# Air Traffic Trajectory Operation Mode Mining Based on Clustering
## 1 Introduction  
Aircraft usually have fixed flight patterns in the terminal area, which is based on flight procedures, fixed patterns, and other factors. Therefore, the mining of typical flight patterns in the airspace uses unsupervised algorithms. Clustering has long-been a hot research topic [1; 2; 3; 4; 5]. [PERSON] [6] transcoded ADS-B data and extracted trajectory feature points for DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clustering analysis, and [PERSON] [7] used a hierarchical clustering algorithm to identify the sample categories of trajectories and the abnormal trajectories. [PERSON] [8] analyzed the characteristics of the track data, filtered the abnormal data, and extracted the track feature points by using the fuzzy clustering method, while [PERSON] et al. [9] demonstrated the advantages of mining traffic flow patterns in terminal areas using a deep autoencoder and a Gaussian mixture model with intuitive display and separability, and shortened clustering time and improved clustering efficiency. [PERSON] et al. [10] obtained through data mining analysis that the flight trajectory largely depends on the airline's strategy, flight type, and operating costs. [PERSON] [11] proposed an air traffic flow identification method based on HDBSCAN clustering with a weighted Euclidean distance function to more accurately identify arrival trajectories. The anomaly detection aspect makes a new distinction between spatial and energy anomalies in ADS-B data and provides key insights into the relationship between these two types of anomalies. However, when the traditional distance measurement DTW (dynamic time warping) or the DBSCAN [12; 13] model are used in the above literature, it takes a long time, the cost is high, and it is difficult to distinguish clusters with large density differences. Some tactical traffic flows with low trajectory density due to control or regional reasons areoften classified as a high-density cluster of nearest neighbors by DBSCAN to reduce the clustering effect. Therefore, here we explore the compression method of high-dimensional trajectory features and the appropriate clustering algorithm. The traffic flow in the terminal area is highly nonlinear, and the dimensionality reduction process of traditional principal component analysis (PCA) is essentially a simple linear transformation of the original features, which cannot capture the nonlinear dependence between the data. In dealing with small samples and nonlinearity in face recognition, [PERSON] [14] combined L21-normand kernel functions and introduced L21-normpenalty terms to effectively improve the recognition rate. [PERSON] [15] proposed a new orthogonal sparse linear discriminant analysis algorithm, which first constructs the \(K\)th nearest neighbor graph to retain the local discriminant information of the sampled points. Then, the L21-normconstraint on the projection matrix is used as a loss function to enhance the robustness to anomalous data points. [PERSON] [16] proposed a robust sparse LDA algorithm to obtain the feature with the maximum discriminant through the L21-norm, combine the orthogonal and sparse matrices to maximize the retention of the original data representation, and enhance the robustness to noise. Therefore, the autoencoder (AE) is used to learn the nonlinear track features, but if the unconstrained conventional stack AE is directly used to compress the data, the result is not ideal. The number of nodes and hidden layers needs frequent parameter adjustment, which is time-consuming and cannot always be guaranteed to find effective parameter groups. Therefore, this paper uses an L21-norm constrained autoencoder to learn the low-dimensional manifold of high-dimensional track data, compress the track data, and limit the model overfitting so that the clustering algorithm can use low-dimensional data for operation.