# Machine Learning with Evolutionary Parameter Tuning for Singing Registers Classification
## 3 Computational Experiments  
The proposed method achieves consistent performance across all the employed evaluation metrics, as shown in Table 5. Notably, the XGB model exhibits superior classification performance compared to SVC and MLP models. The latter is evident from the higher average accuracy and lower standard deviation values obtained by XGB.  
To further confirm the above-reported findings, a comparison between the SVC, MLP, and XGB models' performance across all metrics was carried out via the Analysis of Variance (ANOVA) test. Results of ANOVA were reported in Table 6, and it must be noted that statistically significant differences were observed between XGB and both SVC and MLP models, with \(p\)-values less than 0.05 for all metrics. Conversely, the ANOVA test between SVC and MLP yielded \(p\)-values greater than 0.05 for all metrics, indicating no statistically significant difference in classification performance. Such results confirmed the superiority of the proposed classification method, employing XGB for achieving statistically significant improvements if compared to the other baseline models, i.e., SVC and MLP.  
To complement the performance analysis, Figure 6 reports the average confusion matrices for all models. As anticipated, due to their inherent similarities, the highest classification errors occurred when distinguishing between mixed and chest singing registers. The SVC model had the highest misclassification rate, with 23% of mixed voice records incorrectly classified as chest voice. Its second-highest error occurred in the opposite direction, with 17% of chest voice records classified as mixed voice. The MLP model showed a similar confusion rate between these categories of singing registers (11%). In contrast, the XGB model confusion matrix revealed an opposite trend to SVC, with the highest confusion rate (3.7%) occurring during the chest-to-mixed misclassification, followed by mixed-to-chest (2.4%).  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Models in** & \multicolumn{5}{c}{**Performance Metrics**} \\
**Comparison** & **Acc** & **F1** & **JS** & **PS** & **RS** \\ \hline SVC \(\times\) MLP & 0.011175 & 0.072524 & 0.008140 & 0.091105 & 0.011175 \\ MLP \(\times\) XGB & \(7.76\times 10^{-6}\) & \(4.80\times 10^{-5}\) & \(1.02\times 10^{-6}\) & \(1.37\times 10^{-4}\) & \(7.76\times 10^{-6}\) \\ SVC \(\times\) XGB & \(7.59\times 10^{-16}\) & \(1.80\times 10^{-14}\) & \(8.69\times 10^{-19}\) & \(3.75\times 10^{-14}\) & \(7.59\times 10^{-16}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: The table contains the obtained \(p\)-values from the ANOVA test performed by combining the models two by two. Values below 0.05 indicate a statistically significant difference with 95% confidence.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Estimator** & **Acc** & **F1** & **PS** & **RS** & **JS** \\ \hline SVC & 0.872 (0.081) & 0.866 (0.092) & 0.881 (0.080) & 0.872 (0.081) & 0.794 (0.112) \\ MLP & 0.912 (0.095) & 0.902 (0.121) & 0.911 (0.119) & 0.912 (0.095) & 0.853 (0.137) \\ XGB & **0.976** (0.012) & **0.976** (0.012) & **0.978** (0.012) & **0.976** (0.012) & **0.955** (0.023) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average performance metrics and their respective standard deviation. Standard deviation is computed using a five-fold stratified cross-validation set as a performance assessment strategy.  
Finally, all the employed ML models achieved the highest classification accuracy for the head voice registers. The second-highest correct classification rate was associated with the chest voice for SVC and MLP models and mixed voice for XGB. Notably, the XGB model achieved superior performance with over 96% accuracy in correctly classifying all three singing registers, highlighting its effectiveness in singing register recognition.