## 3 Materials and Methods
### Methodology
#### 3.2.1 Stage I: Feature Selection  
In stage I of our approach, we employed NCA for the identification of the relevant parameters useful for proper classification of the vessel size based on container capacity. In this study, the number of quay crane berths allocated using machine learning is calculated based on the arrival time data of container ships operated in existing container terminals, and quay crane berth allocation is performed in consideration of various characteristics of container ship arrival times. A study was conducted to calculate future data based on existing data through machine learning, and a total of 11 machine learning techniques were applied to find the efficacy of the identified features. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Parameters** & **Definition** \\ \hline
18 & 2000\% Discharging single lift & Number of Discharging Single Containers \\ \hline
19 & 2000\% Discharging twin & Number of Discharging Two Containers \\ \hline
20 & 4000\% Discharging single & Number of Discharging Single Containers \\ \hline
21 & 2000\% Loading Single lift & Number of Loading Single Containers \\ \hline
22 & 4000\% Loading twin & Number of Loading Two Containers \\ \hline
23 & Loading single & Number of Loading Single Containers \\ \hline
24 & DS & Number of Discharging Containers \\ \hline
25 & 20 BOX & Number of 20 ft Containers \\ \hline
26 & 40 BOX & Number of 40 ft Containers \\ \hline
27 & MTY & Number of Empty Containers \\ \hline
28 & IMDG & Number of International Maritime Dangerous Goods Containers \\ \hline
29 & REFER & Number of Reefer Containers \\ \hline
30 & OOG & Number of Discharging Gages \\ \hline
31 & TW & Number of Twin Containers (Two 20 ft Containers) \\ \hline
32 & LD & Number of Loading Containers \\ \hline
33 & L\_20 BOX & Number of Loading 20 boxes \\ \hline
34 & L\_40 BOX & Number of Loading 40 boxes \\ \hline
35 & L\_MTY & Number of Loading MTY Containers \\ \hline
36 & L\_IMDG & Number of Loading IMDG Containers \\ \hline
37 & L\_REFER & Number of Loading Reefer Containers \\ \hline
38 & L\_OOG & Number of Loading OOG Containers \\ \hline
39 & L\_TW & Number of Loading TW (Twin Containers) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._A supervised learning technique called neighborhood components analysis divides multivariate data into discrete groups based on a predetermined distance measure. It performs the same functions as the K-nearest neighbors method and directly applies the related idea of stochastic nearest neighbors. It is a non-parametric strategy for feature selection that aims to increase the predictive power of regression and classification algorithms [10,11]. By identifying a linear transformation of the input data such that the average leave-one-out (LOO) classification performance is maximized in the converted space, neighborhood components analysis seeks to \"learn\" a distance measure. The main idea behind the approach is that, by creating a differentiable objective function for matrix A and using an iterative solution such as conjugate gradient descent, one may find a matrix A that corresponds to the transformation. The ability to calculate the number of k classes as a function of A up to a scalar constant is one advantage of this technique. Thus, the problem of model selection is addressed by this use of this method. Consider predicting a single data point's class label based on the agreement of its k-nearest neighbors using a certain distance measure. This method of categorization is  
Figure 3: Workflow diagram for our proposed two-stage ML approach. called leave-one-out cross-validation. Assume a problem of multiclass classification with \(n\) observations in the training set, as shown in Equation (1):  
\[S=\{(x_{i},\ y_{i}),\ i=1,2,\ldots,n\} \tag{1}\]  
where \(xi\in\mathbb{R}p\) stands for feature vectors, \(yi\in\{1,2,\ldots,c\}\) stands for class labels, and \(c\) denotes the classes.