# Multi-Step Traffic Speed Prediction Based on Ensemble Learning on an Urban Road Network
## 5 Discussion
### Prediction Accuracy
In Figure 4b, the MAPE of southbound DDSELM is 2.10% lower (14.90% versus 17.00%) than KNN in one-step-ahead prediction, 1.05% (16.99% versus 18.04%) in two-step-ahead prediction, and 4.30% (17.82% versus 22.12%) in three-step-ahead prediction, respectively. Notably, the prediction accuracy of the northbound DDSELM is better than southbound, which might be that the correlation between travel speed of the northbound links is higher than the southbound. Furthermore, a more detailed analysis about the two ensemble models of DDSELM and BAGGING was conducted for the multi-step-ahead prediction over a weekday of Wednesday and a weekend of Saturday in Figure 5. Regardless of the ahead-prediction step size, the performance of these two ensemble models performs much better during the off-peak hours (9:00-16:00) than peak ones (7:00-8:00 and 17:00-18:00), and DDSELM is especially better than BAGGING. The reason might be because BAGGING only uses the average of all underlying prediction outputs to make up for the shortcomings of each individual prediction model, but DDSELM uses the ridge regression algorithm in the mega learner. The ridge regression uses L2 regularization for reducing the prediction error. During the peak hours, both southbound and northbound predictions have much higher accuracy in the morning peak period (7:00-9:00) than evening (17:00-19:00). As far as the evening peak period, single-step prediction is better than multi-step-ahead for the northbound segments. This is because the traffic flow during the evening peak hours was much larger than the morning and there was a sharp drop in travel speed around 17:00. Therefore, there is a certain difference in the accuracy of two-way prediction. Compared with the accuracy of weekdays, accuracy of one-step-ahead northbound prediction on weekends slightly increases (8.36% to 7.54%), while the accuracy of one-step-ahead southbound prediction decreases (9.60% to 13.79%). The multi-step prediction (two-step-ahead prediction and three-step prediction) also has a similar trend, namely, prediction accuracy increases in northbound while decreasing in the southbound direction. This may be because the southbound data itself is less relevant than the northbound data in Tables 2 and 3. Figure 5: The prediction comparisons by two ensemble methods on Wednesday and Saturday:(**a**) one-step-ahead prediction result on Wednesday in northbound; (**b**) two-step-ahead prediction result on Wednesday in northbound; (**c**) three-step-ahead prediction result on Wednesday in northbound; (**d**) one-step-ahead prediction result on Saturday in northbound; (**e**) two-step-ahead prediction result on Saturday in northbound; (**f**) three-step-ahead prediction result on Saturday in northbound; (**g**) one-step-ahead prediction result on Wednesday in southbound; (**h**) two-step-ahead prediction result on Wednesday in southbound; (**j**) one-step-ahead prediction result on Saturday in southbound; Saturday in southbound; (**k**) two-step-ahead prediction result on Saturday in southbound; (**l**) three-step-ahead prediction result on Saturday in southbound.