# Prototype Network for Few-Shot Hazard Assessment of Vehicle Lane Changes in Risk Field
## 3 Risk Level Assessment of Vehicle Lane Change Based on Field Strength Theory
### Collision Risk Factor Assignment Based on the Entropy Method  
The entropy method is an objective assignment theory that determines the weight of each index according to the information provided through the observation of each index. The more information is available, the less uncertainty and entropy. The less information is available, the greater the uncertainty and entropy. The entropy value can be used to assess the degree of dispersion of a specific indicator. The more information provided, the greater the impact of the indicator on the comprehensive evaluation. If the value  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Lane Change** & **Quantification** & **v\_vel** & **v\_Acc** & **Space\_Hdavy** & **Time\_Hdavy** & **1/TTC** & **T\_l** & **T\_R** \\ \hline Potential risk & 1 & \(<\)22.22 & \(a<0\,\&\,|a|<2\) & \(>\)55.55 & \(>\)5 & \(<\)0.333 & 1 & 2 \\ \hline Medium risk & 2 & [22.22, 33.33] & \(a<0\,\&\,2\leq|a|\leq 5\) & [33.34, 55.55] & \((2,5)\) & \((0.2273,0.333]\) & 1 & 2 \\ \hline High risk & 3 & \(>\)33.33 & \(a<0\,\&\,|a|>5\) & \(<\)33.34 & \(\leq\)2 & \(\geq\)0.2273 & 1 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Relationships between vehicle lane-change risk level and threshold quantification.  
of an index is equal, it has no effect on the comprehensive evaluation. The indicator's value is more dispersed when more information is provided. Information entropy can be used to calculate the weight of each index and conduct a comprehensive evaluation of multiple indexes.  
Firstly, the selected five characteristic parameters were normalized. The higher the speed and deceleration, the higher the risk level. Therefore, _v_vel_ and _v_Acc_ were used as negative indicators. The other three variables were included as positive indicators to be weighted via the entropy weight method. Through the entropy weight method, the vehicle risk assessment index was calculated. The calculation of objective weights is shown in Equation (5).  
\[w_{j}=\frac{1-e_{j}}{\sum_{j=1}^{n}(1-e_{j})} \tag{5}\]  
where \(w_{j}\) represents the weight assigned to each characteristic parameter j. \(e_{j}\) represents the information entropy associated with characteristic parameter j. Information entropy is calculated as shown in Equations (6) and (7).  
\[\mathbf{e}_{j}=-\frac{1}{\ln n}\sum_{i=1}^{m}p_{ij}\ln p_{ij} \tag{6}\]  
\[p_{ij}=\frac{x_{ij}^{\prime}}{\sum_{i=1}^{n}x_{ij}^{\prime}} \tag{7}\]  
where \(p_{ij}\) represents the probability of an occurrence of interval i for characteristic parameter j. \(x_{ij}^{\prime}\) denotes the frequency of an occurrence of interval i for characteristic parameter j after normalization. According to the difference between positive and negative indicators, the indicators are transformed differently, as shown in Equations (8) and (9).  
If \(x\) is a positive indicator,  
\[x^{\prime}=\frac{x-\min(x)}{\max(x)-\min(x)} \tag{8}\]  
If \(x\) is a negative indicator,  
\[x^{\prime}=\frac{\max(x)-x}{\max(x)-\min(x)} \tag{9}\]  
After switching to the left and right channels to assign weights respectively, the weights of each variable are averaged as the weights of the final variables. In Figure 4, wU1 represents the data of the first time period of US-101, and w11 represents the data of the first time period of 180, giving the weight results of variables in the leftward and rightward permutation channels.  
Figure 4: Weights of the five feature variables for LCL and LCR. (**a**) represents the weight values of various indicators for all vehicles changing lanes to the left. (**b**) represents the weight values of various indicators for all vehicles changing lanes to the right.