# Machine Learning Ship Classifiers for Signals from Passive Sonars
## 5 Results
### Support Vector Machine  
Table 6 presents the optimal hyperparameters and the corresponding classification results for the SVM models.  
The SVM model showed a relatively consistent performance across the Lofar, PCA, and NLPCA datasets, as represented in Table 7. The accuracy of the model decreased significantly when decimation was applied; however, this reduction was consistent across all the datasets. The regularization parameter CC for Lofar was much larger than that for PCA and NLPCA, indicating a stronger regularization applied for Lofar, but this did not lead to a major difference in the performance of the model. Without decimation, the model achieved stable and consistently high accuracy across the datasets. The slight differences in the hyperparameters, such as the loss function and \(C\), did not seem to have a major impact on the overall performance in this case.  
The results indicate that the Lofar dataset without decimation performed notably poorly, where it achieved a mean accuracy of only 8.92%. This suggests that the raw high-dimensional signal substantially hindered the SVM classification ability. Although decimation improved the performance in the Lofar dataset, where it yielded a moderate accuracy of 46.7%, it remained inferior compared with the results obtained from PCA and NLPCA. In contrast, both PCA and NLPCA benefited from the absence of decimation, likely owing to their reduced dimensionality and more structured data representation. Additionally, it was observed that standard errors were generally higher in the decimated models, particularly for Lofar and PCA, indicating greater variability in the model performance across the folds.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Hyperparameter**} & \multicolumn{2}{c}{**Lofar**} & \multicolumn{2}{c}{**PCA**} & \multicolumn{2}{c}{**NLPCA**} \\  & **w/ Dec** & **w/o Dec.** & **w/ Dec** & **w/o Dec.** & **w/ Dec** & **w/o Dec.** \\ \hline C (Regularization Parameter) & 393,520 & 393,520 & 114,026 & 114,026 & 114,026 & 114,026 \\ \hline Loss & Hinge & Hinge & Squared hinge & Squared hinge & Squared hinge & Squared hinge \\ \hline Penalty & \(\ell_{2}\) & \(\ell_{2}\) & \(\ell_{2}\) & \(\ell_{2}\) & \(\ell_{2}\) & \(\ell_{2}\) \\ \hline Mean Accuracy \(Acc\) & 0.517 & 0.612 & 0.515 & 0.0753 & 0.515 & 0.0753 \\ \hline Standard Error (SE) & 8.38\(\cdot\)10\({}^{-2}\) & 3.44\(\cdot\)10\({}^{-2}\) & 8.35\(\cdot\)10\({}^{-2}\) & 1.18\(\cdot\)10\({}^{-2}\) & 8.35\(\cdot\)10\({}^{-2}\) & 1.18\(\cdot\)10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: SVM (\(one\times one\)) configurations with Lofar, PCA, and NLPCA.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Hyperparameter**} & \multicolumn{2}{c}{**Lofar**} & \multicolumn{2}{c}{**PCA**} & \multicolumn{2}{c}{**NLPCA**} \\  & **w/ Dec** & **w/o Dec.** & **w/ Dec** & **w/o Dec.** & **w/ Dec** & **w/o Dec.** \\ \hline C (Regularization Parameter) & 393,520 & 393,520 & 114,026 & 114,026 & 114,026 & 114,026 \\ \hline Loss & Hinge & Hinge & Squared hinge & Squared hinge & Squared hinge & Squared hinge \\ \hline Penalty & \(\ell_{2}\) & \(\ell_{2}\) & \(\ell_{2}\) & \(\ell_{2}\) & \(\ell_{2}\) & \(\ell_{2}\) \\ \hline Mean Accuracy \(Acc\) & 0.467 & 0.0896 & 0.469 & 0.562 & 0.469 & 0.529 \\ \hline Standard Error (SE) & 9.02\(\cdot\)10\({}^{-2}\) & 2.14\(\cdot\)10\({}^{-2}\) & 9.54\(\cdot\)10\({}^{-2}\) & 4.27\(\cdot\)10\({}^{-2}\) & 9.54\(\cdot\)10\({}^{-2}\) & 2.97\(\cdot\)10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: SVM (\(one\times all\)) configurations with Lofar, PCA, and NLPCA.