# Air Traffic Trajectory Operation Mode Mining Based on Clustering
## 4 Simulation
### Validation of Density Peak Clustering Effect  
The track set reconstructed by OFAE obtains two-way compression within and between different tracks. Similar tracks are more cohesive, and the deviated tracks are removed. The Euclidean distance measurement can be directly used. Since the data used are unlabeled sequences, the visual manual observation of the clustering effect and the contour coefficient were used as the evaluation indexes of the clustering effect. The contour coefficient evaluates the clustering effect by two indicators: intra-cluster dissimilarity, \(a_{i}\), and inter-cluster dissimilarity, \(b_{i}\). For the sample sequence \(i\), \(a_{i}\) is the distance between the track and other samples in the same cluster. The higher the value, the more similar the track is to the track in the same cluster, and the better the clustering effect is. \(b_{i}\) is the average distance between the track and the tracks of other clusters. The larger the value, the greater the difference between the track and the tracks of other clusters, and the better the clustering effect. The contour coefficient of the track, \(s_{i}\), is expressed as follows:  
\[s_{i}=\frac{b_{i}-a_{i}}{\max\{a_{i},b_{i}\}} \tag{24}\]  
The effectiveness of the clustering algorithm can be reasonably evaluated by calculating the average contour coefficient of the entire sample set. Firstly, we attempted to use the combination algorithm of DTW and DBSCAN to cluster the trajectories, and after trying to combine multiple sets of hyperparameters, we chose the scan radius \(\mu\) = 4.3 and the minimum number of samples in the cluster \(\eta\) = 9. The clustering results are shown in Figure 12.  
Overall, DBSCAN made a good distinction between the main traffic flows in several areas, but in the area of longitude >114\({}^{\circ}\), i.e., the red and yellow clusters, it can be seen that there was not only one traffic flow in these two clusters, but the interior of these two clusters cannot be separated only by parameter adjustment. This is because DBSCAN uses the same scanning radius on the whole sample set. When the distance between clusters of several clusters is quite different, the algorithm makes it easy to classify the clusters close together, whereas the light blue cluster on the left in the Figure 12 is obviously far away from all other clusters. In the process of parameter adjustment, it can be distinguished by almost any combination of parameters. However, due to the close distance between the red and blue clusters, if the scanning radius is too large, these tracks will directly become a cluster; if the radius is reduced, a large number of abnormal tracks will appear. The adjustment of the minimum number of samples in the cluster \(\eta\) is the same, and a large number of abnormal tracks will appear if the clustering requirements are improved. If the  
Figure 11: High noise area and denoised sample set. (**A**) Sample set before reconstruction. (**B**) Sample set after reconstruction. requirements for clustering are reduced, unreasonable multiple small clusters will appear in the main traffic flow. In addition, although DBSCAN has the ability to recognize noise, in the yellow area with many abnormal tracks, the algorithm was unable to identify the potential traffic flow from the abnormalities, but tended to directly classify the tracks in this area into one category. In summary, the algorithmic shortcomings of DBSCAN mainly lie in the rigidity of the parameters. However, even if the red and yellow clusters in Figure 12 were separated and clustered separately, and the similarity matrix was iterated and clustered again using DTW, DBSCAN still failed to distinguish these more similar trajectory clusters. Next, the sample set reconstructed by OFAE was used to take the conventional Euclidean metric to measure the similarity of the trajectories, and the trajectories were clustered using DPCA.