Spatial-temporal (ST) graph modeling, such as traffic speed forecasting and taxi demand prediction, is an important task in deep learning area. However, for the nodes in graph, their ST patterns can vary greatly in difficulties for modeling, owning to the heterogeneous nature of ST data. We argue that unveiling the nodes to the model in a meaningful order, from easy to complex, can provide performance improvements over traditional training procedure. The idea has its root in Curriculum Learning which suggests in the early stage of training models can be sensitive to noise and difficult samples. In this paper, we propose ST-Curriculum Dropout, a novel and easy-to-implement strategy for spatial-temporal graph modeling. Specifically, we evaluate the learning difficulty of each node in high-level feature space and drop those difficult ones out to ensure the model only needs to handle fundamental ST relations at the beginning, before gradually moving to hard ones. Our strategy can be applied to any canonical deep learning architecture without extra trainable parameters, and extensive experiments on a wide range of datasets are conducted to illustrate that, by controlling the difficulty level of ST relations as the training progresses, the model is able to capture better representation of the data and thus yields better generalization.

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it's fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information. CCS CONCEPTS• Computing methodologies → Neural networks; Artificial intelligence.

Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the underlying relation between entities is pre-determined. However, the explicit graph structure (relation) does not necessarily reflect the true dependency and genuine relation may be missing due to the incomplete connections in the data. Furthermore, existing methods are ineffective to capture the temporal trends as the RNNs or CNNs employed in these methods cannot capture long-range temporal sequences. To overcome these limitations, we propose in this paper a novel graph neural network architecture, Graph WaveNet, for spatial-temporal graph modeling. By developing a novel adaptive dependency matrix and learn it through node embedding, our model can precisely capture the hidden spatial dependency in the data. With a stacked dilated 1D convolution component whose receptive field grows exponentially as the number of layers increases, Graph WaveNet is able to handle very long sequences. These two components are integrated seamlessly in a unified framework and the whole framework is learned in an end-to-end manner. Experimental results on two public traffic network datasets, METR-LA and PEMS-BAY, demonstrate the superior performance of our algorithm.

本文旨在统一非欧几里得空间中的空间依赖性和时间依赖性，同时捕获流量数据的内部空间依赖性。对于具有拓扑结构的时空属性实体，时空是连续的和统一的，而每个节点的当前状态都受到每个邻居的变异时期的邻居的过去状态的影响。大多数用于流量预测研究的空间依赖性和时间相关性的空间神经网络在处理中分别损害了时空完整性，而忽略了邻居节点的时间依赖期可以延迟和动态的事实。为了建模这种实际条件，我们提出了一种新型的空间 - 周期性图神经网络，将空间和时间视为不可分割的整体，以挖掘时空图，同时通过消息传播机制利用每个节点的发展时空依赖性。进行消融和参数研究的实验已经验证了拟议的遍及术的有效性，并且可以从https://github.com/nnzhan/traversenet中找到详细的实现。

由于动态和复杂的时空依赖性，交通预测具有挑战性。但是，现有方法仍然受到两个关键局限性。首先，许多方法通常使用静态预定义或自适应的空间图来捕获流量系统中动态的时空依赖性，这限制了灵活性，并且仅捕获了整个时间的共享模式，从而导致了次优性能。此外，大多数方法在每个时间步骤中都单独和独立地考虑地面真理与预测之间的绝对误差，这无法维持整体时间序列的全球属性和统计数据，并导致地面真相和预测之间的趋势差异。为此，在本文中，我们提出了一个动态自适应和对抗图卷积网络（DAAGCN），该网络将图形卷积网络（GCN）与生成的对抗网络（GANS）结合在一起，以进行流量预测。具体而言，DAAGCN利用带栅极模块的通用范式将时间变化的嵌入与节点嵌入集成在一起，以生成动态自适应图，以在每个时间步骤中推断空间 - 周期依赖性。然后，设计了两个歧视因子，以维持预测时间序列的全局属性的一致性，并在序列和图形级别上具有地面真相。在四个基准数据集上进行的广泛实验表明，DAAGCN的表现平均比最新的5.05％，3.80％和5.27％在MAE，RMSE和MAPE方面，同时加快收敛性高达9倍。代码可从https://github.com/juyongjiang/daagcn获得。

Traffic forecasting has attracted widespread attention recently. In reality, traffic data usually contains missing values due to sensor or communication errors. The Spatio-temporal feature in traffic data brings more challenges for processing such missing values, for which the classic techniques (e.g., data imputations) are limited: 1) in temporal axis, the values can be randomly or consecutively missing; 2) in spatial axis, the missing values can happen on one single sensor or on multiple sensors simultaneously. Recent models powered by Graph Neural Networks achieved satisfying performance on traffic forecasting tasks. However, few of them are applicable to such a complex missing-value context. To this end, we propose GCN-M, a Graph Convolutional Network model with the ability to handle the complex missing values in the Spatio-temporal context. Particularly, we jointly model the missing value processing and traffic forecasting tasks, considering both local Spatio-temporal features and global historical patterns in an attention-based memory network. We propose as well a dynamic graph learning module based on the learned local-global features. The experimental results on real-life datasets show the reliability of our proposed method.

最近，深度学习方法在交通预测方面取得了长足的进步，但它们的性能取决于大量的历史数据。实际上，我们可能会面临数据稀缺问题。在这种情况下，深度学习模型无法获得令人满意的性能。转移学习是解决数据稀缺问题的一种有前途的方法。但是，流量预测中现有的转移学习方法主要基于常规网格数据，这不适用于流量网络中固有的图形数据。此外，现有的基于图的模型只能在道路网络中捕获共享的流量模式，以及如何学习节点特定模式也是一个挑战。在本文中，我们提出了一种新颖的传输学习方法来解决流量预测，几乎可以将知识从数据富的源域转移到数据范围的目标域。首先，提出了一个空间图形神经网络，该网络可以捕获不同道路网络的节点特异性时空交通模式。然后，为了提高转移的鲁棒性，我们设计了一种基于模式的转移策略，我们利用基于聚类的机制来提炼源域中的常见时空模式，并使用这些知识进一步提高了预测性能目标域。现实世界数据集的实验验证了我们方法的有效性。

我们都取决于流动性，车辆运输会影响我们大多数人的日常生活。因此，预测道路网络中流量状态的能力是一项重要的功能和具有挑战性的任务。流量数据通常是从部署在道路网络中的传感器获得的。关于时空图神经网络的最新建议通过将流量数据建模为扩散过程，在交通数据中建模复杂的时空相关性方面取得了巨大进展。但是，直观地，流量数据包含两种不同类型的隐藏时间序列信号，即扩散信号和固有信号。不幸的是，几乎所有以前的作品都将交通信号完全视为扩散的结果，同时忽略了固有的信号，这会对模型性能产生负面影响。为了提高建模性能，我们提出了一种新型的脱钩时空框架（DSTF），该框架以数据驱动的方式将扩散和固有的交通信息分开，其中包含独特的估计门和残差分解机制。分离的信号随后可以通过扩散和固有模块分别处理。此外，我们提出了DSTF的实例化，分离的动态时空图神经网络（D2STGNN），可捕获时空相关性，还具有动态图学习模块，该模块针对学习流量网络动态特征的学习。使用四个现实世界流量数据集进行的广泛实验表明，该框架能够推进最先进的框架。

时空人群流量预测（STCFP）问题是一种经典问题，具有丰富的现有研究工作，这些努力受益于传统的统计学习和最近的深度学习方法。虽然STCFP可以参考许多现实世界问题，但大多数现有研究都侧重于相当特定的应用，例如预测出租车需求，乘资顺序等。这会阻碍STCFP研究作为针对不同应用的方法几乎没有比较，因此如何将应用驱动的方法概括为其他场景尚不清楚。要填补这一差距，这篇论文进行了两项努力：（i）我们提出了一个叫做STANALYTIC的分析框架，以定性地调查其关于各种空间和时间因素的设计考虑的STCFP方法，旨在使不同的应用驱动的方法进行不同的方法; （ii）（ii）我们构建一个广泛的大型STCFP基准数据集，具有四种不同的场景（包括RideSharing，Bikesharing，Metro和电动车辆充电），其流量高达数亿个流量记录，以定量测量STCFP方法的普遍性。此外，为了详细说明STANalytic在帮助设计上推广的STCFP方法方面的有效性，我们提出了一种通过整合STANALYTIC鉴定的可推广的时间和空间知识来提出一种称为STETA的时空元模型。我们利用不同的深度学习技术实施STMETA的三种变体。通过数据集，我们证明Stmeta变体可以优于最先进的STCFP方法5％。

多变量时间序列预测是一个具有挑战性的任务，因为数据涉及长期和短期模式的混合，具有变量之间的动态时空依赖性。现有图形神经网络（GNN）通常与预定义的空间图或学习的固定邻接图模拟多变量关系。它限制了GNN的应用，并且无法处理上述挑战。在本文中，我们提出了一种新颖的框架，即静态和动态图形学习 - 神经网络（SDGL）。该模型分别从数据获取静态和动态图形矩阵分别为模型长期和短期模式。开发静态Matric以通过节点嵌入捕获固定的长期关联模式，并利用图规律性来控制学习静态图的质量。为了捕获变量之间的动态依赖性，我们提出了基于改变节点特征和静态节点Embeddings生成时变矩阵的动态图。在该方法中，我们将学习的静态图信息作为感应偏置集成为诱导动态图和局部时空模式更好。广泛的实验是在两个交通数据集中进行，具有额外的结构信息和四个时间序列数据集，这表明我们的方法在几乎所有数据集上实现了最先进的性能。如果纸张被接受，我将在GitHub上打开源代码。

准确的交通预测对于智能城市实现交通控制，路线计划和流动检测至关重要。尽管目前提出了许多时空方法，但这些方法在同步捕获流量数据的时空依赖性方面缺陷。此外，大多数方法忽略了随着流量数据的变化而产生的道路网络节点之间的动态变化相关性。我们建议基于神经网络的时空交互式动态图卷积网络（STIDGCN），以应对上述流量预测的挑战。具体而言，我们提出了一个交互式动态图卷积结构，该结构将序列划分为间隔，并通过交互式学习策略同步捕获流量数据的时空依赖性。交互式学习策略使StidGCN有效地预测。我们还提出了一个新颖的动态图卷积模块，以捕获由图生成器和融合图卷积组成的流量网络中动态变化的相关性。动态图卷积模块可以使用输入流量数据和预定义的图形结构来生成图形结构。然后将其与定义的自适应邻接矩阵融合，以生成动态邻接矩阵，该矩阵填充了预定义的图形结构，并模拟了道路网络中节点之间的动态关联的产生。在四个现实世界流量流数据集上进行的广泛实验表明，StidGCN的表现优于最先进的基线。

交通预测是智能交通系统的问题（ITS），并为个人和公共机构是至关重要的。因此，研究高度重视应对准确预报交通系统的复杂的时空相关性。但是，有两个挑战：1）大多数流量预测研究主要集中在造型相邻传感器的相关性，而忽略远程传感器，例如，商务区有类似的时空模式的相关性; 2）使用静态邻接矩阵中曲线图的卷积网络（GCNs）的现有方法不足以反映在交通系统中的动态空间依赖性。此外，它采用自注意所有的传感器模型动态关联细粒度方法忽略道路网络分层信息，并有二次计算复杂性。在本文中，我们提出了一种新动态多图形卷积递归网络（DMGCRN），以解决上述问题，可以同时距离的空间相关性，结构的空间相关性，和所述时间相关性进行建模。那么，只使用基于距离的曲线图来捕获空间信息从节点是接近距离也构建了一个新潜曲线图，其编码的道路之间的相关性的结构来捕获空间信息从节点在结构上相似。此外，我们在不同的时间将每个传感器的邻居到粗粒区域，并且动态地分配不同的权重的每个区域。同时，我们整合动态多图卷积网络到门控重复单元（GRU）来捕获时间依赖性。三个真实世界的交通数据集大量的实验证明，我们提出的算法优于国家的最先进的基线。

Accurate short-term traffic prediction plays a pivotal role in various smart mobility operation and management systems. Currently, most of the state-of-the-art prediction models are based on graph neural networks (GNNs), and the required training samples are proportional to the size of the traffic network. In many cities, the available amount of traffic data is substantially below the minimum requirement due to the data collection expense. It is still an open question to develop traffic prediction models with a small size of training data on large-scale networks. We notice that the traffic states of a node for the near future only depend on the traffic states of its localized neighborhoods, which can be represented using the graph relational inductive biases. In view of this, this paper develops a graph network (GN)-based deep learning model LocaleGN that depicts the traffic dynamics using localized data aggregating and updating functions, as well as the node-wise recurrent neural networks. LocaleGN is a light-weighted model designed for training on few samples without over-fitting, and hence it can solve the problem of few-sample traffic prediction. The proposed model is examined on predicting both traffic speed and flow with six datasets, and the experimental results demonstrate that LocaleGN outperforms existing state-of-the-art baseline models. It is also demonstrated that the learned knowledge from LocaleGN can be transferred across cities. The research outcomes can help to develop light-weighted traffic prediction systems, especially for cities lacking historically archived traffic data.

交通速度预测是运输系统中的核心问题之一。为了进行更准确的预测，最近的研究不仅开始使用时间速度模式，还开始使用图形卷积网络上的道路网络上的空间信息。即使由于其非欧亚人和方向性特征，道路网络非常复杂，但以前的方法主要集中于仅使用距离对空间依赖性进行建模。在本文中，我们确定了两个基本的预测中的基本空间依赖性，除了距离，方向和位置关系，以将基本的图形元素设计为基本构建块。我们建议使用构建块，建议DDP-GCN（距离，方向和位置关系图卷积网络）将三个空间关系纳入深神经网络。我们使用两个大型现实世界数据集评估了提出的模型，并在高度复杂的城市网络中找到了长期预测的积极改进。通勤时间的改进可能会更大，但也可以限制短期预测。

Traffic forecasting as a canonical task of multivariate time series forecasting has been a significant research topic in AI community. To address the spatio-temporal heterogeneity and non-stationarity implied in the traffic stream, in this study, we propose Spatio-Temporal Meta-Graph Learning as a novel Graph Structure Learning mechanism on spatio-temporal data. Specifically, we implement this idea into Meta-Graph Convolutional Recurrent Network (MegaCRN) by plugging the Meta-Graph Learner powered by a Meta-Node Bank into GCRN encoder-decoder. We conduct a comprehensive evaluation on two benchmark datasets (METR-LA and PEMS-BAY) and a new large-scale traffic speed dataset in which traffic incident information is contained. Our model outperformed the state-of-the-arts to a large degree on all three datasets (over 27% MAE and 34% RMSE). Besides, through a series of qualitative evaluations, we demonstrate that our model can explicitly disentangle the road links and time slots with different patterns and be robustly adaptive to any anomalous traffic situations. Codes and datasets are available at https://github.com/deepkashiwa20/MegaCRN.

Reliable forecasting of traffic flow requires efficient modeling of traffic data. Different correlations and influences arise in a dynamic traffic network, making modeling a complicated task. Existing literature has proposed many different methods to capture the complex underlying spatial-temporal relations of traffic networks. However, methods still struggle to capture different local and global dependencies of long-range nature. Also, as more and more sophisticated methods are being proposed, models are increasingly becoming memory-heavy and, thus, unsuitable for low-powered devices. In this paper, we focus on solving these problems by proposing a novel deep learning framework - STLGRU. Specifically, our proposed STLGRU can effectively capture both local and global spatial-temporal relations of a traffic network using memory-augmented attention and gating mechanism. Instead of employing separate temporal and spatial components, we show that our memory module and gated unit can learn the spatial-temporal dependencies successfully, allowing for reduced memory usage with fewer parameters. We extensively experiment on several real-world traffic prediction datasets to show that our model performs better than existing methods while the memory footprint remains lower. Code is available at \url{https://github.com/Kishor-Bhaumik/STLGRU}.

预测抗流动过程中感染的数量对政府制定抗流动策略极为有益，尤其是在细粒度的地理单位中。以前的工作着重于低空间分辨率预测，例如县级和预处理数据到同一地理水平，这将失去一些有用的信息。在本文中，我们提出了一个基于两个地理水平的数据，用于社区级别的COVID-19预测，该模型（FGC-COVID）基于数据。我们使用比社区更细粒度的地理水平（CBG）之间的人口流动数据来构建图形，并使用图形神经网络（GNN）构建图形并捕获CBG之间的依赖关系。为了预测，为了预测更细粒度的模式，引入了空间加权聚合模块，以将CBG的嵌入基于其地理隶属关系和空间自相关，将CBG的嵌入到社区水平上。在300天LA COVID-19数据中进行的大量实验表明，我们的模型的表现优于社区级Covid-19预测的现有预测模型。

流量预测是智能交通系统中时空学习任务的规范示例。现有方法在图形卷积神经操作员中使用预定的矩阵捕获空间依赖性。但是，显式的图形结构损失了节点之间关系的一些隐藏表示形式。此外，传统的图形卷积神经操作员无法在图上汇总远程节点。为了克服这些限制，我们提出了一个新型的网络，空间 - 周期性自适应图卷积，并通过注意力网络（Staan）进行交通预测。首先，我们采用自适应依赖性矩阵，而不是在GCN处理过程中使用预定义的矩阵来推断节点之间的相互依存关系。其次，我们集成了基于图形注意力网络的PW注意，该图形是为全局依赖性设计的，而GCN作为空间块。更重要的是，在我们的时间块中采用了堆叠的散布的1D卷积，具有长期预测的效率，用于捕获不同的时间序列。我们在两个现实世界数据集上评估了我们的Staan，并且实验验证了我们的模型优于最先进的基线。

准确的实时流量预测对于智能运输系统（ITS）至关重要，它是各种智能移动应用程序的基石。尽管该研究领域以深度学习为主，但最近的研究表明，开发新模型结构的准确性提高正变得边缘。取而代之的是，我们设想可以通过在具有不同数据分布和网络拓扑的城市之间转移“与预测相关的知识”来实现改进。为此，本文旨在提出一个新型的可转移流量预测框架：域对抗空间 - 颞网（DASTNET）。 Dastnet已在多个源网络上进行了预训练，并通过目标网络的流量数据进行了微调。具体而言，我们利用图表表示学习和对抗域的适应技术来学习域不变的节点嵌入，这些嵌入式嵌入将进一步合并以建模时间流量数据。据我们所知，我们是第一个使用对抗性多域改编来解决网络范围的流量预测问题的人。 Dastnet始终优于三个基准数据集上的所有最新基线方法。训练有素的dastnet应用于香港的新交通探测器，并且在可用的探测器可用时（一天之内）可以立即（在一天之内）提供准确的交通预测。总体而言，这项研究提出了一种增强交通预测方法的替代方法，并为缺乏历史流量数据的城市提供了实际含义。

Traffic forecasting is an important application of spatiotemporal series prediction. Among different methods, graph neural networks have achieved so far the most promising results, learning relations between graph nodes then becomes a crucial task. However, improvement space is very limited when these relations are learned in a node-to-node manner. The challenge stems from (1) obscure temporal dependencies between different stations, (2) difficulties in defining variables beyond the node level, and (3) no ready-made method to validate the learned relations. To confront these challenges, we define legitimate traffic causal variables to discover the causal relation inside the traffic network, which is carefully checked with statistic tools and case analysis. We then present a novel model named Graph Spatial-Temporal Network Based on Causal Insight (GT-CausIn), where prior learned causal information is integrated with graph diffusion layers and temporal convolutional network (TCN) layers. Experiments are carried out on two real-world traffic datasets: PEMS-BAY and METR-LA, which show that GT-CausIn significantly outperforms the state-of-the-art models on mid-term and long-term prediction.