## 4 Methods  
### Gcn  
The GCN is a type of neural network with a graph structure in each node so that the graph can utilize the graph structure's information. Compared to the original neural network, the GCN interacts with other nodes as a graph structure. It has been widely used in social networks and natural language processing. In this study, the \(p\)-th layer and \(p+1\)-th layer are propagated through the following equation:  
\[\mathbf{X}^{p+1}=\sigma(\hat{\mathbf{D}}^{-\frac{1}{2}}\hat{\mathbf{A}}\hat{ \mathbf{D}}^{-\frac{1}{2}}\mathbf{X}^{p}\mathbf{W}^{p}), \tag{1}\]  
where \(\mathbf{X}^{p}\) is the \(p\)-th \(|\mathcal{N}|\times F^{p}\) feature matrix; \(p\) is the number of hidden layers; \(|\mathcal{N}|\) is the cardinality of the number of nodes \(\mathcal{N}\); \(F^{p}\) is the number of features of each node of the  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Pearson Correlations** & **Traffic—UB** & **Traffic—LB** & **Temp.** & **Rainfall.** & **Wind Speed** & **Wind Direction** & **Humidity** & **hPa** \\ \hline Traffic—UB & 1.00 & 0.80 & 0.20 & \(-\)0.02 & 0.19 & 0.23 & \(-\)0.28 & 0.05 \\ Traffic—LB & 0.80 & 1.00 & 0.28 & \(-\)0.02 & 0.33 & 0.37 & \(-\)0.48 & 0.04 \\ Temp. & 0.20 & 0.28 & 1.00 & 0.07 & 0.18 & 0.13 & 0.00 & 0.86 \\ Rainfall & \(-\)0.02 & \(-\)0.02 & 0.07 & 1.00 & 0.05 & \(-\)0.00 & 0.13 & 0.13 \\ Wind speed & 0.19 & 0.33 & 0.18 & 0.05 & 1.00 & 0.50 & \(-\)0.49 & \(-\)0.03 \\ Wind direction & 0.23 & 0.37 & 0.13 & \(-\)0.00 & 0.50 & 1.00 & \(-\)0.48 & \(-\)0.07 \\ Humidity & \(-\)0.28 & \(-\)0.48 & 0.00 & 0.13 & \(-\)0.49 & \(-\)0.48 & 1.00 & 0.40 \\ hPa & 0.05 & 0.04 & 0.86 & 0.13 & \(-\)0.03 & \(-\)0.07 & 0.40 & 1.00 \\ \hline \hline \end{tabular}
\end{table}
Table 2: A correlation matrix.  
Figure 2: Weekly meteorological information from 2019 to 2022.  
\(p\)-th layer; \(\sigma(\cdot)\) is a rectified linear unit (ReLU) function, one of the widely-used activation functions in the neural network techniques; \(\hat{\mathbf{D}}\) is a diagonal node degree matrix of \(\hat{\mathbf{A}}\); \(\hat{\mathbf{A}}\) is a sum of adjacency matrix \(\mathbf{A}\); \(\mathbf{W}^{p}\) is the \(p\)-th \(F^{p}\times F^{p+1}\) weight matrix with trainable parameters; and identity matrix \(\mathbf{I}\) is to consider self-features of each node. Note that \(\hat{\mathbf{D}}^{-\frac{1}{2}}\hat{\mathbf{A}}\hat{\mathbf{D}}^{-\frac{1}{2} }\mathbf{X}^{p}\) represents the symmetric approximation of the matrix \(\hat{\mathbf{A}}\mathbf{X}^{p}\).  
The overall data structure of this study is visualized in Figure 3. Each node of a deep learning approach has a graph structure containing 168 nodes. Each node of the graph represents 1 h. For example, 168 nodes are interconnected in two ways. The first way is the consideration of hourly interdependence. For instance, a node from 0 to 1 a.m. and another node from 1 to 2 a.m. are connected. Furthermore, a node from 0 to 1 a.m. of day 0 and a node from 0 to 1 a.m. of day 1 are connected. Therefore, the graph structure contains 311 nodes representing a 1-week graph structure.  
The overall graph structure is different from that in previous studies. Instead of focusing on the spatial dependencies, this study focused on the temporal dependencies between the nodes representing every hour. We found strong temporal dependencies, as shown in Figure 1. Holidays were the exception to the strong dependencies, so we considered holidays as a node attribute. Spatial dependencies were not considered since we only targeted one detector point with two directions.