# Identification of Critical Road Links Based on Static and Dynamic Features [PERSON]
## 3 Methodology
### Traffic Link Importance Evaluation  
In previous studies, clustering was often used to evaluate the importance of road links after obtaining some link importance characteristics. The importance of road links is typically classified into three categories: critical, normal, and unimportant [11]. Following this concept, the embedding vectors obtained by TraLink2 vec are clustered in this paper. Generally speaking, the importance of a road link is positively related to its traffic demand, with higher traffic demand indicating greater importance. Traffic demand is directly reflected by the traffic flow of the road link, and higher traffic flow indicates higher traffic demand. Additionally, the traffic state of the road link can also characterize its traffic demand. When a road link is congested, its traffic flow may be small, but this does not necessarily mean that its traffic demand is also small. Therefore, the importance evaluation indicator of road link is defined as follows:  
\[I_{v}=flow_{v}\times\frac{speed_{design}}{speed_{v}} \tag{6}\]  
where \(flow_{v}\) is the traffic flow of link node \(v\), \(speed_{v}\) is the average speed of link node \(v\), \(speed_{design}\) is the design speed of link node \(v\). This indicator represents the ratio of traffic demand to traffic state in a road link. The larger \(I_{v}\) means that the traffic demand on the road link is greater as well as the road link is more important.  
After computing the importance evaluation indicator of each link node, the average importance of each clustering category is then calculated based on the clustering results, which serve as the evaluation index of road link importance. The traffic link importance evaluation process is demonstrated in Algorithm 1.  
```
0: Link node, \(V\); Link length, \(W\); Traffic flow, \(F_{T}\); Average speed of road, \(S_{T}\); Link design speed, \(S_{design}\); Time interval, \(T\);
0: Nodes label and important rating, \(IR\)
1: G = Constructing Directed Dual Traffic Network \((V,E,S_{T},F_{T})\);
2: Calculating embedding vectors of link nodes \(E(V)=TraLink2 vec(G)\);
3: Clustering embedding vectors of traffic networks \(C=clustering(E(V))\);
4: Calculating the importance evaluation indicator \(i=index(EV)\)
5: Initializing the importance of link, \(IR=list()\);
6:for\(v\) in \(V\)do
7:for\(c\) in \(C\)do
8:if cluster results of \(v\in c\)then
9:\(v.ir=\) calculating the average importance of link of all \(V\in c\);
10:endif
11:endfor
12:endfor
13:for\(v\) in \(V\)do
14: Calculating importance rank result \(r\) = sort by \(v.ir\)
15:\(IR\). append \((v,r)\)
16:endfor
```  
**Algorithm 1** Traffic Link Importance Evaluation  
In this paper, we utilized the K-means clustering algorithm [23] to cluster the embedding vectors due to its simplicity and efficiency. The algorithm initiates by randomly selecting k samples as cluster centers and then computes the distance between each sample and the cluster center. Subsequently, each sample is assigned to the closest cluster center, and the samples assigned to each center form a cluster. After all samples are allocated, the centroid within each cluster is recalculated and reassigned until it converges to a stationary position. This clustering method is well-suited for datasets with clusters of arbitrary shapes.