## 3 Data Processing and Methodology
### Short-Term Traffic Speed Prediction Models  
The methods used in this study are STGCN and CNN. STGCN was applied to deal with spatio-temporal and graph-based information. The STGCN used in this study consists of two ST-conv blocks, and one ST-Conv block consists of two temporal gated-conv layers and one spatial graph-conv layer. The architectures of STGCN and the temporal gated-conv layer are shown in Figure 6 [50]. As illustrated in Figure 6, STGCN consists only of convolutional layers. However, CNN cannot deliver long-term dependency because it simply looks at the currently entered image. Generally, it is imperative to consider the previous state for predicting time-series data. Therefore, it has been customary for models used primarily to predict time-series data to use RNN-based models that can learn sequences. STGCN uses the temporal gated-conv layer to learn temporal features with CNN-based models. The temporal gated-conv layer consists of a 1D-conv and gated linear unit (GLU) [51]. GLU was first introduced by presenting a method based on CNN in language modeling, where RNN was initially dominant. It has long-term dependencies such as LSTM by extracting hierarchical features. The performance was better than that of the existing RNN method and had less computation. The temporal gated-conv layer of STGCN to which this GLU is applied expresses the data as a vector through 1D-conv. We applied the sigmoid function to half of the vector and determined the weight of the vector sequence by the elementwise product with the other half. Finally, by adding the input, GLU was generated as a form of residual learning. The following equation can express a temporal gated-conv:  
\[\Gamma*\tau Y=P\odot\sigma(Q)\in\mathbb{R}^{M-K_{t}+1\times C_{0}}, \tag{1}\]  
where a three-dimensional variable can be generated using the convolution kernel \(\Gamma\) equally for all nodes \(Y\). \(P\) and \(Q\) represent each half of the vectors converted into 1D vectors, \(M\) represents the size of the time step to be considered, \(K_{t}\) represents the kernel size of the temporal convolution, and \(C_{0}\) represents the channel size. In this study, the kernel size was determined to be 3 through the grid search, and the time step to be considered was 12, which means 120 min. STGCN, which learns temporal features through the temporal gated-conv layer, uses the spatial graph-conv layer to reflect the spatial features. However, the convolution operation cannot be applied directly to the graph. As a solution, STGCN employs spectral graph convolution to apply a convolution operation to the graph data. Spectral graph convolution performs convolution operations using Fourier transform used in signal processing. Graph Fourier basis \(U\in\mathbb{R}^{n\times n}\) is the matrix of eigenvectors of the normalized graph Laplacian \(\mathcal{L}\), defined as follows:  
\[\mathcal{L}=I_{n}-D^{-\frac{1}{2}}\ \hat{A}D^{-\frac{1}{2}}=U\Lambda U^{T}\in \mathbb{R}^{n\times n}, \tag{2}\]  
where \(I_{n}\) is an identity matrix, \(D\) is the diagonal degree matrix, and \(A\) denotes the weighted adjacency matrix. Figure 6: STGCN and temporal gated-conv. The spatial graph-conv layer performs spectral graph convolution by reshaping data that have passed through the temporal gated-conv layer. The spatial graph-conv layer updates the status of the current node with information from the peripheral nodes and is performed via the Laplacian matrix. Multiplying the Laplacian matrix by the feature matrix of the node provides the difference between the node and neighboring node for the feature. The notion of the spectral graph convolution operator '\(*\mathcal{G}\)' is defined as the multiplication of a signal \(x\in\mathbb{R}^{n}\) with a kernel \(\Theta\). \[\Theta*\mathcal{G}x=\Theta(\mathcal{L})x=\Theta\Big{(}U\Lambda U^{T}\Big{)}xs =U\Theta(\Lambda)U^{T}x, \tag{3}\]  
It requires a substantial computational cost, such as \(\Theta\).