## 6 Results and Discussion
### Stability Analysis of the Greedy Decision Tree Algorithm  
The results in Section 6.2 highlight the superior performance of GDT variants compared to other recent algorithms. However, a further in-depth analysis is required to \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Algorithm** & **Validation** & **Sampling** & **Accuracy \%** & **Recall \%** & **Specificity \%** & **FAR \%** & **Precision \%** & **F1-Score \%** \\ \hline GDT & K-fold & Stratified & 99.997 & 99.995 & 100 & 0 & 100 & 99.997 \\ \hline GDT & K-fold & Random & 99.997 & 99.995 & 100 & 0 & 100 & 99.998 \\ \hline AdaBoost & K-fold & Stratified & 99.998 & 99.998 & 99.998 & 0.001 & 99.998 & 99.998 \\ \hline LogitBoost & K-fold & Stratified & 99.996 & 99.996 & 99.996 & 0.003 & 99.996 & 99.996 \\ \hline GentleBoost & K-fold & Stratified & 99.995 & 99.995 & 99.995 & 0.004 & 99.995 & 99.995 \\ \hline RUSBoost & K-fold & Stratified & 99.341 & 99.323 & 99.301 & 0.617 & 99.332 & 99.341 \\ \hline RF & K-fold & - & - & 99.995 & - & - & 99.99 & 99.997 \\ (Elsayed) & \multicolumn{1}{c}{} & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of GDT variants with RF of [PERSON] et al. [2] and other algorithms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Validation** & **Sampling** & **Average Training Time** & **Throughput (Predictions/Sec)** \\ \hline  & & **Ahuja** & **Elsayed** & **Ahuja** & **Elsayed** \\ \hline GDT & K-fold & Stratified & 8.0 & 7.6 & 2,658,798 & 5,723,790 \\ \hline GDT & K-fold & Random & 8.0 & 7.6 & 2,509,367 & 5,714,573 \\ \hline GDT & Monte Carlo & Random & 8.0 & 7.6 & 2,753,333 & 5,718,750 \\ \hline AdaBoost & K-fold & Stratified & 10.1 & 9.7 & 147,618 & 252,850 \\ \hline LogitBoost & K-fold & Stratified & 11.5 & 8.5 & 164,636 & 283,262 \\ \hline GentleBoost & K-fold & Stratified & 8.9 & 7.9 & 193,814 & 294,309 \\ \hline RUSBoost & K-fold & Stratified & 13.1 & 16.4 & 195,295 & 269,154 \\ \hline SVC-RF ([PERSON]) & - & - & - & - & - & - \\ \hline RF ([PERSON]) & K-fold & - & - & 42.5 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of average training time and throughput of GDT with other algorithms. evaluate the stability of the GDT approach. [PERSON] et al. [83] propose that overall misclassification rate is a very basic measure of the stability of decision trees. They further point towards the direction of measuring variations in the prediction to measure the stability of decision trees. In accordance with this, the plots in Figure 4 depict variance for the three GDT variants with respect to the different evaluation metrics. As far as the variance in evaluation parameters is concerned, the GDT algorithm results in an extremely lower variance, as can be verified from the bar graphs in Figure 4. The bar graphs show that in case of the dataset in [PERSON] et al. [1], k-fold cross validation with stratification (Figure 4b) gives the lowest variance, and k-fold without stratification (Figure 4a) gives a higher variance than k-fold stratified data, while Monte Carlo gives the highest variance (Figure 4e) for all performance measures. In the case of the dataset of [PERSON] et al. [2], the lowest variance is achieved when using k-fold without stratification (Figure 4c), a higher variance is obtained with Monte Carlo (as shown in Figure 4f), and the highest variance is shown when using k-fold with stratification (Figure 4d). The stability of the GDT algorithm was also evaluated in terms of the variance in the number of features selected and the tree size. Such a stabi  
Figure 4: Variance in performance measures for the two datasets using GDT. trees was advocated by [PERSON] [84], who identified how class agreement on different folds and decision tree structures can help measure the stability of decision trees. Keeping this under consideration, Table 10 summarizes the results of experiments to measure the variance in tree structure and features used in different combinations of validation testing.