# Time-Evolving Graph Convolutional Recurrent Network for Traffic Prediction
## 4 Experiments and Discussion
### Ablation Study  
We conduct an ablation study on the METR-LA dataset to validate the effectiveness of the graph convolution module with adaptive time-evolving graphs. We first build a model that replaces the time-evolving graphs in TEGCRN with a static adaptive graph as the manner in [14]. Additionally, we further remove the time-evolving graph generation module and use only static predefined distance-based graph, as per the manner in [12]. For these models, we calculate the average metrics of all the output time steps. The results are reported in Table 5. We can see that, with learned global dependencies, the convolution with adaptive graph achieves higher performance than that with only predefined distance-based graph. Furthermore, the proposed time-evolving graph convolution in TEGCRN further improves the prediction performance by capturing more implicit inter-node dynamics. Figure 5 shows the heatmaps of the normalized distance-based static adjacency graph and the learned time-evolving adjacency graphs in some selected time slots. A darker color means a higher value of weight between the corresponding nodes. When the static graph  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**15 min (3 Steps)**} & \multicolumn{3}{c}{**30 min (6 Steps)**} & \multicolumn{3}{c}{**60 min (12 Steps)**} \\  & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** \\ \hline HA & 2.88 & 5.59 & 6.80\% & 2.88 & 5.59 & 6.80\% & 2.88 & 5.59 & 6.80\% \\ ARIMA & 1.62 & 3.30 & 3.50\% & 2.33 & 4.76 & 5.4\% & 3.38 & 6.50 & 8.30\% \\ FC-LSTM & 2.05 & 4.19 & 4.80\% & 2.20 & 4.55 & 5.20\% & 2.37 & 4.96 & 5.70\% \\ DCRNN & 1.38 & 2.95 & 2.90\% & 1.74 & 3.97 & 3.90\% & 2.07 & 4.74 & 4.90\% \\ STGCN & 1.36 & 2.96 & 2.90\% & 1.81 & 4.27 & 4.17\% & 2.49 & 5.69 & 5.79\% \\ Graph-WaveNet & 1.30 & 2.74 & 2.73\% & 1.63 & 3.70 & 3.67\% & 1.95 & 4.52 & 4.63\% \\ MTGNN & 1.32 & 2.79 & 2.77\% & 1.65 & 3.74 & 3.69\% & 1.94 & 4.49 & 4.53\% \\ TEGCRN & 1.29 & 2.72 & 2.69\% & 1.60 & 3.67 & 3.59\% & 1.88 & 4.39 & 4.43\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Prediction Results of PEMS-BAY Dataset.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**15 min (3 Steps)**} & \multicolumn{3}{c}{**30 min (6 Steps)**} & \multicolumn{3}{c}{**60 min (12 Steps)**} \\  & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** & **MAE** & **RMSE** & **MAPE** \\ \hline HA & 4.16 & 7.80 & 13.00\% & 4.16 & 7.80 & 13.00\% & 4.16 & 7.80 & 13.00\% \\ ARIMA & 3.99 & 8.21 & 9.60\% & 5.15 & 10.45 & 12.70\% & 6.90 & 13.23 & 17.40\% \\ FC-LSTM & 3.44 & 6.30 & 9.60\% & 3.77 & 7.23 & 10.90\% & 4.37 & 8.69 & 13.20\% \\ DCRNN & 2.77 & 5.38 & 7.30\% & 3.15 & 6.45 & 8.80\% & 3.60 & 7.60 & 10.50\% \\ STGCN & 2.88 & 5.74 & 7.62\% & 3.47 & 7.24 & 9.57\% & 4.59 & 9.40 & 12.70\% \\ Graph-WaveNet & 2.69 & 5.15 & 6.90\% & 3.07 & 6.22 & 8.37\% & 3.53 & 7.37 & 10.01\% \\ MTGNN & 2.69 & 5.18 & 6.86\% & 3.05 & 6.17 & 8.19\% & 3.49 & 7.23 & 9.87\% \\ TEGCRN & 2.65 & 5.10 & 6.74\% & 3.04 & 6.16 & 8.22\% & 3.49 & 7.32 & 10.03\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Prediction Results of METR-LA Dataset.  
assigns high weights to the neighboring node pairs in a local manner, the time-evolving graphs can learn some other sparse connections among the nodes from a global view. In different time slots, the trained time-evolving graphs attach different importance to the traffic node pairs and form dynamic topologies. These learned implicit dynamics of inter-node dependency can act as the complement of the static distance-based graph. This helps the graph convolution to capture more urban semantics, which contributes to the better prediction performance. In sum, the proposed graph convolution with adaptive time-evolving graphs is effective to model more comprehensive inter-node dependencies than those with only static graphs.