## 6 Discussion  
This study introduces and investigates a new perspective in CF modeling, that is, modeling CF driving modes rather than for an individual human driver or an entire CF event (or a CF period in some studies). Although we have known and verified many times that the CF behavior of human beings is not static in the driving process, this study is the first in-depth study to discover the driving modes of the CF process and the improvements that can be achieved by modeling CF driving modes, with the help of the application of a novel approach in the clustering of multivariate time series data. This study also benefits from large-scale naturalistic driving data, which provides sufficient and diverse samples of drivers' CF behavior. In past research, a \"consensus\" has gradually formed that well-constructed driver-based models, which can reproduce CF trajectories better than those of driving-status-based models, such as the Wiedemann model. To some extent, these kinds of investigation results may lead to an emphasis on the inter-driver or inter-CF-period differences rather than intra-driver or intra-period variances in future CF modeling research. [PERSON] et al. proposed that the imprecise sub-models in Wiedemann lead to unsatisfactory results and pointed out a pathway to combine the state division of the Wiedemann with other CF models. That is why we also introduced a Wiedemann-IDM model for comparison. The result shows that this combination can be better than the original Wiedemann model, even IDM, but the error improvement of the IDM is relatively limited. This drives us to think about another aspect, that being how much potential improvement there could be if driving modes are well partitioned and modeled. Therefore, we introduced a novel and recent unsupervised multivariate time series clustering approach. The large accuracy increase in the DMBM has proved the effectiveness of the adopted clustering method. By using the graphical dependency structure of each subsequence, the algorithm can dig out the underlying multidimensional time-invariant relationship that cannot be expressed and distinguished using a simple threshold division. Meanwhile, once a TICC model has been trained, it can be applied to a new multivariate CF time series to predict clusters, which will not reduce applicability due to the inability to provide threshold division. The results confirm our initial conjecture, which is that modeling accuracy can be improved by modeling several shared underlying driving modes in the CF process. This is encouraging since it has been verified with only five driving mode classifications. As mentioned above, some researchers [7] have attempted to preliminary verify a conclusion, but on a scale of up to 30 classifications and with only 20 drivers, and the parameter number used for the DMBM is far more than the DBM (120 versus 80, based on the 4-parameter GHR model). That means that the CF event will be too fragmented, and it is hard to determine whether the accuracy improvement is due to reasonable behavior segmentation or that more parameters are used to describe shorter segments. Meanwhile, based on our experience in CF research, an enormous number of parameters will bring about an extreme increase in the calibration time, which is very negative for the practice of CF modeling. In contrast, we proved that only 25 parameters could well describe the CF behavior from 30 drivers rather than 120 parameters from the DBM. In a word, the error caused by the neglect of behavioral differences between driving modes has been underestimated before, and it is promising and necessary to involve targeted driving modes modeling in future CF modeling practices. We expect our model to be mainly applied in two aspects, as mentioned in the introduction: accurate traffic flow simulation and ADASs on intelligent vehicles. Both require a better understanding of human driver behavior. In traffic flow simulation, traditional approaches assign uniform behavioral parameters to all vehicles.