## 4 Results
### Comparison of the Classification Results
However, the significance of the proposed method compared to group lasso lies in its ability to provide the relative importance of all group features. The proposed method demonstrated superior performance in terms of accuracy and F1 score across all datasets. For instance, on the GLA-BRA-180 dataset, the proposed method achieved the highest accuracy of 89%, surpassing the group lasso method, which achieved an accuracy of 88%, and outperforming the No-FS approach, which achieved only 74% accuracy. Additionally, the proposed method achieved an F1 score of 89%, while the group lasso and No-FS methods achieved scores of 83% and 68%, respectively. This highlighted the effectiveness of the proposed method, which outperformed the group lasso by 1% in accuracy and by 15% compared to No-FS. Moreover, in terms of F1 score, the proposed method outperformed the group lasso by 6% and No-FS by 21%. Similarly, on the CLL-SUB-111 dataset, the proposed method achieved the highest accuracy of 97%, while the group lasso and No-FS methods achieved 90% and 85%, respectively. The F1 score of the proposed method was 98%, compared to 93% for group lasso and 88% for No-FS. This demonstrated the superior performance of the proposed method across the various classification metrics. On the TOX-171 dataset, the proposed method achieved an accuracy of 98%, slightly outperforming group lasso with 97% and No-FS with 90%. This further validated the effectiveness of the proposed method in achieving superior performance compared to existing methods across different datasets. A key advantage of our method is its ability to provide not only the selection of group features but also their ranking and the relative importance of these group features. This rich information enables a more informed decision-making process for the group feature selection. While group lasso focuses primarily on selecting groups of features, our method goes beyond quantifying the importance of each feature group. Thus, we can identify the groups that contribute most to the predictive power of the model. Our method offers a significant advantage by not only selecting group features but also by providing their ranking and delineating the relative importance of these groups. This capability affords a nuanced understanding that aids in informed decision-making for feature selection, whereas group lasso primarily selects feature groups without ranking them. By utilizing the rankings and importance scores, we ascertain the comprehensive contribution of each group feature, which facilitates the effective prioritization of the most impactful ones. Furthermore, the proposed method is not limited to specific algorithms and its insights can be applied to various classifiers. This flexibility allows it to be adapted to different machine-learning tasks. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Classifier**} & \multicolumn{2}{c}{**No-FS**} & \multicolumn{2}{c}{**Group-Lasso**} & \multicolumn{2}{c}{**Proposed Method**} \\ \cline{3-8}  & & **Accuracy** & **F1 Score** & **Accuracy** & **F1 Score** & **Accuracy** & **F1 Score** \\ \hline \multirow{3}{*}{GLA-BRA-180} & LR & 0.74 & 0.68 & 0.81 & 0.79 & 0.83 & 0.82 \\  & SVM & 0.73 & 0.67 & 0.88 & 0.83 & 0.89 & 0.89 \\  & RF & 0.7 & 0.57 & 0.71 & 0.63 & 0.71 & 0.65 \\ \hline \multirow{3}{*}{CLL-SUB-111} & LR & 0.82 & 0.83 & 0.87 & 0.91 & 0.95 & 0.97 \\  & SVM & 0.85 & 0.88 & 0.9 & 0.93 & 0.97 & 0.98 \\  & RF & 0.71 & 0.75 & 0.83 & 0.87 & 0.88 & 0.91 \\ \hline \multirow{3}{*}{TOX-171} & LR & 0.86 & 0.85 & 0.87 & 0.88 & 0.9 & 0.89 \\  & SVM & 0.9 & 0.89 & 0.97 & 0.97 & 0.98 & 0.98 \\ \cline{1-1}  & RF & 0.72 & 0.72 & 0.71 & 0.72 & 0.74 & 0.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prediction accuracy and F1 score of the proposed method and group lasso. In summary, the advantage of our method lies in its ability to offer a more detailed understanding of group feature importance, facilitating better decision-making in feature selection.