## 3 Data and Methods
### Features and Clustering  
In analyzing trajectory clustering data, both COG and longitude and latitude are crucial features. Therefore, this study will use three-dimensional features for clustering analysis. In theoretical statistics, parametric normalization can often lead to pivotal quantities--functions whose sampling distribution does not depend on the parameters--and to ancillary statistics--pivotal quantities that can be computed from observations without knowing the parameters. Normalization ensures that all features contribute equally during computation by adjusting and aligning probability distributions. After normalizing the three-dimensional features, they are transformed into X, Y, and Z, with values ranging between 0 and 1. Before applying the algorithm, analyzing Figure 1, using the human visual clustering method, the trajectories group can be roughly divided as follows (see Table 2): (1) The shape of ship trajectory clustering in the TC area is like a funnel. North of 23.6\({}^{\circ}\) N, the tracks are more dispersed, but the southern ones are more concentrated. The shape of the track \begin{table}
\begin{tabular}{l r} \hline
**Ship’s Dynamic Conditions** & **Reporting Interval** \\ \hline Ship at anchor and not moving faster than 3 knots & 3 min \\ Ship at anchor and moving faster than 3 knots & 10 s \\ Ship 0–14 knots & 10 s \\ Ship 0–14 knots & 3 1/3 s \\ Ship 14–23 knots & 6 s \\ Ship 14–23 knots & 2 s \\ Ship high than 23 knots & 2 s \\ \hline \end{tabular}
\end{table} 
Table 1: ITU-R M.1371-1. clusters is related to the depth and topography of the water. (2) The path between the TC and KM A cluster of east-west trajectories. (3) Tug boats frequently operate at offshore wind farms. (4) Traditional fishing activities at Changhua Fishing Port (CH) lead to complex sea routes. (5) A cluster of trajectories along the coast of mainland China also shows NE-SW distribution. The goal is to confirm these observations further using algorithms. DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering algorithm that is particularly effective for arbitrary-shaped clusters and for handling noisy data. DBSCAN does not require a pre-specified number of clusters and can identify noise points, clustering based on density. The algorithm identifies clusters in a given dataset using two key parameters: the maximum distance epsilon to form a neighborhood and the minimum number of points required to form a cluster (_minPts_). However, since DBSCAN assumes that all particles have a similar density, it may not produce good clustering results when the data distribution does not clearly distinguish between dense and sparse areas. HDBSCAN Algorithm Data Processing Steps: According to [PERSON], [PERSON], and [PERSON] (2015) [30], the HDBSCAN algorithm is introduced in Section 4.1, and the data processing steps of the HDBSCAN algorithm are explained in detail. Step 1: Core Distance Calculation  
The core distance is calculated by determining the distance between all data points, usually using Euclidean distance or other distance metrics. The core distance for each data point \(p\) is defined as the distance from \(p\) to its \(k\) nearest neighbor, as represented by Equation (1):  
\[CoreDistance(p)=d(p,q_{k}) \tag{1}\]  
where \(q_{k}\) is the \(k\) nearest neighbor of \(p\). Step 2: Constructing the Minimum Spanning Tree (MST) Based on the Distance Matrix  
The MST is a subgraph of a connected undirected graph that includes all the vertices of the original graph. It has a tree-like structure, clearly representing branches and hierarchy. The thickness of the branches represents the magnitude of the values. The visualization of the tree structure is a key feature of the HDBSCAN algorithm, helping users understand the structure and persistence of the clusters. Step 3: Calculating the Stability of Clusters  
Since hierarchical clustering is used, the more frequently a cluster appears at different levels, the higher its stability.