## 4 Data Description and Processing
### Data Reduction and Extraction  
The purpose of data reduction was to reduce the amount of data collected by the VBOX. The time frequency of the data recording was 10 Hz, and for a day-trip's records, a huge amount of data was generated. In this paper, the time window method was applied to achieve data reduction. Let \(\omega\) be window size and \(\Delta\)t be time step. Therefore, at any given time \(t_{c}\), the time window can be expressed as a range from \(t_{c}-\omega\) to \(t_{c}\). The next window starts at time \(t_{c}+\Delta\)t. In a previous study, window size was 6 s or 9 s [18]. In this paper, since the location of the study was at an intersection, the window size must be small enough to show all phenomena. If the time window is too large, the minor state change may be ignored. At the same time, the time window cannot be too small, so that data cannot be redundant, and data noise will be retained. As a result, the window size applied in this paper was 6 s, and the step was 2 s. The step is used to make sure all the state changes will be retained, and the trend of state changes will be smoother. In other words, it helps keep the state consistent in one progress of passing through the intersection. The size of 6 s and step of 2 s of the time window in this study is able to capture the transient behavior accurately and avoid the capture of multiple events in one interval. For instance, given a time of 6 s, the time window range will be \([0,6]\), and the step of 2 s, the next window is \([2,8]\). The illustration of time window and window step is shown in Figure 4.  
Figure 3: Boxplots of Kinematic Variables. All selected raw data were allocated to different segments by unit time window (6 s). Using data of 2500 s as a sample time period in one trip shows the effectiveness of using time windows for data reduction. The raw data of acceleration and jerk is shown in Figure 5a,b, and the data processed by the time window is presented in Figure 5c,d. The time period includes several intersections, and as seen in the above figure, there are several separate groups. This reflects that it was a good decision to use the method with acceleration, jerk, and their derivative parameters. The group clearly shows the state changes of the truck when it passes through intersections. After extracting the specific data, according to Equations (1)-(6), the four derivative features were calculated. Figure 5a,b illustrates the acceleration and jerk in the raw data. As shown in Figure 5a,b, the acceleration in the raw data has a large number of peaks and valleys, and the amplitudes are similar for a certain period of time. These short-term continuous and intensive changes make it difficult to detect accurate driving behaviors and classify driving styles. These state changes cannot be ignored for the accuracy of detection and classification. Figure 4: Time Window and Window Step. Figure 5: Data reduction of acceleration and jerk by time window. By using time windows to process the original VBOX data, as seen in Figure 5c,d, the noise in the data was removed, and the number of data reduced. This helps to reduce the difficulty of data feature extraction and data cluster. In Figure 5c,d, the changes in mean acceleration and jerk are clear and visible. As shown in the figure, the most obvious state changes are retained. At the same time, the integration and elimination of redundancy in the minor state changes have been carried out, reducing a large amount of subtle or repeated data while retaining most of the characteristics of the data. As a result, data processed by time window is better for classifying driving styles based on these features. It can also help prevent classifying multistyle states in the same driving time period. Figure 5c,d also shows the relationship between acceleration and jerk in the period during which a truck passes through an intersection.