###### Abstract
Recently, [PERSON] et al. [7] applied a distance-based time series clustering method to the CF records and found up to 30 driving modes for car drivers and another 30 modes for truck drivers. This quantity is outside of the scope of the basic driving modes we are aiming to investigate, which will lead to an unacceptable number of parameters if it is applied to the DMBM. Furthermore, conventional clustering methods relying on distance-based metrics may emphasize matching values rather than searching for nuanced structural similarities in the CF process. In summary, how to precisely segment and determine CF behavior modes from empirical data records remains elusive. Furthermore, both the volume and accuracy of data are critical for accurately identifying potential subtle data changes and dependencies in different driving modes through data-driven approaches. Despite the increasing use of real-world trajectories in CF model calibration and comparison [8; 9], due to the development of data collection and storage, the accuracy of some commonly used data cannot be well guaranteed. For example, Next Generation Simulation (NGSIM) data [10], a contributive dataset has been widely adopted in traffic flow and travel behavior modeling, has also been criticized for its accuracy issues [11]. On the other hand, for comparison with the DBM, sufficient records for each driver are necessary to obtain accurate fitting parameters for drivers. Some recent datasets such as High D [12] have indeed been improved with new recording approaches, but their observations of each driver are extremely limited. [PERSON] et al. introduced naturalistic driving data with long records for each driver, but the fact that there are only ten drivers for each type of vehicle limits the credibility of the results. Therefore, to fully overcome the challenges mentioned above, we first introduce a novel data-driven approach, named Toeplitz Inverse Covariance-based Clustering (TICC), to solve the driving modes mining. Then, a large-scale naturalistic driving study (NDS) is adopted to validate and compare the DMBM and the DBM. The main contributions of this study are:* With up to 40 representative drivers from the large-scale NDS data, a total of 4000 high-resolution CF events were extracted for CF behavior modes mining. The duration of each event is longer than 30 s to guarantee that more continuous data dependencies in the CF behavior can be found;
* An accurate subsequence clustering tool of multivariate time series, TICC, is introduced for driving mode recognition. Rather than conventional distance-based clustering, it is based on the graphical dependency structure of each subsequence to recognize the potential reoccurred CF behavior patterns more precisely;
* The number of CF behavior modes is determined by careful consideration of the clustering results and the CF behavior modeling results. Based on this, a comparison of the DBM and the DMBM is conducted to demonstrate the potential of the DMBM to improve the accuracy of CF modeling. The rest of this paper is organized as follows. Section 2 reviews the related works regarding CF behavior and mode discovery techniques; Section 3 describes the data information and extraction of CF events; Section 4 details the methodology of mode recognition and CF model calibration; Section 5 determines the number of driving modes and shows the modeling performance; Section 6 provides discussions; and Section 7 concludes the study and discusses future work.