## 4 Data Analysis Framework Application
### Comparison of Different Classifiers  
Based on Figure 16, the resolution of 64 seems to be a trade-off between computational efficiency and validation accuracy, so to enhance training performance, alternative supervised ML models for classification tasks have been investigated. In this order, different classifiers are examined on the set of engineering features to seek further improvement. To achieve this goal, the data has undergone testing with seven classifiers, and the results are depicted in Figure 18.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**ML Model** & **Hardware** & **Batch Size** & **Validation Accuracy (\%)** & **Training Time (s)** \\ \hline CNN on raw data & CPU & 128 & 98.38 & 29,591 \\ CNN on raw data & GPU & 128 & 98.42 & 2413 \\ SVR on engineered data & CPU & 128 & 91.92 & 4.7 \\ CNN on engineered data & CPU & 256 & 91.10 & 154 \\ ANN on engineered data & CPU & 256 & 94.67 & 50 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of training time and accuracy between CNN and SVR utilized with new data processing.  
Figure 17: Architecture of CNN.  
The linear discriminant classifier (LDA) has demonstrated the most favorable balance between accuracy and computational time, boasting a 96.24% accuracy rate and a training time of nearly 4 s. To delve deeper into the factors contributing to the compatibility of LDA with the data, a more thorough examination is warranted. So, to limit the dimensional space to a more meaningful representation, the model has been trained by a resolution of 8 corresponding to 10 feature arrays.  
To address this, Figure 19 indicates the linear cluster representation of features 5 and 7 for all classes of wave conditions. As can be seen, despite overlaps between classes, they are discernible and separable. As indicated in Figure 20a, the LDA works perfectly on the features with higher separability due to its mathematical model. In short, the DA algorithm endeavors to maximize the separability between known categorical groups by maximizing the distance between the mean value of the groups and minimizing the variance in each group. As such, the discriminant can be obtained by eigenvectors of matrix S, which is constructed according to Equation (12) [30], in which B denotes the matrix of variance between the group, and W is the matrix of variance within the group.  
\[\text{S}=\text{W}^{-1}\text{B}=\frac{\text{Covariance (Total) - Covariance (W)}}{\text{Covariance (W)}} \tag{12}\]  
So, as per Figure 20b, the linear boundary perfectly separated two features' clusters. To explore the potential for further enhancing classification performance, quadratic discriminant analysis was employed as the separator. However, the results indicated a high error rate. Capturing the mutual linear representation of clusters with respect to certain classes has revealed the reason behind this. As indicated in Figure 21a,b, some clusters showed a scatter distribution, where the quadratic boundary missed the scattered features, so they contributed to the error. However, according to Figure 21b, the LDA inclusively covered the scattered features, resulting in high separability and less classification error.  
Figure 18: The performance of classifiers on the feature engineered data (Orange bar for error and blue bar for computational time).