# Identification of Critical Road Links Based on Static and Dynamic Features [PERSON]
## 4 Experimental Setup
### Evaluation Metrics  
1. In this study, we adopt the Calinski-Harabaz Index (CHI) [24] to evaluate the performance of the clustering results and to identify the optimal parameters for the representation learning algorithm. The CHI is calculated as follows: \[CHI=\frac{tr(B_{k})(m-k)}{tr(W_{k})(k-1)}\] (7) where \(m\) is the number of link nodes, \(k\) is the number of clusters, \(B_{k}\) is the covariance matrix between different clusters, \(W_{k}\) is the covariance matrix between data within clusters, \(tr(\cdot)\) is the traces of matrix. This indicator is the ratio of all inter-class distances to intra-class distances. A higher value of CHI indicates that the intra-classes are more tightly packed, and the inter-classes are more widely separated, which leads to a better clustering effect.
2. The transportation network is a typical open and complex system. The failure of a few links can have a cascading effect, ultimately impacting the efficiency of the surrounding local networks. Therefore, we consider using the variation of network efficiency [25] to evaluate the performance of the proposed method in this study.  
Figure 3: Directed dual traffic network construction.  
In the urban transportation system, the traffic demand of each road link is different. Generally speaking, road links with higher traffic demand have a greater impact on the surrounding road links. Based on this principle, we propose a method for calculating traffic network efficiency that considers urban travel demand. We define the traffic network efficiency as follows:  
\[e_{i}=\frac{1}{(n-1)}{\sum_{i\
eq j}\frac{1}{d_{ij}}\times I_{i}} \tag{8}\]  
\[E(G)=\frac{1}{n}{\sum_{i\in V}e_{i}} \tag{9}\]  
where \(e_{i}\) is the link node efficiency of link node \(v_{i}\), \(d_{ij}\) is the shortest path distance between link node \(v_{i}\) and link node \(v_{j}\), \(I_{i}\) is the importance evaluation indicator of the link node \(v_{i}\). \(E(G)\) is the overall traffic network efficiency, which is the average link node efficiency of all link nodes in the traffic network. \(n\) is the number of link nodes. The link node efficiency characterizes the importance of nodes in urban traffic networks, with a larger \(e_{i}\) indicating a greater importance of link node \(v_{i}\) in the traffic network. \(E(G)\) is used to evaluate the overall efficiency of the traffic network, with a larger \(E(G)\) indicating a more efficient urban traffic network.  
In the urban transportation network, the critical link nodes have a more significant impact on the overall traffic network efficiency. Therefore, after obtaining the importance of each road link, a certain percentage (such as 10%, 30%, 50%, or 70%) of critical road link nodes can be removed from the original network with an overall traffic network efficiency \(E\) to obtain the overall traffic network efficiency \(E^{\prime}\) after removing the road link nodes. The traffic network efficiency ratio is calculated as follows:  
\[\eta=\frac{E^{\prime}}{E} \tag{10}\]  
where \(E\) is the original traffic network efficiency, \(E^{\prime}\) is the traffic network efficiency after removing a certain percentage of critical road link nodes. This indicator indicates the change in urban traffic network efficiency. When removing the same proportion of link nodes, a smaller value of \(\eta\) indicates a greater impact of the removed link nodes on the traffic network, thereby emphasizing the higher importance of the removed road links in the urban traffic system.