## 5 Results Analysis
\begin{table}
\begin{tabular}{l r r r r r r r r r r} \hline \hline
**Type** & **P.** & \multicolumn{2}{c}{\(k\)**NN**} & \multicolumn{2}{c}{**DTC**} & \multicolumn{2}{c}{**RFC**} & \multicolumn{2}{c}{**ETC**} & \multicolumn{2}{c}{**XGBC**} \\  & & **noF** & **Val.** & **noF** & **Val.** & **noF** & **Val.** & **noF** & **Val.** & **noF** & **Val.** \\ \hline RFE [4] & — & 13 & 0.6427 & 13 & **0.7409** & 13 & 0.6620 & 13 & 0.6374 & 13 & 0.6404 \\ \hline \multirow{3}{*}{GA} & 0.3 & 10 & 0.6702 & 25 & 0.6444 & 16 & 0.7164 & 18 & **0.7018** & 14 & 0.6690 \\  & 0.5 & 11 & 0.6117 & 25 & 0.6690 & 9 & 0.6942 & 12 & 0.6784 & 9 & **0.7035** \\  & 0.7 & 8 & 0.6550 & 12 & 0.6538 & 7 & 0.7047 & 9 & 0.6579 & 9 & 0.6965 \\ \hline \multirow{3}{*}{GA with VarPenalty} & 0.3 & 10 & 0.6702 & 25 & 0.6871 & 19 & **0.7245** & 37 & 0.6456 & 34 & 0.6930 \\  & 0.5 & 9 & 0.6714 & 18 & 0.6830 & 9 & 0.7170 & 13 & 0.6906 & 13 & 0.6906 \\ \cline{1-1}  & 0.7 & 4 & **0.7070** & 15 & 0.7228 & 7 & 0.6661 & 11 & 0.6743 & 9 & 0.6848 \\ \hline \multirow{3}{*}{DE} & — & 14 & 0.5883 & 33 & 0.6035 & 72 & 0.6708 & 41 & 0.6719 & 14 & 0.6491 \\ \hline \hline \end{tabular} Values in green indicate validation accuracy over the majority rate. Boldfaced values are the best results for each classifier.  
\end{table} 
Table 9: Comparison of feature selection for each classifier based on validation results. metric allows for an assessment of the balance between precision and recall in the classifiers evaluated [21]. Therefore, its inclusion complements the accuracy metric by highlighting the trade-off between false positives and false negatives, which is especially relevant in medical decision-making contexts. F1-score (\(F_{1}\)) is defined as the harmonic mean of precision and recall, providing a single measure that balances both concerns, as shown in Equation (5),  
\[F_{1}=2\cdot\frac{\text{Precision}\cdot\text{Recall}}{\text{Precision}+\text{ Recall}} \tag{5}\]  
where _Precision_ is the ratio of true positive predictions to the total number of positive predictions made, as shown in Equation (6),  
\[\text{Precision}=\frac{\text{True Positives}}{\text{True Positives}+\text{ False Positives}} \tag{6}\]  
and _Recall_ is the ratio of true positive predictions to the total number of actual positive instances, as shown in Equation (7). \[\text{Recall}=\frac{\text{True Positives}}{\text{True Positives}+\text{ False Negatives}} \tag{7}\]  
\(F_{1}\) ranges from 0 to 1, where 1 indicates perfect precision and recall and 0 indicates the worst performance. As we considered Toxic as the positive class, in this metric, the baseline established by majority classifiers, that we set to be be beaten, is given by Equation (8) or (9), where \(p\) is the probability of the majoritarian class (0.6725). \[\text{If negative class is majoritarian:}\quad F_{1}=0 \tag{8}\]  
\[\text{If positive class is majoritarian:}\quad F_{1}=\frac{2p}{1+p},\quad\text{ where }p>0.5 \tag{9}\]  
As in this case the majoritarian class is the negative class (Non-toxic), any classifier with \(F_{1}\) over 0 is performing better than a majority classifier with respect to detecting toxicity. The results in Table 10 show that the best performing classifiers coincide with those identified by the accuracy metric. The values show that there is much space to improve in this challenging dataset.