## 7 Experiments and Results
### Analysis and Discussion  
The results from our experiments indicated that for highly imbalanced datasets, the proposed method had a significant positive impact on the g-mean score (which measures the balance between the classification performances for both the majority and minority  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Classifier** & **Oversampling** & **Feature Selection** & **G-Mean** \\ \hline Random Tree [34] & No & No & 0.602 \\ AB-J48(20) [34] & No & No & 0.609 \\ Random Tree [34] & Yes & No & 0.696 \\ AB-Rep Tree/(90) [34] & Yes & No & **0.730** \\ AB-Rep Tree/(90) [34] & Yes & Yes & 0.720 \\ \hline ENS\_PSONN\_cost & No & No & 0.877 \\ ENS\_CSONN\_cost & No & No & **0.893** \\ \hline \hline \end{tabular}
\end{table}
Table 16: The best results for the g-mean scores of the hybrid methods that were used in the related work compared to those of the two methods that are proposed in this work using the dataset of Spanish companies. The best g-mean result per classification approach is marked in boldface  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Classifier** & **G-Mean** \\ \hline SVM+SDA+FC [35] & 0.814 \\ \hline ENS\_PSONN\_cost & 0.875 \\ ENS\_CSONN\_cost & **0.897** \\ \hline \hline \end{tabular}
\end{table}
Table 17: The best results for the g-mean scores that were obtained in the related work compared to those of the two methods that are proposed in this work using the dataset of Taiwanese companies. The best g-mean result is marked in boldface.  
classes) while maintaining an acceptable accuracy score. We found that the cost sensitivity fitness function helped to shift the bias away from the majority class and toward the minority classes and that ensemble learning could help to decrease the side effects of that bias shift.  
In line with our hypothesis, applying a weight to the misclassified positive instances increased the number of TP predictions and decreased the number of FN predictions. However, as a side effect, the number of FP predictions increased and the number of TN predictions decreased. Since we were dealing with highly imbalanced datasets, the number of instances that belonged to the minor class \((\text{TP}+\text{FN})\) was much lower than the number of instances that belonged to the major class \((\text{FP}+\text{TN})\); so, the improvement in the sensitivity score was significant and the drop in the specificity score was not as drastic, which led to an overall improved g-mean score, as observed in the results from all experiments.  
Moreover, when applying ensemble learning, we observed an overall improvement in all of the evaluation measurements that were used. This proved that the MHOANN was diverse and could be used in a homogeneous ensemble learning system. The ensemble learning created a stronger learner that approximately maintained the number FN predictions but decreased the number of FP predictions, resulting in a slightly better g-mean score and a significant improvement in the accuracy score.  
In terms of performance, as previously mentioned, the CSO outperformed the PSO regarding execution time. In contrast to the PSO, only half of the population was updated in the CSO, which explained the faster execution times.  
In Appendix A, we show the convergence (learning) curve graphs for sample runs using both optimizers (the PSO and CSO) for each fitness function and each dataset. We noticed that the fitness values were minimal in the cases of the MSE and accuracy fitness functions, which indicated that the model had a high accuracy (as confirmed by the previous results) but was biased toward the majority class and failed to predict the minority classes (as previously discussed). On the other hand, the fitness value was higher when using the cost sensitivity fitness function, which was expected because the number of FN predictions was multiplied by the allocated weight. Additionally, in all of our experiments, the fitness scores stabilized when approaching 100 iterations, which indicated that additional training would not significantly improve the model.