Graph WaveNet for Deep Spatial-Temporal Graph Modeling

TL;DR

The paper addresses the challenge of modeling spatial-temporal data without relying on pre-defined graphs and with long-range temporal dependencies. It introduces Graph WaveNet, combining a self-adaptive adjacency learning mechanism with diffusion-like graph convolution and a dilated causal temporal backbone (Gated TCN) to capture complex spatiotemporal patterns. The model is trained end-to-end and demonstrates state-of-the-art performance on METR-LA and PEMS-BAY, with efficient inference due to simultaneous multi-step forecasting. These contributions enable better discovery of hidden inter-node relationships and more scalable temporal modeling in traffic forecasting settings.

Abstract

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.

Figures (6)

• Figure 1: Spatial-temporal graph modeling. In a spatial-temporal graph, each node has dynamic input features. The aim is to model each node's dynamic features given the graph structure.
• Figure 2: Dilated casual convolution with kernel size 2. With a dilation factor $k$, it picks inputs every $k$ step and applies the standard 1D convolution to the selected inputs.
• Figure 3: The framework of Graph WaveNet. It consists of $K$ spatial-temporal layers on the left and an output layer on the right. The inputs are first transformed by a linear layer and then passed to the gated temporal convolution module (Gated TCN) followed by the graph convolution layer (GCN). Each spatial-temporal layer has residual connections and is skip-connected to the output layer.
• Figure 4: Comparison of prediction curves between WaveNet and Graph WaveNet for 60 minutes ahead prediction on a snapshot of the test data of METR-LA.
• Figure 5: The heatmap of the learned self-adaptive adjacency matrix for the first 50 nodes.