## 2 Materials and Methods
### Density Analysis for Extracting Main Maritime Traffic Routes  
The AIS data collected consist of data in the form of points that constitute a coordinate system converted to World Geodetic System 84 (WGS) coordinates. One point is made up of spatial information and ship attribute data, and it can be used for a variety of purposes, including weight application. The ship's point data are represented as a line to represent the ship's trajectory. The ship trajectory is created by listing the points of the ship in chronological order based on the same MMSI. The exceptional trajectory of a single vessel can clarify the vessel's navigation pattern, and the density can be used to determine which sea area the vessel has passed through the most. The density analysis based on the wake equator includes the estimation of line density and kernel density (KDE). As a result of the characteristics of AIS data, data are continuously accumulated in berthing ships and drafting ships at almost no speed, resulting in a difference in data amount in some areas. However, if the density analysis is performed based on the ship's track record, the limitation of concentration in some sea areas can be solved. In addition, KDE analysis was performed to explain the difference between point and line analysis results [35]. As such, KDE is a nonparametric method for estimating data distributions. We could add all of the formed kernel functions and then total them before dividing this figure by the number of data [36] after generating the kernel function with a focus on the value of the data for each observed dataset. Equation (1) is used to calculate KDE. \[f_{h}(x)=\frac{1}{n}\sum_{i=1}^{n}K_{h}(x-x_{i})=\frac{1}{nh}\sum_{i=1}^{n}K \bigg{(}\frac{x-x_{i}}{h}\bigg{)} \tag{1}\]  
\(x=\) random variable; \(x_{i}=\) observation; \(K=\) kernel function; \(h=\) bin width  
Here, \(h\) is replaced with the bin size of the histogram and used as a parameter for adjusting the kernel; the kurtosis of the kernel is determined according to the size of \(h\). With the kernel function applied to the total number of observations, \(K\) is divided by the sum of the observations. In other words, Equation (1) describes a method for calculating the average distribution after it has been mapped to the kernel. It is important to select an  
Figure 3: This figure shows a box plot and a normal distribution form to identify the statistical characteristics of the data used for analysis. (**a**) As a result of showing the COG, the mean value is about 139.5\({}^{\circ}\), 25% and 75% of the data distribution are analyzed from about 118\({}^{\circ}\) to 164\({}^{\circ}\). (**b**) As a result of representing SOG, the mean value was about 7.5 kts, 25% and 75% of the data distribution were analyzed from about 6 kts to about 9 kts. (**c**) GT of the ship by showing the results; it can be seen that the mean value is analyzed as about 22,241 tons, and the outlier appears as a value of 73,756 tons. (**d**) As a result of showing the LOA, the distribution of percentage was analyzed from about 111 to 138 m.  
appropriate bandwidth for KDE because over-smoothing may occur in areas with high data density and under-smoothing may occur in areas with low data density. In short, the resulting bandwidth is a \"free parameter\" that has a significant impact on the estimates. In addition, line density analysis is a method of calculating the density of linear characteristics near each output grid cell. It is possible to apply a weight to the ship property data to indicate the density of each track map. Equation (2) is the calculation formula. \[Line\;Density=\frac{\left((L_{n}\times V_{n})+(L_{n+1}\times V_{n+1})\right) }{Area\;of\;Circle} \tag{2}\]  
By applying a search radius to any grid cell, a circle is formed around the center of each raster cell. We multiplied the field value by the trajectory of ships in this circle. Here, \(L_{n}\) means the ship's track record of \(n\), and \(L_{n+1}\) represents the ship's track chart of \(n+1\).