Graph WaveNet for Deep Spatial-Temporal Graph Modeling

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.

Spatiotemporal Adaptive Gated Graph Convolution Network for Urban Traffic Flow Forecasting

“…Error-prone predictions are used as input with previous observations for further predictions, resulting in rapid error accumulation, especially for long-term predictions where the error will continue to rise. Therefore, we adopt the same method as Wu et al [26] to directly predict the future steps, as shown in Figure5(b), to avoid the error dispersion caused by inaccurate prediction. To achieve this, we set the number of output channels of the linear layer as a factor of step length to get our desired output Y ′ and use Mean Square Error (MSE) loss to train the model which can be formulated as:…”

Global Spatial-Temporal Graph Convolutional Network for Urban Traffic Speed Prediction

“…Afterward, ST-MetaNet [37] utilizes sequence-to-sequence structure and combines the graph attention network (GAT) with the recurrent neural network (RNN) for capturing the spatial-temporal correlations. Wu et al [14] integrated Wavenet [15] into the GCN to extract the dynamic temporal dependencies of traffic data, while using an adaptive adjacency matrix to obtain hidden spatial dependencies in the road network. This self-adaptive adjacency matrix is constructed by the similarity of different node embeddings on the road network.…”

“…We compared our model with the following eight models: Graph WavaNet [14]: Graph WavaNet employs graph convolution network (GCN) with self-adaptive matrix and a stacked dilated 1D convolution to model the spatial-temporal graph.…”

“…Based on the experimental result shown in Figure 8, we found that GSTGCN performs better than Graph WaveNet, which demonstrates that GSTGCN is more effective in modeling the complex spatiotemporal correlations. In this section, we mainly discuss the structural differences between STGCN [13], ST-MetaNet [37], Graph WaveNet [14], and our proposed model GSTGCN.…”

“…The graph convolution network here represents the road network structure as a fixed weighted graph. Wu et al [14] integrated Wavenet [15] into the GCN to capture the dynamic spatial-temporal correlations of traffic data, while using an adaptive adjacency matrix to obtain hidden spatial dependencies in the road network. However, there are still some limitations in these methods: (i) RNN-based models are challenging to train well [16] due to the problem of gradient disappearance or gradient explosion, and the receptive field of RNNs is limited; (ii) many existing methods only consider localized spatial correlations but ignore non-local ones; and (iii) they do not utilize more complicated traffic-related features such as the existing periodicity, repeating patterns, and external factors.…”