## 4 Prediction Algorithm of Maritime Traffic Condition
### Feature Augmentation  
There are many factors to be considered when predicting maritime traffic. The main factors include the number of ships and the maritime traffic volume, among others. Additionally, there are other factors such as weather conditions, waves, tidal and surface currents, the depth of water, the shape of the seabed as obtained from electronic navigational charts, and maritime traffic regulations, including port speed limits.  
Features for predicting maritime traffic congestion include the predicted values of the number of ships and the maritime traffic volume, which means length squared conversion traffic volume; however, more features are required for a highly reliable prediction. Therefore, new features were obtained from the existing features through feature augmentation to improve the performance of the developed algorithm. Feature augmentation is a technique used in machine learning to increase the size of the dataset. It is achieved by generating new instances of the data using transformations or operations that preserve the underlying structure of the data. These new instances are combined with the original data to create a larger dataset that can be used to train a machine learning model.  
The maritime traffic congestion variance width; variance rate; variance probability; 3-day, 6-day, 9-day, and 24-day averages; and maximum maritime traffic congestion were selected as features in addition to the number of ships and maritime traffic volume. The maritime traffic congestion of major gate lines around the target gate line was additionally selected. The annual average was found to be 11.3% and the maximum value was 94.4%, when the maritime traffic congestion of gate line A (No. 1 fairway) was analyzed. The monthly average was the lowest in June (9.4%) and the highest in February (12.9%).  
Figure 2: AIS Data visualization of target sea area.  
Among the features, the variance refers to the numerical expression of the degree of change in maritime traffic congestion over a certain period. The variance analysis includes the variance width, variance rate, and variance probability.  
The variance width is used to obtain the magnitude of the average change in time-series data; it has the benefit of obtaining estimates on a non-parametric scale because no specific distribution is assumed. It is obtained using  
\[\frac{1}{(n-1)}\ \ \sum_{t=1}^{n}(T_{c}(t)-T_{c}(t-1)) \tag{10}\]  
The variance rate is the ratio between the variance width and the maritime traffic congestion value, and it is expressed as  
\[\frac{\frac{1}{n}\ \sum_{t=1}^{n}T_{c}(t)}{\frac{1}{(n-1)}\ \sum_{t=1}^{n}(T_{c}(t)-T_{c}(t-1))} \tag{11}\]  
The variance probability is expressed in binary notation by comparing the variance width with the maritime traffic congestion value. The variance probability is calculated using  
\[\frac{(n-1)-\alpha}{(n-1)} \tag{12}\]  
\[a=(n-1)-\sum_{t=1}^{n}(T_{c}(t)-T_{c}(t-1))\]  
\[\gamma_{n}=\begin{cases}1\ \ \,T_{c}(t)>F_{range}\\ 0\ \ \,T_{c}(t)\leq F_{range}\end{cases} \tag{13}\]  
where  
\(\alpha\) = Coefficient of inclusion of fluctuation range considering the period,  
\(\gamma_{n}\) = Specifies whether the fluctuation range is included.  
In addition, considering the characteristics of maritime traffic congestion, the average and maximum values for 3, 6, 12, and 24 days were selected as the features. Figure 5 illustrates the results of analyzing the average, maximum, and minimum maritime traffic congestion for 3, 6, 12, and 24 days.