## 2 Methodology
### Potential Conflict Risk Index
EDR reflects the extent of conflict exposure by measuring the exposure distance between the subject vehicle's trajectory and the risk region of the lead vehicle [43]. It reflects the risk of conflicts by characterizing the spatial proximity. Figure 5 shows the geometric schematic of the exposure distance of the subject vehicle within the risk region. The calculation for EDR is shown in Equation (6). The longer the subject vehicle stays within this risk region, the greater the risk of conflict, and consequently, the higher the value of EDR. Therefore, the magnitude of the EDR value can quantify the conflict risk associated with the exposure distance. \[EDR= \begin{cases}2\sqrt{R^{2}-d_{\min}^{2}},d_{\min}<R\\ 0,d_{\min}\geq R\end{cases}  \tag{6}\]  
In this paper, the severity of potential collisions refers to the consequences if collisions happen. During the relative motion of two vehicles, the higher their speeds, the more severe the consequences of potential collisions will be. Thus, TRSD is proposed to quantify the severity of potential collisions. The calculation for TRSD is shown in Equation (7). Figure 6 shows the variables related to TRSD for two vehicles. \[TRSD=\beta\cdot\frac{d_{\min}}{(\frac{\left|\mathbf{v_{i}}\right|+\left| \mathbf{v_{j}}\right|}{2})}=\beta\cdot\frac{2d_{\min}}{\left|\mathbf{v_{i}} \right|+\left|\mathbf{v_{j}}\right|} \tag{7}\]  
where \(\mathbf{v_{i}}\) and \(\mathbf{v_{j}}\) represent the speed of the lead and subject vehicles, respectively. \(\mathbf{v_{i}}\) and \(\mathbf{v_{j}}\) are introduced to reflect the severity of potential collisions. And \(d_{\min}\) represents the  
Figure 4: Three position relationships between the subject vehicle and the risk region. Figure 5: The exposure distance of the subject vehicle within the risk region. minimum distance between the subject vehicle's trajectory and the lead vehicle, which further reflects the risk of a collision between two vehicles. If the distance between two vehicles is large enough, it is impossible for vehicles to collide. In this case, the severity of the potential collisions should be low, even if the speed of the two vehicles is high. The introduction of \(d_{\text{min}}\) makes TRSD better meet the needs of such situations. \(\beta\) is a scaling factor that takes into account the size and mass of the vehicles. \(\beta\) can be defined based on the attributes and characteristics of data. Commonly, trajectory datasets do not contain information on vehicle mass and precise vehicle size. And information on these dimensions is not the focus of this study. Therefore, we defined \(\beta\) = 1 [44]. The higher the average absolute speed difference between two vehicles, the greater the conflict risk. Conversely, a higher TRSD value indicates a less severe potential collision, signifying a reduced risk of conflict. The aforementioned variates are capable of reflecting the temporal and spatial proximity of conflicts and the severity of the potential collision through their magnitudes and signs. In the framework of TTC, signs represent the relative motion between two vehicles, where the numerical magnitude reflects the conflict risk level. Lower values are indicative of a heightened risk of conflicts. By aligning with the format of TTC and integrating the three variates with the risk level, a conflict risk factor (CRF) can be derived that characterizes the level of conflict risk. The expression of CRF is presented in Equation (8). \[CRF=-\frac{\left|\dot{d^{2}}\right|}{\dot{d^{2}}}\times\frac{1}{EDR}(TTR+TRSD) \tag{8}\]  
where \(\dot{d^{2}}\) represents the change rate for the square of the distance between the two vehicles. The calculation for \(\dot{d^{2}}\) is shown in Equation (9). \[\dot{d^{2}}=\lim_{\Delta t\to 0^{+}}\frac{d_{t+\Delta t}^{2}-d_{t}^{2}}{ \Delta t}=2\big{(}v_{x}x_{t}+v_{y}y_{t}\big{)} \tag{9}\]  
where time \(t\), \(\delta_{t}\) denotes a sufficiently small time interval, \(d^{2}\) is the square of the relative distance between the two vehicles at a given moment.