## 6 Results and Discussion
### GAN Hyperparameter Optimization  
In order to investigate the impact of hyperparameter optimization of GAN-based methods on defect prediction performance, we compared the performance of the GAN-based methods combined with boosting ensembles using the default against the optimized hyperparameters. Table 5 presents the MCC values of the default and optimized GAN-based methods of the proposed approach on all defect datasets. The difference will be positive if optimizing the hyperparameters increases the defect prediction performance compared to the default values, and the negative difference has the opposite meaning. To quantify the difference between the performance of the default and optimized methods, we calculated the Wilcoxon effect size of the methods as shown in Table 6.  
Empirical results demonstrated that GAN is slightly affected by hyperparameter optimization. Optimizing hyperparameters had a minor effect on 70% of the defect datasets, as shown in Table 6. This effect was found to be negative on 40% of the defect datasets. In other words, there is a slight reduction in MCC values of GAN on JM1, PC2, Lucene, and Eclipse-2.0 after performing the hyperparameters optimization process. Additionally, there \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **GAN** & **CWGANGP** & **CTGAN** \\ \hline CM1 & Medium & Negligible & Small \\ JM1 & Negligible & Large & Negligible \\ MC1 & Small & Large & Small \\ MC2 & Medium & Large & Small \\ PC2 & Small & Large & Medium \\ Tomcat & Small & Medium & Large \\ Lucene & Negligible & Negligible & Small \\ Eclipse-2.0 & Negligible & Negligible & Small \\ Zxing & Large & Large & Medium \\ Prop-43 & Negligible & Negligible & Large \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Wilcoxon effect size of the GAN methods. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{3}{c}{**Default**} & \multicolumn{3}{c}{**Optimized**} & \multicolumn{3}{c}{**Difference**} \\ \cline{2-10}  & **GAN** & **CWGANGP** & **CTGAN** & **GAN** & **CWGANGP** & **CTGAN** & **GAN** & **CWGANGP** & **CTGAN** \\ \hline CM1 & 0.05 & 0.12 & 0.07 & 0.10 & 0.07 & 0.11 & 0.05 & \(-\)0.05 & 0.04 \\ JM1 & 0.14 & 0.16 & 0.19 & 0.11 & 0.20 & 0.20 & \(-\)0.03 & 0.03 & 0.00 \\ MC1 & 0.18 & 0.04 & 0.15 & 0.24 & 0.28 & 0.18 & 0.06 & 0.24 & 0.03 \\ MC2 & 0.08 & 0.02 & 0.14 & 0.20 & 0.20 & 0.25 & 0.12 & 0.18 & 0.10 \\ PC2 & 0.11 & \(-\)0.02 & 0.09 & 0.11 & 0.59 & 0.16 & \(-\)0.01 & 0.61 & 0.08 \\ Tomcat & 0.22 & 0.23 & 0.22 & 0.24 & 0.27 & 0.33 & 0.02 & 0.04 & 0.11 \\ Lucene & 0.11 & 0.08 & 0.13 & 0.10 & 0.08 & 0.16 & 0.00 & 0.01 & 0.03 \\ Eclipse-2.0 & 0.35 & 0.36 & 0.34 & 0.33 & 0.36 & 0.35 & \(-\)0.02 & 0.00 & 0.01 \\ Zxing & 0.07 & 0.14 & 0.15 & 0.19 & 0.28 & 0.22 & 0.12 & 0.13 & 0.06 \\ Prop-43 & 0.29 & 0.40 & 0.28 & 0.30 & 0.38 & 0.30 & 0.00 & \(-\)0.02 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: MCC values of default and optimized GAN methods. was a positive moderate performance impact on the CM1 and MC2 defect datasets and a large positive impact on the Zxing defect dataset. In the CWGANGP method, we observed that it was severely influenced by hyperparameter optimization. There was a large positive impact on 50% of the defect datasets and a medium impact on one defect dataset. In addition, there was a negligible impact on 40% of the defect datasets. This negligible impact was negative on CM1, Eclipse-2.0, and prop-43 defect datasets. Lastly, in the case of CTGAN methods, hyperparameter optimization yielded a positive performance impact on all defect datasets. It was slightly affected on 60% of the defect datasets; there was a negligible impact on JM1 and a small impact on CM1, MC1, MC2, Lucene, and Eclipse-2.0 datasets. Furthermore, it was highly impacted by hyperparameter optimization on 40% of the defect datasets, with a medium impact on PC2 and Zxing datasets and a large impact on Tomcat and Prop-43 datasets.