## 5 Experiments and Results
### Effect of Leaders Ratio  
In this experiment, we study the effect of the ratio of the number of leaders to the swarm size on the performance of the proposed SSA-KELM. Tables 2 and 3 show the evaluation results of the SSA-KELM at different ratios of leaders. From the results, it can be seen that the best results in terms of most evaluation measures are obtained at a ratio of 50%. Remarkably, it can be noticed that all ratios achieved approximately a high reduction rate which is around (44%), while the difference between the reduction rates is slight. For instance, when the leaders' ratio is (20%), the algorithm obtained the maximal reduction rate of 49%, where the number of features was 160 out of 314. However, there is no obvious relation between the reduction rate and the number of leaders; this is demonstrated at the ratio (80%) where the reduction rate was 44.8%. In contrast, at leaders' ratio (50%), even that the algorithm achieved the minimal reduction rate, but it markedly exhibited the best performance as it is shown by Table 3.  
In this table, average accuracy, recall, FPR, TNR, Precision, G-mean, and AUC were reported at different ratios of leaders. At 50% of leaders' ratio, the SSA performed the best results and gained superior results in terms of accuracy, TNR, precision, g-mean, and AUC, which was (98%), which is reinforced by reasonable standard deviation values. Additionally, in regards to the FPR, \(SSA_{L=50\%}\) accomplished the minimal false positive rate (0.020), whereas at the other ratios from the highest to the lowest, they were 0.032, 0.032, 0.034, 0.024, and 0.028, respectively. Notably, regarding the recall, at all ratios, the recall was relatively close, while ratio (80%) achieved the highest recall value (98.4%). Overall, the SSA algorithm performed the best in terms of all evaluation metrics when the proportion \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ratio of Leaders** & **Number of Leaders** & **Reduction Rate** & **Average No. of Features** \\ \hline
80\% & 40 & 44.8\% & 173.3 \\
66\% & 33 & 45.2\% & 177.2 \\
50\% & 25 & 29.9\% & 220.3 \\
32\% & 16 & 45.8\% & 170.1 \\
24\% & 12 & 46.4\% & 168.2 \\
20\% & 10 & **49.0\%** & **160.0** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The effect of the ratio of leaders on the reduction rate and the average number of selected features. of leaders was half the swarm. As the number of leaders has tested next is to study the influence of the SSA population size. Figure 8 shows a box plot presentation of the error rate of the SSA algorithm at the six different ratios of leaders. Obviously, when the ratio (L) is 50%, the algorithm obtained the minimal error rate. In terms of the convergence rate, Figure 9 presents the convergence plot by depicting the obtained fitness value of the SSA algorithm at each iteration of the algorithm and at six ratios of the leaders. In which, the y-axis is the fitness, and the x-axis is the iterations. It is clear from the plot that when (L=20%), the algorithm experiences a premature convergence rate, that converges very fast to the best fitness value at the eleventh iteration and then remains constant over the rest of iterations. Whereas, the other variants of leaders' ratios exhibited different trends of convergence over the course of iterations reaching relatively optimal minimal fitness values.