## 4 Discussion  
The conducted investigation showed the procedure of how highly imbalanced datasets can be balanced and used to obtain the symbolic expression for the detection of hepatitis C patients from blood samples. The kernel PCA method provided a better insight into the distribution of class samples in the kernel PCA plane. The random oversampling method generated enlarged the number of samples however those are the same samples as the originals. Among the remaining three balancing methods the distribution of class samples in the kernel PCA plane showed that class samples overlap which could be a problem for the ML algorithm to distinguish between the overlapping classes. The ADASN and SMOTE \begin{table}
\begin{tabular}{c c} \hline \hline
**Evaluation Metric** & **Values** \\ \hline \(ACC\) & 0.9932 \\ \(AUC\) & 0.9722 \\ \(Precision\) & 0.98148 \\ \(Recall\) & 0.9464 \\ \(F1-Score\) & 0.9636 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The results of evaluation metric values obtained with application of the best symbolic expression (\(y_{1}\)) in binary problem on the original dataset. \begin{table}
\begin{tabular}{c c} \hline \hline
**Evaluation Metrics** & **Values** \\ \hline \(ACC\) & 0.983 \\ \(AUC\) & 0.85 \\ \(Precision\) & 0.74 \\ \(Recall\) & 0.72 \\ \(F1-Score\) & 0.721 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The results of evaluation metric values obtained with application of the best symbolic expressions (\(y_{21},y_{22},y_{23}\), and \(y_{24}\)) in multiclass on the original dataset. method enlarged the area of class samples and overlapping between class samples is the most evident in those two cases. However, in the case of the Borderline SMOTE balancing method the distribution of class samples is more condensed i.e., the synthetic samples are generated around the original class samples. In binary problem, the best symbolic expression was obtained in the case of the dataset balanced with the BorderlineSMOTE method as seen from Figure 10 and Table 4. However, the symbolic expression obtained in the case of the dataset balanced with SMOTE method showed similar classification accuracy but the size of the symbolic expression, in this case, is much larger than the symbolic expression obtained in the Borderline SMOTE case. Based on size and evaluation metric values the best symbolic expression in binary problem was the symbolic expression obtained on dataset balanced with BorderlineSMOTE method. The symbolic expression in the final evaluation on the original dataset showed similar classification accuracy (Table 7) as in the case of the Borderline SMOTE method. Regarding the GPSC hyperparameters in binary problems, the hoist and point mutation were dominating genetic operations. Due to the low parsimony coefficient value (9.19 \(\times 10^{-6}\)) in the SMOTE case the large symbolic expression was obtained however the bloat phenomenon did not occur because the GPSC execution time was similar to other cases and classification accuracy is similar to one obtained in BorderlineSMOTE case. In multi-class problems, the best symbolic expressions were obtained in the case of dataset oversampled with random oversampling and the Borderline SMOTE method. However, in the case of SMOTE and ADAYN datasets, the obtained symbolic expressions performed poorly i.e., the results of evaluation metrics are in the range from 0.8-0.99. The symbolic expressions obtained in the case of the BorderlineSMOTE method are smaller when compared to those symbolic expressions obtained in the case of the random oversampling method. The classification accuracy of the symbolic expressions obtained in the case of Borderline SMOTE is slightly lower than of those symbolic expressions obtained with random oversampling. Regarding the size the smallest size of symbolic expression was obtained in the BorderlineSMOTE case while the largest was in the case of Random Oversampling.