# Maritime Traffic Evaluation Using Spatial-Temporal Density Analysis Based on Big AIS Data
## 3 Results
### Creating Density Maps  
#### 3.4.1 Logarithmic Scale and Symbolization  
The density calculation results show a broad statistical distribution with large skewness and kurtosis values. The analyzed datasets reduced the normality because they are asymmetric and heavily concentrated around the mean. In general, values that range by orders of magnitude are logarithmically scaled to close the gap between the large and small values while reducing the skewness and kurtosis. The logarithmically scaled dataset with increased normality is suitable for a broad range of data analysis [49]. In this study, the density distribution was logarithmically scaled to improve the visibility of low values in particular. Figure 5 shows the histograms developed by applying a logarithmic scale to the density analysis results of each ship type and the set of all ships. After log-transformation, the data distribution closely approached the normal distribution.  
To improve the visualization of the log-transformed density-analysis results, this study adopted a raster data symbolization method called stretch. When applied to a raster dataset histogram, stretch increases the visual contrast among the cells and enhances the image by spreading the pixel values along a histogram. The color of a stretched data point indicates the extent of the value along the color ramp [50]. This method is advantageous because it emphasizes the variation among the most common values without overemphasizing the lowest or highest values. That is, it adapts to the specified range of values by focusing on the common input values while ignoring outliers and tails of the distribution. Stretch types include minimum maximum, percent clip, and standard deviation. In general, most of the values can be assumed to fall within the upper and lower limits, and therefore trimming off the extreme values is statistically reasonable [50].  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Ship Type** & **N Total** & **Mean** & **SD** & **Sum** & **Skewness** & **Kurtosis** & **Min** & **Median** & **Max** \\ \hline Cargo ship & 323,674 & 2.34 & 8.22 & 756,840 & 56.36 & 7933 & \(7.9\times 10^{-10}\) & 0.8621 & 1718 \\ Tanker & 321,424 & 1.15 & 7.58 & 368,430 & 87.94 & 12,876 & \(1.7\times 10^{-10}\) & 0.2462 & 1617 \\ Passenger ship & 92,948 & 0.33 & 5.25 & 30,300 & 90.67 & 10,533 & \(5.2\times 10^{-11}\) & 0.0316 & 757 \\ Towing ship & 106,030 & 0.12 & 0.96 & 12,671 & 47.78 & 3260 & \(9.7\times 10^{-11}\) & \(8.5\times 10^{-5}\) & 86 \\ All ships & 323,688 & 3.61 & 14.0 & 1,168,241 & 43.12 & 3578 & \(5.5\times 10^{-9}\) & 1.2078 & 1725 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Descriptive statistics of density calculation results by ship type.  
In this study, standard deviation was adopted as the stretch type and linear stretching was applied between the limit values defined by the standard deviation. In normally distributed data, these limits cover \(\sim\)68.2% of the data at \(\pm\)1 standard deviation, \(\sim\)95.4% at \(\pm\)2 standard deviations, and \(\sim\)99.5% at \(\pm\)3 standard deviations from the mean [51]. Here, the number of standard deviations in the stretch method was set to one for identifying the customary maritime traffic patterns that are relatively unaffected by extremely high-traffic ports or low-traffic sea areas. As shown in Figure 5, stretching redistributed the range corresponding to one standard deviation on both sides of the mean in the original histogram of density values. The redistribution was achieved by linearly extending the selected range over the entire observed range.