## 3 Methodology
### Derivation of Promising Evaluation Indicators and Development of an Integrated Evaluation Index
Then, binary indicators representing DRI-based hazardous road sections and normal sections were used as output variables to derive promising evaluation indicators that affect the classification of real hazardous road sections. A DT is an analytical method that categorizes or predicts data by plotting decision rules in a tree structure according to specific criteria. DTs are intuitively easy to understand and are often used to determine which variables have the most significant impact by providing key variables and separation criteria, allowing for the easy interpretation of results [27]. It is necessary to apply an optimal parameter, a hyperparameter, to prevent overfitting and select an appropriate tree \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable Name** & **Definition** & **Equation** \\ \hline \multirow{3}{*}{TTC-based conflict count} & A safety assessment metric that determines safe/unsafe conditions based on TTC & \(TTC_{t}=\frac{\pi_{t}}{\
u_{TV,t}-\
u_{TV,t}}\) \\ \cline{2-3}  & A safety assessment metric that determines safe/unsafe conditions based on the difference of minimum stopping distances between the leading and following vehicles & \(SDI_{t}=d_{LV,t}-d_{FV,t}\) \\ \hline \multirow{3}{*}{Avg. DRAC} & The average collision evasion deceleration rate when the following vehicle begins to perceive a hazardous situation and initiates deceleration & \(DRAC_{t}=\frac{\left(V_{PV,t}-V_{LV,t}\right)^{2}}{2\pi_{t}}\) \\ \cline{2-3}  & When the DRAC is greater than 3.35 m/s\({}^{2}\), it is defined as a conflict & \(\frac{Number\ of\ DRAC>}{3.35\ m/s^{2}}\) \\ \hline \multirow{3}{*}{CPI} & The probability of the DRAC exceeding the MADR within a given time interval & \(CPI=\frac{\sum P_{t}(MADR<DRAC_{t})}{T}\) \\ \hline \multirow{3}{*}{Avg. spacing} & The average distance from the rear of the leading vehicle to the front of the following vehicle & \(\overline{s}=\frac{1}{n}\frac{T}{T}s_{t}\) \\ \cline{2-3}  & The standard deviation of vehicle spacing & \(\sigma_{s}=\sqrt{\frac{\Sigma(t-\overline{s})^{2}}{n}}\) \\ \hline \multirow{3}{*}{VF spacing} & The spacing variability over time & \(VF_{s}=\sqrt{\frac{1}{n-1}\sum\limits_{t=1}^{T}(r_{t}-\overline{r})^{2}}\) \\ \cline{2-3}  & The time difference between the preceding vehicle and following vehicles when passing a specific point on the road & \(\overline{t}=\frac{1}{n}\frac{T}{T}h_{t}\) \\ \hline \multirow{3}{*}{Std. headway} & The standard deviation of headway & \(\sigma_{h}=\sqrt{\frac{\Sigma(h_{t}-\overline{s})^{2}}{n}}\) \\ \cline{2-3}  & The headway variability over time & \(VF_{h}=\sqrt{\frac{1}{n-1}\sum\limits_{t=1}^{T}(r_{t}-\overline{r})^{2}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Candidate indicators for driving safety analysis. size for DT analysis. The information gain is a quantification of the independent variable and the criterion value that results in the lowest entropy between parent and child nodes when classifying data [28]. The information gain quantifies the impact of each input variable on the classification of the output variable and can be used to determine the importance of variables. Information gain is a value between 0 and 1, where higher values mean that the independent variable has a greater impact on classification. Thus, indicators with large information gains are good indicators for identifying hazardous sections. An evaluation indicator with a nonzero information gain is defined as a promising evaluation indicator that increases the accuracy of real-world hazardous road section classification, which can be computed through the formula in Equation (6). \[Information\ gain=Entropy(before)-\sum_{j=1}^{k}Entropy(j,after) \tag{6}\]  
where \(Entropy(before)\) is the prior entropy, \(Entropy(j,after)\) is the posterior entropy, and \(j\) is a child node. The definition of an integrated evaluation index according to MPR requires weighting by promising indicators. Weights are assigned using the information gain, which allows for comparisons of the importance of variables.