通网络和基础设施变化带来的挑战。 Mallick 等人提出了一种新颖的 DCRNN 迁移学习方法。 [2021]，以便在高速公路网络的数据丰富区域上训练的模型可以用于预测高速公路网络中不可见区域的交通。作者使用 PeMS 的加州道路网的不同部分证明了旧金山和洛杉矶地区之间模型可转移性的有效性。

Meta-learning. Meta-learning, or learning how to learn, has recently become a potential learning paradigm that can absorb information from a task and effectively generalize it to an unseen task. Meta-learning is proposed for the challenge of GNN-based multi-task prediction, especially those involving mutiple graphs. There are different types of meta learning methods and some of them are combined with graph structures for describing relationships between tasks or data samples [Satorras & Estrach, 2018, Liu et al., 2019]. Based on a deep meta learning method called network weight generation, ST-MetaNet⁺ is proposed in Pan et al. [2020], which leverages the meta knowledge extracted from geo-graph attributes and dynamic traffic context learned from traffic states to generate the parameter weights in graph attention networks and RNNs, so that the inherent relationships between diverse types of spatiotemporal correlations and geo-graph attributes can be captured.
元学习。元学习，或者说学习如何学习，最近已成为一种潜在的学习范式，它可以从任务中吸收信息并有效地将其推广到看不见的任务。元学习是为了应对基于 GNN 的多任务预测的挑战而提出的，特别是那些涉及多个图的预测。元学习方法有不同类型，其中一些与图结构相结合，用于描述任务或数据样本之间的关系 [Satorras & Estrach, 2018, Liu et al., 2019]。 Pan 等人提出了基于称为网络权重生成的深度元学习方法的 ST-MetaNet ⁺ 。 [2020]，利用从地理图属性中提取的元知识和从交通状态中学习到的动态交通上下文来生成图注意力网络和RNN中的参数权重，从而使不同类型的时空相关性和地理图之间的内在关系可以捕获属性。

Generative Adversarial Network (GAN) [Goodfellow et al., 2014]. GAN is a machine learning framework that has two components, namely, a generator, which learns to generate plausible data, and a discriminator, which learns to distinguish the generator’s fake data from real data. After training to a state of Nash equilibrium, the generator may generate undistinguished data, which helps to expand the training data size for many problems, including GNN-based traffic forecasting. GAN is proposed for the challenges caused by the small data amount used in previous studies or the changes in the transportation networks and infrastructure when not enough historical traffic data are available. In Xu et al. [2020a], the road network is used directly as the graph, in which the nodes are road state detectors and the edges are built based on their adjacent links. DeepWalk is used to embed the graph and the road traffic state sensor information is transferred into a low-dimensional space. Then, the Wasserstein GAN (WGAN) [Arjovsky et al., 2017] is used to train the traffic state data distribution and generate predicted results. Both public traffic flow (i.e., Caltrans PeMSD7) and traffic speed (i.e., METR-LA) datasets are used for evaluation, and the results demonstrate the effectiveness of the GAN-based solution when used in graph-based modeling.
生成对抗网络（GAN）[Goodfellow 等人，2014]。 GAN 是一个机器学习框架，有两个组件，即生成器（学习生成可信数据）和鉴别器（学习区分生成器的假数据和真实数据）。在训练到纳什均衡状态后，生成器可能会生成不可区分的数据，这有助于扩大许多问题的训练数据大小，包括基于 GNN 的流量预测。 GAN是针对以往研究中使用的数据量较小或在没有足够的历史交通数据时交通网络和基础设施发生变化所带来的挑战而提出的。在徐等人中。 [2020a]，直接使用道路网络作为图，其中节点是道路状态检测器，边缘是基于其相邻链路构建的。使用DeepWalk嵌入图，将道路交通状态传感器信息转移到低维空间。然后，使用 Wasserstein GAN (WGAN) [Arjovsky et al., 2017] 训练交通状态数据分布并生成预测结果。公共交通流量（即 Caltrans PeMSD7）和交通速度（即 METR-LA）数据集均用于评估，结果证明了基于 GAN 的解决方案在基于图的建模中使用时的有效性。

Automated Machine Learning (AutoML). The application of machine learning requires considerable manual intervention in various aspects of the process, including feature extraction, model selection, and parameter adjustment. AutoML automatically learns the important steps related to features, models, optimization, and evaluation, so that machine learning models can be applied without manual intervention. AutoML would help to improve the implementation of machine learning models, including GNNs. AutoML is proposed for the challenge for computational requirements in graph-based modeling, in which case the hyper parameter tuning for GNNs can be more efficient with state-of-the-art AutoML techniques. An early attempt to combine AutoML with GNNs for traffic prediction problems is an Auto-STGCN algorithm, proposed in Wang et al. [2020a]. This algorithm searches the parameter space for STGCN models quickly based on reinforcement learning and generates optimal models automatically for specific scenarios.
自动机器学习 (AutoML)。机器学习的应用需要在过程的各个方面进行大量的人工干预，包括特征提取、模型选择和参数调整。 AutoML自动学习与特征、模型、优化和评估相关的重要步骤，使得机器学习模型无需人工干预即可应用。 AutoML 将有助于改进机器学习模型（包括 GNN）的实施。 AutoML 是为了应对基于图的建模中的计算要求的挑战而提出的，在这种情况下，使用最先进的 AutoML 技术可以更有效地调整 GNN 的超参数。将 AutoML 与 GNN 结合起来解决流量预测问题的早期尝试是 Auto-STGCN 算法，由 Wang 等人提出。 [2020a]。该算法基于强化学习快速搜索STGCN模型的参数空间，并针对特定场景自动生成最优模型。

Bayesian Network. Most of the existing studies aim for deterministic models that make mean predictions. However, some traffic applications rely on uncertainty estimates for the future situations. To tackle this gap, the Bayesian network, which is a type of probabilistic graphical model using Bayesian inference for probability computations, is a promising solution. The combination of GNNs with Bayesian networks is proposed for the challenge of GNN model interpretation. With probabilistic predictions, uncertainty estimates are generated for the future situations, especially the chance of extreme traffic states. A similar alternative is Quantile Regression, which estimates the quantile function of a distribution at chosen points, combined with Graph WaveNet for uncertainty estimates [Maas & Bloem, 2020].
贝叶斯网络。大多数现有研究的目标是做出平均预测的确定性模型。然而，一些交通应用依赖于对未来情况的不确定性估计。为了解决这一差距，贝叶斯网络是一种很有前途的解决方案，它是一种使用贝叶斯推理进行概率计算的概率图形模型。为了应对 GNN 模型解释的挑战，提出了 GNN 与贝叶斯网络的结合。通过概率预测，可以生成对未来情况的不确定性估计，特别是极端交通状态的可能性。类似的替代方案是分位数回归，它估计选定点处分布的分位数函数，并结合 Graph WaveNet 进行不确定性估计 [Maas & Bloem, 2020]。

6.2.4 Applications in Real-World ITS Systems
6.2.4实际ITS系统中的应用

Last but not the least, most of the surveyed GNN-based studies are only based on the simulations with historical traffic data, without being validated or deployed in real-world ITS systems. However, there are a number of potential applications, especially for GNN-based models with the better forecasting performance. To name a few potential cases, the GNN-based forecasting model can be used for traffic light control in signalized intersections, when each intersection is modeled as a node in the graph and the corresponding traffic flow forecasting result can be used to design the traffic light control strategy. Another example is the application in map service and navigation applications, in which each road segment is modeled as a node in the graph and the corresponding traffic speed and travel time forecasting result can be used to calculate the estimated time of arrival. A third example is the application in online ride-hailing service providers, e.g., Uber and Lyft, in which each region is modeled as a node and the corresponding ride-hailing demand forecasting can be used to design a more profitable vehicle dispatching and scheduling system. Inspired by these potential application scenarios, there are a lot of potential research opportunities for researchers from both the academia and the industry.
最后但并非最不重要的一点是，大多数受调查的基于 GNN 的研究仅基于历史交通数据的模拟，而没有在现实世界的 ITS 系统中进行验证或部署。然而，有许多潜在的应用，特别是对于具有更好预测性能的基于 GNN 的模型。仅举几个潜在的例子，基于 GNN 的预测模型可用于信号交叉口的交通灯控制，将每个交叉口建模为图中的一个节点，并使用相应的交通流预测结果来设计交通灯控制策略。另一个例子是地图服务和导航应用中的应用，其中每个路段被建模为图中的节点，并且可以使用相应的交通速度和旅行时间预测结果来计算预计到达时间。第三个例子是在Uber和Lyft等网约车服务提供商中的应用，其中每个区域被建模为一个节点，并利用相应的网约车需求预测来设计更有利可图的车辆调度和调度系统。受这些潜在应用场景的启发，学术界和工业界的研究人员都有很多潜在的研究机会。

7 Conclusion 7结论

In this paper, a comprehensive review of the application of GNNs for traffic forecasting is presented. Three levels of traffic problems and graphs are summarized, namely, road-level, region-level and station-level. The usages of recurrent GNNs, convolutional GNNs and graph autoencoders are discussed. We also give the latest collection of open dataset and code resource for this topic. Challenges and future directions are further pointed out for the follow-up research.
本文对 GNN 在交通预测中的应用进行了全面的回顾。总结了三个层面的交通问题和图表，即道路层面、区域层面和车站层面。讨论了循环 GNN、卷积 GNN 和图自动编码器的用法。我们还提供了该主题的最新开放数据集和代码资源。进一步指出了后续研究面临的挑战和未来的方向。

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Graph Neural Network for Traffic Forecasting: A Survey用于交通预测的图神经网络：调查