## 3 Data Processing and Methodology
### Short-Term Traffic Speed Prediction Models
To alleviate this problem, one study [52] developed a localized technique to reduce the number of parameters of spectral graph convolution. \[\Theta*\mathcal{G}x=\Theta(\mathcal{L})x\approx\sum_{k=0}^{\mathcal{K}-1} \theta_{\mathcal{K}}P_{\mathcal{K}}\big{(}\hat{\mathcal{L}}\big{)}x, \tag{4}\]  
where \(P_{k}\big{(}\hat{\mathcal{L}}\big{)}\) represents a Chebyshev polynomial of order k evaluated on the scaled Laplacian. \(\hat{\mathcal{L}}=2\mathcal{L}/\lambda_{max}-I_{n}\), \(\theta\in\mathbb{R}^{\mathcal{K}}\), and \(\lambda_{max}\) denote the vector of polynomial coefficients, kernel size of the graph convolution, and the maximum eigenvalue of \(\mathcal{L}\), respectively. STGCN constructs ST-conv blocks that deal with temporal and spatial features through temporal gated-conv and spatial graph-conv. The sandwich structure comprises two temporal gated-convs with a spatial graph-conv in between and supports bottleneck strategies through upscaling and downscaling of the channels. Dropout and batch normalization were involved in mitigating overfitting. The output for the input \(v\) follows the equation:  
\[v^{l+1}=\Gamma_{1}^{l}*\tau ReLU\Big{(}\Theta^{l}*_{\mathcal{G}}\left(\Gamma_ {0}^{l}*\tau v^{l}\right)\Big{)}, \tag{5}\]  
where \(v\) is an observation vector, \(\Gamma_{0}^{l}\) and \(\Gamma_{1}^{l}\) are the upper and lower temporal kernel within block \(l\), respectively, and \(\Theta^{l}\) is the spectral kernel of graph convolution. In this study, we used speed data as a feature matrix. Moreover, the brake and TSR data were learnt in the same structure and then concatenated to observe the change in performance. The other deep learning method, CNN, was trained with the same data and observed the performance change to find the appropriate data for each method. Unlike STGCN, the CNN model, which learns image data consisting of time and node indexes as an axis, extracts the feature of the data as a combination of convolutional and pooling layers. The output of the model is calculated using the following formula:  
\[o_{i}=pool(ReLU(W_{i}x_{i}+b_{i})), \tag{6}\]  
where \(pool\) denotes average pooling, and \(i\) denotes the depth of CNN. We used a simple CNN structure owing to the relatively high computational cost, and there was no significant change in performance when using a model with many layers, such as ResNet, called the revolution of depth. Traffic speed, brake, and TSR data acquired from urban road networks were learnt using CNN and STGCN models. To develop a model with optimal performance, we observed which data could have the highest performance when applied to various model learning. In this study, we found that the best performance is to learn TSR and brake data that could reflect the intention of the driver and road environment by CNN and traffic speed data by STGCN. We defined a hybrid model by converging the two models based on the results of the experiment. The architecture of the model derived through this study is shown in Figure 7.  
After the feature extraction was achieved using the presented STGCN and CNN model, the weights for each feature were learned with a multi-layer perceptron. For learning, we used 80% (49 days) of the total data, with 10% (6 days) used for validation, 10% used for testing, and the batch size set to 256. For model evaluation, we used mean absolute error (MAE) and root mean square deviation (RMSE), as follows:  
\[MAE=\frac{\sum_{i=1}^{n}\lvert y_{i}-x_{i}\rvert}{n}, \tag{7}\]  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_{i}-y_{i})^{2}}, \tag{8}\]  
where \(n\) denotes the number of samples, \(y\) denotes the ground truth, and \(x\) denotes the predicted value. RMSE is a root form of mean square error (MSE). MSE squares the difference between the predicted and target values, and those features cause some issues. MSE is sensitive to outliers. If the error is between 0 and 1, it reflects as smaller than the original; if the error is greater than 1, it reflects as larger than the original. RMSE can solve MSE problems to some extent.