## 3 Materials and Methods
### Performance Assessment  
Confusion matrix-based metrics are widely used to measure the performance of the methods used in solving binary classification problems. The confusion matrix is an indicator that numerically represents the accuracy or inaccuracy of the instance predictions made using the classifiers that are proposed in the classification problems. This indicator gives us the number of correctly predicted positive instances, \"True Positive (TP)\" ones, the number of incorrectly predicted positive instances, \"False Negative (FN)\" ones, the number of correctly predicted negative instances, \"True Negative (TN)\" ones, and the number of incorrectly predicted negative instances, \"False Positive (FP)\" ones. Based on this information, the evaluation metrics for the classifiers based on the confusion matrix can be calculated. In this study, the accuracy (Acc), recall (Rec), precision (Prec), specificity (Spec), F-measure (F-m) and area under the curve (AUC) metrics are used to measure the performance of the proposed FL-BDE model and the ML-based models for comparison purposes. The information about these metrics and their calculations is presented below. Accuracy: This metric, which represents a heuristic performance measure, gives the correct prediction ratio among all of the instances. As it can be understood from Equation (15), its score can be found by dividing the number of correctly predicted instances by the total number of instances. \[Acc=\frac{TP+TN}{TP+TN+FP+FN} \tag{15}\]  
Recall: It is also known as sensitivity. This metric, which gives the correct prediction ratio within positive instances, can be obtained using Equation (16). \[Rec=\frac{TP}{TP+FN} \tag{16}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{5}{c}{I\({}_{\text{FIS}}\)(1)} \\ \hline  & **VS** & **S** & **M** & **B** & **VB** & \\ \hline
**VS** & D0 & D1 & D2 & D3 & D4 & \\ \hline
**S** & D1 & D2 & D3 & D4 & D5 & **VS** \\ \hline
**\(\bullet\)** & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \\ \hline
**VB** & D5 & D6 & D7 & D8 & D9 & \\ \hline
**VS** & D1 & D2 & D3 & D4 & D5 & \\ \hline
**S** & D2 & D3 & D4 & D5 & D6 & **S** & I\({}_{\text{FIS}}\)(3) \\ \hline
**\(\bullet\)** & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \\ \hline
**VB** & D6 & D7 & D8 & D9 & D10 & \\ \hline
**\(\bullet\)** & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ \hline
**VS** & D4 & D5 & D6 & D7 & D8 & \\ \hline
**S** & D5 & D6 & D7 & D8 & D9 & \\ \hline
**\(\bullet\)** & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \\ \hline
**VB** & D8 & D9 & D10 & D11 & D12 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A cross-section of the rules used to combine ML-based classifiers. Precision: It is a ratio that shows the relationship between the total number of positively predicted instances and the number of correctly predicted positive instances. Its score can be calculated by the formula given in Equation (17). \[Prec=\frac{TP}{TP+FP} \tag{17}\]  
Specificity: It is simply a metric that gives the ratio of the number of correctly predicted negative instances to the number of negative instances. The formula that gives its score is Equation (18). \[Spec=\frac{TN}{TN+FP} \tag{18}\]  
F-measure: It is a generally preferred useful metric in performance measurements, especially in cases where there is an unbalanced class distribution. This metric determines its own score based on the harmonic mean of precision and recall, as seen in Equation (19). \[F-m=2\times\frac{Prec\times Rec}{Prec+Rec} \tag{19}\]  
Area under the curve: It is an important metric used to test whether the model can work correctly to solve classification problems. Its score can be obtained using the formula given in Equation (20), which gives the area of the receiver operating characteristic (ROC) curve. \[AUC=\int TPR.d(FPR) \tag{20}\]  
Here, \(TPR\) is the true positive rate, and \(FPR\) is the false positive rate.