时空图建模是分析图形结构系统中各要素空间关系与时间趋势的一个基础工作.传统的时空图建模方法主要基于图中节点与节点关系固定的显式结构进行空间关系挖掘，这严重限制了模型的灵活性.此外，未考虑节点间的时空依赖关系的传统建模方法不能捕获节点间的长时时空趋势.为了克服这些缺陷，研究并提出了一种新的用于时空图建模的图神经网络模型，即面向时空图建模的图小波卷积神经网络模型（graph wavelet convolutional neural network for spatiotemporal graph modeling，简称GWNN-STGM）.在GWNN-STGM中设计了一个图小波卷积神经网络层，并在该网络层中设计并引入了自适应邻接矩阵进行节点嵌入学习，使得模型能够在不需要结构先验知识的情况下，从数据集中自动发现隐藏的结构信息.此外，GWNN-STGM还包含了一个堆叠的扩张因果卷积网络层，使模型的感受野能够随着卷积网络层数的增加呈指数增长，从而能够处理长时序列.GWNN-STGM成功将图小波卷积神经网络层和扩张因果卷积网络层两个模块进行有效集成.通过在公共交通网络数据集上实验发现，提出的GWNN-STGM的性能优于其他的基准模型，这表明设计的图小波卷积神经网络模型在从输入数据集中探索时空结构方面具有很大的潜力.

The spatiotemporal graph modeling is a basic work to analyze the spatial relationship and time trend of each element in the graph structure system. The traditional spatiotemporal graph modeling method is mainly based on the explicit structure of nodes and the fixed relationship between nodes in the graph for spatial relationship mining, which severely limits the flexibility of the model. Besides, traditional methods cannot capture long-term trends. To overcome these shortcomings, a novel end-to-end neural network model for spatiotemporal graph modeling is proposed, i.e., a graph wavelet convolutional neural network for spatiotemporal graph modeling called GWNN-STGM. A graph wavelet convolutional neural network layer is designed in GWNN-STGM. A self-adaption adjacency matrix is introduced in this network layer for node embedding learning so that the model can be used without prior knowledge of the structure. The hidden structural information is automatically found in the training dataset. In addition, GWNN-STGM includes a stacked dilated causal convolutional network layer so that the receptive field of the model can grow exponentially with the increase in the number of convolutional network layers that can handle long-term sequences. The GWNN-STGM successfully integrated the two modules of graph wavelet convolutional neural network layer and dilated causal convolutional network layer. Experimental results on two public transportation network datasets show that the performance of the proposed GWNN-STGM is better than other latest benchmark models, which shows that the designed graph wavelet convolutional neural network model has a great ability to explore the spatial-temporal structure from the input dataset.

国家自然科学基金（61703013，91646201）；北京市自然科学基金（4192004）