# Hybrid Graph Models for Traffic Prediction
## 6 Experimental Results
### Ablation Studies
#### 6.2.1 Impact of STA Module  
The proposed method uses the STA module which mainly includes spatial attention and temporal attention to extract complex spatial-temporal features. Some experiments are conducted to evaluate the impact of the STA module on the proposed method. We analyze the impact of different variants on the predictive performance based on the proposed method. The HGM-V1 uses 1D convolutions instead of temporal attention to extract temporal information. The HGM-V2 indicates that the spatial-temporal attention module consists of static graph convolution and 1D convolution operations. HGM-V3 performs graph convolution operations on static adjacency matrices. The HGM-V4 represents the extraction of spatial-temporal information of traffic networks in stages. In other words, the features extracted by spatial attention are used as the input information of temporal attention. The HGM-V5 indicates that the model only considers dynamically generated topology. Table 2 records the predictive performance of different methods on the two datasets. According to the experimental results, it can be concluded that the proposed method achieves the best prediction performance. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Data**} & \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**15 min**} & \multicolumn{3}{c}{**30 min**} & \multicolumn{3}{c}{**60 min**} \\  & & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** \\ \hline \multirow{6}{*}{PeMS} & HGM-V1 & 1.33 & 2.76 & 2.74\% & 1.66 & 3.71 & 3.68\% & 1.95 & 4.47 & 4.57\% \\  & HGM-V2 & 1.50 & 3.15 & 3.10\% & 2.02 & 4.54 & 4.52\% & 2.66 & 5.93 & 6.59\% \\  & HGM-V3 & 1.32 & 2.78 & 2.75\% & 1.70 & 3.95 & 3.80\% & 1.93 & 4.45 & 4.58\% \\  & HGM-V4 & 1.32 & 2.79 & 2.73\% & 1.64 & 3.71 & 3.64\% & 1.97 & 4.52 & 4.60\% \\  & HGM-V5 & 1.30 & 2.74 & 2.67\% & 1.62 & 3.69 & 3.60\% & 1.90 & 4.41 & 4.48\% \\  & HGM & 1.25 & 2.66 & 2.64\% & 1.54 & 3.57 & 3.47\% & 1.85 & 4.31 & 4.29\% \\ \hline \multirow{2}{*}{Data} & \multirow{2}{*}{Method} & \multicolumn{3}{c}{15 min} & \multicolumn{3}{c}{30 min} & \multicolumn{3}{c}{60 min} \\  & & MAE & RMSE & MAPE & MAE & RMSE & MAPE & MAE & RMSE & MAPE \\ \hline \multirow{6}{*}{METR-LA} & HGM-V1 & 2.66 & 5.11 & 6.86\% & 3.03 & 6.15 & 8.35\% & 3.45 & 7.20 & 10.14\% \\  & HGM-V2 & 3.19 & 6.09 & 8.41\% & 3.83 & 7.60 & 10.74\% & 4.69 & 9.20 & 14.55\% \\ \cline{1-1}  & HGM-V3 & 2.65 & 5.08 & 6.77\% & 3.04 & 6.15 & 8.42\% & 3.50 & 7.34 & 10.36\% \\ \cline{1-1}  & HGM-V4 & 2.70 & 5.25 & 6.97\% & 3.12 & 6.42 & 8.64\% & 3.55 & 7.47 & 10.21\% \\ \cline{1-1}  & HGM-V5 & 2.67 & 5.17 & 6.84\% & 3.10 & 6.30 & 8.57\% & 3.57 & 7.49 & 10.54\% \\ \cline{1-1}  & HGM & 2.58 & 5.06 & 6.60\% & 3.04 & 6.10 & 8.19\% & 3.35 & 7.03 & 9.65\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Prediction results of different variants of STA module. The HGM-V1 stands for using 1D convolution instead of temporal attention. The HGM-V2 means that the spatial–temporal attention module is composed of static graph convolution and 1D convolution operation. The HGM-V3 performs a static graph convolution operation on static graph. The HGM-V4 means extracting spatial–temporal information in stages. The HGM-V5 means using dynamic graphs instead of static graphs. Compared with the HGM-V1, the proposed method uses temporal attention to extract temporal information. On the PeMS-BAY and METR-LA datasets, MAPE decreases by 0.28% and 0.49% over the next 12 time steps, respectively. The HGM-V2 combines 1D convolution and static graph convolution operations to extract nonlinear temporal dependencies and complex spatial correlations. Compared with the HGM-V2, the proposed method shows a significant drop in both long-range and short-range predictive performance. On the PeMS-BAY and METR-LA datasets, the proposed method outperforms the HGM-V2 by 0.81 and 1.34 in MAE over the next 12 time steps.