## 2 Data Acquisition and Pre-Processing
### Data Fundamental Analysis
#### 2.4.2 Variable Threshold Definition  
In this paper, THW and longitudinal acceleration were selected as the state index and action index [30], respectively. In order to provide a semantic explanation for driving behaviors, we classified each variable into different levels based on their statistical features. In addition, we use different distributions to fit them and determine the threshold of each variable from a statistical perspective. Figure 5a shows the fitting results of acceleration (\(a_{e}\)) and THW, using two distributions, i.e., the normal distribution (N) and Student's t (t) distribution. It can be seen that for both acceleration and THW, the t-distribution achieved a better fitting performance than the normal distribution. Based on the characteristics of the variable's thresholds, we selected the percentile value of the range with the t-fitting results, as illustrated in Figure 5b. Generally, dangerous events were small probability events. Therefore, events with values less than 5% and higher than 95% were taken as small probability events, and the corresponding TWH and \(a_{e}\) values were calculated according to the inverse function of the cumulative distribution function (CDF) [31].  
\[t_{THW}^{\text{min}}=F_{t}^{-1}(p_{0.05}\big{|}v_{THW}) \tag{3}\]  
\[t_{THW}^{\text{max}}=F_{t}^{-1}(p_{0.95}\big{|}v_{THW}) \tag{4}\]  
\[a_{e}^{\text{min}}=F_{t}^{-1}(p_{0.05}\big{|}v_{a_{e}}) \tag{5}\]  
\[a_{e}^{\text{max}}=F_{t}^{-1}(p_{0.95}\big{|}v_{a_{e}}) \tag{6}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Driving Styles** & **Sample Number** & **Cluster Center** \\ \hline Cautious & 7 & 6.49 \\ Normal & 16 & 8.42 \\ Aggressive & 10 & 9.30 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Drivers information statistic.  
Figure 5b shows the statistical results of driving data and the fitting results of the cumulative distribution function. It can be seen in Figure 5b that the \(a_{e}\) values were \(-1.42\) m/s\({}^{2}\) and \(1.59\) m/s\({}^{2}\), corresponding to probabilities of 5% and 95%, respectively. The THW values were 1.19 s and 2.98 s, corresponding to probabilities of 5% and 95%, respectively. In order to facilitate the calculation, the thresholds were rounded, as shown in Table 3.  
According to the results of statistical analysis and literature [32], the semantics of states and actions corresponding to each threshold range were defined. For instance, the driving state was divided into three categories, i.e., near following (NF), middle following (MF), and far following (FF), based on THW. Moreover, the driving action was divided into aggressive acceleration (AA), normal acceleration (NA), normal deceleration (ND), and aggressive deceleration (AD) based on acceleration. In total, 3 \(\times\) 4 = 12 driving behaviors were analyzed. Each driving behavior had a semantic explanation. For example, when acceleration \(a_{e}\) > 1.6 m/s\({}^{2}\), and THW < 1.2 s, the semantic was defined as near following with aggressive acceleration (NFAA). A similar semantic explanation could be obtained according to other thresholds. It is worth noting that these thresholds can be adjusted considering the change in the actual driving scenarios or application fields.