###### Abstract  
Car-following (CF) behavior is one of the most important driving behaviors. Accurately understanding and modeling CF behavior is essential for traffic flow simulation and user-acceptable advanced driving assistance systems (ADASs). In previous decades, CF models were calibrated based on drivers or trajectories, with short-term changes ignored. Recent studies have indicated that these changes could be caused by occasional irritations or regular switches of driving modes, but there is still a lack of specific understanding of driving modes and how these modes affect simulation accuracy in the reproduction of CF behavior. This paper explored the existence of driving modes and the quantified modeling influence of driving modes. Specifically, we first extracted 4000 high-resolution CF events of 40 drivers from large-scale naturalistic driving data for the discovery of underlying driving modes. Then, we introduced a novel multivariate time series method, Toeplitz Inverse Covariance-based Clustering (TICC), to achieve the segmentation and classification extraction of different driving modes. Finally, calibrated by the CF dataset, the proper cluster number of the driving mode was determined, and a comparison of driving-mode-based modeling (DMBM) and driver-based modeling (DBM) was conducted. The results showed that the driving process could be viewed as five core driving modes, and the DMBM has the potential to bring upwards of a 13% accuracy improvement with fewer parameters. driving mode; car-following behavior; naturalistic driving data; multivariate time series clustering +
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in the external environment. On the contrary, the driving mode, defined as a certain behavior consistency or repetition in the CF interaction in a time segment, can be viewed as the basic component of CF behavior. Both objective environmental changes and subjective adjustments of drivers in driving task realization can lead to behavior variance in different driving modes, which almost exists in all the CF events. However, the core pathway of the current DBM is to apply a complex mapping function to pool what are essentially different states and, as a result, the CF model based on the DBM is likely to be inaccurate in the description of each mode, but to achieve a kind of average we lower the total error level. Therefore, the concept of driving-mode-based modeling (DMBM) is proposed; that is, to convert the parameters of a CF model from the mapping of different drivers to the mapping of different driving modes. However, our understanding of driving modes remains limited. Specifically, there is a dearth of knowledge regarding the fundamental modes that constitute the car-following process and how the behavior of these different driving modes influences the accuracy of existing car-following models. To recognize several basic CF behavior modes from massive empirical driving data is a process of segmenting data and then categorizing these segments according to the potential data characteristics. A long multivariate CF time series is to be segmented into short sequences which contain repeatedly reoccurring behavior \"patterns\" or \"modes\", such as certain slight fluctuations in the velocity dimension. For consistency, we use \"mode\" to refer to it. Meanwhile, these short sequences of common repeat features will be labeled with the same mode number. Conventionally, the rule-based division is applied. Taking a common example, the classical Wiedemann model consists of different threshold-determined state-action regimes representing drivers' differentiated behavior modes, such as unconscious reaction, reaction, deceleration, etc. Nevertheless, this mode segmentation is subjective and provides less insight into structural similarities in the data, and therefore the Wiedemann model has not shown advantages in modeling accuracy in the past compared with those traditional nonlinear models based on the DBM [1]. In contrast, an unsupervised data-driven method is more promising and adaptable for this question.