# Analysis of Trends in Mega-Sized Container Ships Using the K-Means Clustering Algorithm
## 2 Materials and Methods
### Comparison with Previous Study  
In this study, the results of the study that classified groups from the subjective viewpoint of the researcher without clustering [15] were compared with respect to the range of adjusted R-squared value and residual standard deviation value of linear graph of the regression analysis results for each cluster. Table 7 shows the accurate comparison results of the previous study and this study. As a result of obtaining the p-value for the linear regression analysis using the R studio program version 4.1.1, the relationship between the variables was analyzed to have a significant result by showing a \(p\)-value smaller than \(2.2\times 10^{-16}\) in all cases.  
In this study, more than 1896 ships were added and analyzed compared to the previous study. In previous studies, the analysis target sections were divided according to the subjective intuition of the researcher. Therefore, the least adjusted R-squared value of log(DWT) \(-\) log(d) was 0.46 m. Further, in the section of 55,000 DWT or more, only the \(\mathbf{y}=\mathbf{a_{0}}\) graph having a slope of 0 was analyzed and the maximum deviation in the LOA was 21.99 m. A deviation of \(\sim\)9 m was observed compared to the LOA maximum standard deviation of 12.93 m in this study. The maximum standard deviation corresponding to Cluster 3 in this study is similar to the external standard of a 40-ft container (Length: 12.19 m, width: 2.44 m). The size of the 40-ft container is closely related to the trend in the large ship because the size of the ship is determined according to the cargo characteristics.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Classification**} & \multirow{2}{*}{\begin{tabular}{c} **Adjusted \(\mathbf{R}^{2}\)** \\ \end{tabular} } & \multicolumn{2}{c}{**Residual Standard Deviation**} \\ \cline{3-6}  & & **This Study** & **Previous Study**[15] & **This Study** & **Previous Study**[15] \\ \hline \multirow{6}{*}{\begin{tabular}{c} 0–55,000 DWT \\ (Cluster 1) \\ \end{tabular} } & Log(LOA) & 0.93 & 0.94–0.95 & 0.03 & 0.02 \\ \cline{2-6}  & Log(Lpp) & 0.94 & 0.94–0.95 & 0.02 & 0.02 \\ \cline{2-6}  & Log(B) & 0.91 & 0.88–0.90 & 0.02 & 0.02 \\ \cline{2-6}  & Log(d) & 0.91 & 0.46–0.78 & 0.04 & 0.04 \\ \cline{2-6}  & \multirow{2}{*}{\begin{tabular}{c} \(y=a_{0}\) \\ \end{tabular} } & LOA & - & - & - & 10.13–15.12 \\ \cline{2-6}  & & Lpp & - & - & - & 9.59–14.75 \\ \cline{2-6}  & B & - & - & 1.45–1.76 & 1.00–1.65 \\ \cline{2-6}  & & d & - & - & - & 0.71–0.73 \\ \hline \multirow{6}{*}{\begin{tabular}{c} 55,000–125,000 \\ (Cluster 2) \\ \end{tabular} } & Log(LOA) & 0.63 & - & 0.03 & - \\ \cline{2-6}  & Log(Lpp) & 0.62 & - & 0.02 & - \\ \cline{2-6}  & Log(B) & - & - & - & - \\ \cline{2-6}  & Log(d) & 0.66 & - & 0.01 & - \\ \cline{2-6}  & \multirow{2}{*}{\begin{tabular}{c} \(y=a_{0}\) \\ \end{tabular} } & LOA & - & - & - & 7.98–21.99 \\ \cline{2-6}  & & Lpp & - & - & - & 7.83–15.97 \\ \cline{2-6}  & & B & - & - & 1.63–3.48 & 1.59–3.62 \\ \cline{2-6}  & & d & - & - & - & 0.59–0.99 \\ \hline \multirow{6}{*}{\
\begin{tabular}{c} 125,000–241,000 \\ (Cluster 3) \\ \end{tabular} } & LOA & - & - & 3.09–12.93 & 1.19–21.99 \\ \cline{2-6}  & \multirow{2}{*}{
\begin{tabular}{c} \(y=a_{0}\) \\ \end{tabular} } & Lpp & - & - & 2.87–12.04 & 3.30–9.45 \\ \cline{2-6}  & & B & - & - & 1.18–2.42 & 1.67–3.29 \\ \cline{2-6}  & & d & - & - & 0.33–0.38 & 0.47–0.64 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of accuracy of results with previous study.