# Meta-Extreme Learning Machine for Short-Term Traffic Flow Forecasting
## 3 Experiments
### Performance Evaluation
It can be visually seen that the ABC-ELM model performance is good in four different scenarios, and the relative errors fluctuate above and below 0 in most cases. The relative error of our ABC-ELM model remains almost near 0 when the traffic flow is relatively stable, such as when the traffic flow is low and stable in the middle of the night or when the traffic flow gradually increases in the early morning. However, when the traffic volume changes rapidly, the relative error of the ABC-ELM model also fluctuates greatly. Figure 5: Comparison of MAPE values of three learning models GA-ELM, GSA-ELM, and ABC-ELM. ABC-ELM has the lowest MAPE values in all four datasets A1, A2, A4, and A8. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Models** & **Data A1** & **Data A2** & **Data A4** & **Data A8** \\ \hline ELM & 15.429 & 15.544 & 15.168 & 14.267 \\ GA-ELM & 15.416 & 15.522 & 15.136 & 14.161 \\ GSA-ELM & 15.324 & 15.431 & 15.066 & 14.151 \\
**ABC-ELM** & **15.323** & **15.429** & **14.992** & **14.136** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The comparison of AIC for four models based on ELM. Finally, Figure 7a-f represent the partial comparison of predicted values for each learning model in different cases. Since we are taking nine elements as input feature values, the predicted value segments obtained here are also nine moments. It represents the traffic flow values for the first ten-minute moment, the traffic flow values for the second ten-minute moment, and so on. The red line represents the actual value, the blue line represents the predicted value from the ABC-ELM model, the green line represents the predicted value from the GSA-ELM model, and the black line represents the predicted value from the ELM model. The period selected for part Figure 7a is early morning, and it can be seen that the traffic flow on the road shows a steady increase with time. The predicted values of ABC-ELM, GSA-ELM, and ELM models also show a steady increase, but the ABC-ELM model is smoother, and it is smoother than the ELM model. In addition, the ABC-ELM model is more sensitive to changes in traffic flow values. The period selected for part Figure 7b is around 11:40 a.m., which is at the peak of the traffic flow, and the traffic flow is large and changes repeatedly within a short period. It can be seen that the ABC-ELM model forecasting at the fourth moment is the closest to the actual traffic flow. Although there is still a certain gap with the actual value error, the ABC-ELM model is more accurate compared with the same type of model. Figure 6: The (**a**–**h**) represent the forecasting–measurement value comparison plots and the forecasting–measurement value relative error of ABC-ELM model under four training sets. Figure 7c is selected with the period around 10:00 p.m. As night comes, the traffic flow gradually decreases, and the three models perform well. Figure 7d is also taken from the peak traffic flow hours. The GSA-ELM model is not as responsive as the ABC-ELM model to large changes in traffic flow in the short-term. In addition, most of the time the gradient of the predicted values of the GSA-ELM model is insufficient, When the actual traffic flow changes significantly in the short-term, we have less accurate forecasts than with the ABC-ELM model. Figure 7e shows the predictions of each model when a huge drop in traffic flow occurs. It can be seen that during the fourth moment, a precipitous drop in the actual traffic flow occurs, followed by an increase to about 4000. While the ABC-ELM model deviates more from the actual value in the fifth moment of forecasting, this is because the ABC-ELM model is more sensitive to changes in the data. Figure 7f shows a steady growth trend similar to a convex function, and the ABC-ELM model works well for that case as well.