## 2 Materials and Methods
### Data Clustering  
The DBSCAN algorithm is a representative clustering methodology that is suitable for handling spatial data, including noise, based on the density of data in the same cluster. It functions in contrast to existing methodologies that divide the cluster using the distance between the data [20]. Research on clustering AIS data based on the DBSCAN algorithm is being actively conducted through the development of automatic navigation technology and the use of maritime data cloud services. A method aimed at clustering the AIS coordinate data to explore the latitude and longitude lattice and spot areas of the cluster range was recently proposed [21]. In addition, a model for analyzing ship route patterns and predicting dangerous situations using DBSCAN was introduced [22], and the ship trajectory anomaly detection models such as unexpected stop, deviation from the prescribed route, or inconsistent speed, were proposed [23]. The DBSCAN algorithm was also used in another case as a method to reconstruct the damaged or missing AIS coordinate data [24]. Recently, \begin{table}
\begin{tabular}{c c} \hline
**Station Type** & **Nominal Interval** \\ \hline AIS Class B speed \textless{} 2 knots & 3 min \\ \hline AIS Class A speed \textless{} 3 knots in ’At anchor’ or ’Moored’ status & 3 min \\ \hline AIS Class B speed \textgreater{} 2 knots & 30 s \\ \hline AIS Class A speed \textgreater{} 3 knots in ’At anchor’ or ’Moored’ status & 10 s \\ \hline AIS Class A speed 0–14 knots & 10 s \\ \hline AIS Class A speed 0–14 knots and changing course & 3 1/3 s \\ \hline AIS Class B speed 14–23 knots & 15 s \\ \hline AIS Class A speed 14–23 knots & 6 s \\ \hline AIS Class B speed \textgreater{} 23 knots & 5 s \\ \hline AIS Class A speed 14–23 knots and changing course, & 2 s \\ or speed \textgreater{} 23 knots & 10 s \\ \hline Search And Rescue Aircraft (airborne mobile equipment) & 10 s \\ \hline AIS Base Station & 10 s \\ \hline AIS AtoN & 3 min \\ \hline Transmissions of AIS Application Specific Messages & 3 min \\ \hline Transmissions of AIS Long-Range Reports & 6 min \\ \hline \end{tabular}
\end{table} 
Table 1: AIS station reporting intervals. Figure 3: Position interpolation by standard time intervals. to predict the spread of COVID-19, the AIS data and DBSCAN algorithm were used, and they helped predict infectious diseases in ports and neighboring countries [25]. The DBSCAN is widely used as a method for clustering data related to the AIS coordinates. To perform DBSCAN, data of various distributions can be clustered based on these parameters through the definition of minimum neighboring data (MinPts) and cluster size (Epsilon, Eps). Here, Eps is the radius for forming a cluster based on one piece of data, and MinPts is the minimum number of data points included in Eps to form one cluster. According to the parameter-based location information, each piece of data is classified into core, border, and noise points, as shown in Figure 5. If there are more data than MinPts in Eps based on any point \(p\) in the dataset, point \(p\) is referred to as a core point. Meanwhile, a border point refers to a point that is not a core point but a piece of neighboring data of a core point. Further, noise points are data points that do not belong to a cluster; in other words, they are data excluding core and border points. The following definitions are required to apply the DBSCAN algorithm [20; 26]. **Definition 1**. : _Eps-neighborhood of a point: The Eps-neighborhood of a point \(p\) is the set of points \(q\) in database \(D\) that lie within radius Eps of point \(p\)._  
\[N_{Eps}(p)=\{q\in D|dist(p,q)\leq Eps\}\]  
Figure 4: Protocol for AIS data transmission. Figure 5: Concept of DBSCAN: density-reachable and density-connected. **Definition 2**. : _Directly density-reachable: If point \(p\) is in the Eps-neighborhood of point \(q\) and point \(q\) is of high density \(\left(\left|N_{Eps}(q)\right|\right.\geq Min\)Pts\()\), point \(q\) is a core point._  
\[