## Materials and Methods
### Structures of the Three Spatial-Temporal Components
#### 3.3.2 Global Correlated Spatial Module  
This paper proposes a global correlated spatial module for capturing complex spatial correlations between nodes on the traffic network. The module contains a localized graph convolution and a global correlated mechanism with residual connection [16], where the former is used to extract local spatial correlations while the latter is used to capture the non-local spatial correlations. **Localized Graph Convolution:** Since traditional convolutions fail to effectively extract the complicated spatial correlations between different nodes on the traffic network, the spectral graph theory extends the convolution to the graph-structured data. In spectral graph theory, the Laplacian matrix of a graph represents its topological structure. Therefore, we can study the properties of the graph by analyzing the eigenvalues and eigenvectors of the Laplacian matrix. The Laplacian matrix of a graph is defined as \(\mathbf{L}=\mathbf{D}-\mathbf{A}\), and the normalized Laplacian matrix \(\mathbf{L}=\mathbf{I}_{N}-\mathbf{D}^{-\frac{1}{2}}\mathbf{A}\mathbf{D}^{- \frac{1}{2}}\in\mathbb{R}^{N\times N}\), where \(\mathbf{I}_{N}\) is a unit matrix with \(N\) dimensions, \(\mathbf{A}\in\mathbb{R}^{N\times N}\) is the adjacency matrix, and the \(\mathbf{D}\in\mathbb{R}^{N\times N}\)  
Figure 6: Dilated casual convolution with kernel size 2. With dilation factor \(d\), it performs a standard 1D convolution on the selected sequence that is picked from the input every \(d\) steps. is the degree matrix, with \(\mathbf{D}_{ii}=\sum_{j}\mathbf{A}_{ij}\). The eigenvalue decomposition of the normalized Laplacian matrix is \(\mathbf{L}=\mathbf{U}\mathbf{\Lambda}\mathbf{U}^{T}\), where \(\mathbf{U}\) is eigenvectors of the normalized \(\mathbf{L}\) and \(\mathbf{\Lambda}\) is the diagonal matrix with corresponding eigenvalues. Let \(\mathbf{x}\in\mathbb{R}^{N}\) be the signal of all nodes on the traffic network. The Fourier transform of the signal \(\mathbf{x}\) is \(\mathbf{\hat{x}}=\mathbf{U}^{T}\mathbf{x}\). According to the properties of the Laplacian matrix, \(\mathbf{U}\) is an orthogonal matrix, so the inverse Fourier transform of the signal \(\mathbf{\hat{x}}\) is \(\mathbf{x}=\mathbf{U}\mathbf{\hat{x}}\). Based on these concepts, the signal \(\mathbf{x}\) on graph \(\mathbf{G}\) is filtered by the convolution kernel \(g_{\theta}\):  
\[g_{\theta}*_{\mathbf{G}}\mathbf{x}=g_{\theta}(\mathbf{L})\mathbf{x}=g_{\theta}(\mathbf{U} \mathbf{\Lambda}\mathbf{U}^{T})\mathbf{x}=\mathbf{U}g_{\theta}(\mathbf{\Lambda}) \mathbf{U}^{T}\mathbf{x} \tag{7}\]  
The spectral graph convolution first uses the Fourier transform to map the graph signal \(\mathbf{x}\) and the kernel \(g_{\theta}\) into an orthogonal space formed by the Laplacian matrix eigenvectors, then performs convolution in the Fourier domain, and last conducts the inverse Fourier transform to obtain the final graph convolution results. However, this method requires explicit Laplacian matrix eigenvalue decomposition, and the computational complexity is too high, when the scale of the graph is large. Therefore, in this paper, we employ the Chebyshev polynomial [29] to approximate the convolution kernel and solve this problem. The formula is as follows:  
\[g_{\theta}*_{\mathbf{G}}\mathbf{x}=g_{\theta}(\mathbf{L})\mathbf{x}=\sum_{k=0}^{K-1}\theta _{k}T_{k}(\widetilde{\mathbf{L}})\mathbf{x} \tag{8}\]  
where the parameter \(\theta\in\mathbb{R}^{K}\) is a vector of polynomial coefficients and \(\widetilde{\mathbf{L}}=\frac{2}{\lambda_{max}}\mathbf{L}-\mathbf{I}_{N}\), with \(\lambda_{max}\) the maximal eigenvalue of the Laplacian matrix. The Chebyshev polynomials are recursively defined as \(T_{k}(\mathbf{x})=2\mathbf{x}T_{k-1}(\mathbf{x})-T_{k-2}(\mathbf{x})\), in which \(T_{0}(\mathbf{x})=1\), \(T_{1}(\mathbf{x})=\mathbf{x}\). We denote \(x_{i,t}\in\mathbb{R}^{C}\) as all extracted features of the \(i\)th node at the \(t\)th historical timestamp, where \(C\) is the number of the input channels.