## 5 Results
### Comparative Results  
Before we compare the calibration errors, it should be clear what the quantities of the parameters for the CF modeling are. For the DBM, the calibration process must be conducted once for every driver so that the CF model can well replicate the inter-driver heterogenous behavior of each driver. Thus, the number of parameters for the DBM are \(N\) times the number of model parameters, where \(N\) represents the number of drivers. For example, 200 parameters are needed to be calibrated for 40 drivers using IDM, while 440 parameters are needed when using Wiedemann. Meanwhile, the DBDM is not related to the number of drivers because it is determined by the kinds of segmented driving modes, so the number of parameters for the DMBM is \(K\) times five, where \(K\) represents the number of driving modes. In this study, this means that 25 parameters are needed for the IDM and 55 are needed for the Wiedemann.  
First, on the comparison of the calibration errors of three DBM models, which is shown in Figure 9a, the IDM shows a clear advantage over the Wiedemann model, reaching 15%, but the error of the IDM is higher than that of the hybrid model. Considering that the parameters of the hybrid model are four times more than those of IDM, this reduction in error was expected. Meanwhile, the calibration error of the DBM is significantly higher than that of the DMBM. The latter reduces the error by 13.12%. This indicates that DMBM could better reproduce CF behavior with much less parameters than DBM.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Cluster** & **Explanation** & **Acc** & **Vel** & **Gap** & **Vel Diff** \\ \hline
0 & Slow and stable CF with & & At a relatively low velocity & With a large gap (\(>\)about & \\  & large gaps & \(\sim\) & (\(<\)about 12 m/s) & 10 m) & \(\sim\) \\
1 & Slow and stable CF with & & At a relatively low velocity & With a small gap (\(<\)about & \\  & small gaps & \(\sim\) & (\(<\)about 12 m/s) & 10 m) & \(\sim\) \\
2 & High-velocity stable CF & \(\sim\) & At a relatively high velocity & \(\sim\) & \(\sim\) \\  & & & (\(>\)about 12 m/s) & & \\
3 & Keeping away from & & \(\sim\) & - & Increase & Positive \\  & the leader & & \(\sim\) & - & Decrease & Negative \\
4 & Approaching the leader & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Qualitative interpretation of clustered driving modes.  
Figure 9: Comparative results of the models from two CF modeling perspectives. (**a**) Modeling errors of the investigated models; (**b**) calibration and validation errors of the hybrid model and the DMBM model.  
When examining the results more deeply, we found that in the five-fold cross-validation process, the mean validation error of the DBM is clearly higher than its calibration error (over 13%), while this does not exist in the DMBM (only 4.53% error growth), as shown in Figure 9b. This may indicate another advantage of the DMBM, that is the better portability or practicality. The parameters from the DBM may specialize in specific CF events, but the existing behavior variance between different events, even from the same driver, makes these parameters invalid to some extent, which can be viewed as a kind of \"overfitting\".