# Multi-View Multi-Attention Graph Neural Network for Traffic Flow Forecasting
## 4 Experiments
### Results and Analyses
#### 4.3.1 Overall Comparison  
1. Traditional HA and ARIMA performed the worst in both the short and long term. The reason is that the two models capture only a limited temporal correlation and ignore some important but indispensable influences, such as the cyclical impact of urban residents' daily travel patterns on subway traffic. In addition, important spatial and topological information about the subway network is missing. 2. LSTM, TCN and GCN perform better than traditional models because they capture more temporal correlations and GCN captures more spatial correlations. However, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**10 Min**} & \multicolumn{3}{c}{**15 Min**} & \multicolumn{3}{c}{**30 Min**} \\ \cline{2-10}  & **RMSE** & **MAE** & **WMAPE** & **RMSE** & **MAE** & **WMAPE** & **RMSE** & **MAE** & **WMAPE** \\ \hline HA [1] & 58.45 & 31.28 & 17.20\% & 101.73 & 51.17 & 18.92\% & 312.10 & 159.71 & 29.99\% \\ ARIMA [2] & 51.53 & 29.38 & 15.58\% & 81.94 & 42.21 & 15.97\% & 189.89 & 102.36 & 19.25\% \\ LSTM [3] & 38.21 & 22.85 & 13.51\% & 42.92 & 29.03 & 12.86\% & 97.35 & 57.82 & 11.79\% \\ TCN [25] & 36.18 & 19.77 & 12.71\% & 40.28 & 26.34 & 10.45\% & 65.21 & 39.68 & 7.47\% \\ GCN [12] & 37.21 & 19.82 & 12.82\% & 42.59 & 28.65 & 11.78\% & 67.23 & 40.05 & 7.62\% \\ AGCRN [26] & 31.09 & 17.78 & 11.95\% & 38.18 & 25.63 & 10.22\% & 57.66 & 35.81 & 6.89\% \\ ST-GCN [17] & 30.31 & 17.74 & 12.49\% & 36.94 & 21.31 & 8.67\% & 56.30 & 33.85 & 6.64\% \\ MTGNN [21] & 29.56 & 16.94 & 11.65\% & 35.76 & 20.40 & 8.89\% & 54.41 & 32.50 & 6.36\% \\ AMGC-AT (ours) & **25.32** & **16.65** & **10.62\%** & **31.24** & **19.67** & **8.45\%** & **50.79** & **30.68** & **5.86\%** \\ Improvement & 16.74\% & 5.54\% & 12.52\% & 14.47\% & 3.71\% & 5.20\% & 7.12\% & 5.93\% & 8.53\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison of different methods on in-flow dataset. the performance of the LSTM was significantly reduced in the long-term forecast. As can be observed, in most cases, complex deep-learning architectures (such as AGCRN, ST-GCN and MTGNN) yield more favorable results than single models. This is mainly because spatiotemporal features can be extracted from these models simultaneously. 3. Notably, our self-attention based multi-graph approach has better performance in extracting joint spatiotemporal features compared to AGCRN, STGCN and MTGNN. Compared to STGCN, our model showed a significant increase in the accuracy of the predictions, because the AMGC-AT has two mechanisms of self-attention while the STGCN does not. For AGCRN and MTGNN, there are a number of differences compared to our proposed model. Firstly, AGCRN and MTGNN rely on their own adaptive graph-learning modules in order to learn the spatial correlations, while our proposed AMGC-AT relies on four different graph structures that use domain knowledge in order to learn spatial correlations, and our model is more direct and effective at learning spatial correlations. Secondly, MTGNN uses a mix-hop propagation graph solution, whereas STGCN, AGCRN, and our AMGC-AT all make use of spectral convolution, which is more suitable for node prediction on a metro network of this size. AGCRN also uses RNN to extract temporal features, which hurts the robustness of the model due to severe sample fluctuations and specific gradient explosions, while our AMGC-AT uses a more efficient gated convolution for extracting and outputting temporal features. In conclusion, compared to the most advanced models to date, only our model incorporates two self-attention mechanisms that are an integral part of AMGC-AT's state-of-the-art performance. The effectiveness of the components of the AMGC-AT model will be analyzed and validated in the next chapter of the ablation experiment. 4. In the case of RMSE, the significant improvements in three time intervals compared to the best (available) models were 16.74%, 14.47%, and 7.12%, respectively. The MAE improvement rates were 5.54%, 3.71% and 5.93%, respectively.