## 3 Results and Discussions
Figure 10: _Cont._  
To summarize the hyperparameter adjustments, Table 2 lists the optimal values of each hyperparameter used in our proposed RF. All of these hyperparameters are selected using an original version of RF before combining any attribute selection algorithm. Using these hyperparameter values, we developed the five RFs (original and four improved RFs). All of these RFs are implemented using the same setting of parameters and evaluated by k-fold cross-validation. In each iteration of k, we assessed the following statistical measurements and calculated the average for the final evaluation results. \[Accuracy\ (Acc)=\frac{TP+TN}{TP+TN+FP+FN} \tag{20}\]  
\[Sensitivity\ (Sen)\ =\frac{TP}{TP+FN} \tag{21}\] \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Hyperparameter** & **Range** & **Accuracy** & **Selected Value** \\ \hline Number of decision trees & 100 to 500 & 0.9304 & 230 \\ Maximum number of features & 1 to 25 & 0.9232 & 15 \\ Maximum number of depth & 2 to 20 & 0.9285 & 18 \\ Minimum number of samples to split & 2 to 20 & 0.9267 & 5 \\ Minimum number of samples at the leaf node & 1 to 5 & 0.9178 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameter adjusting for RF. Figure 10: Adjusting the hyperparameter values for RF. (**a**) Number of decision trees in the forest, (**b**) maximum number of features selected for each tree, (**c**) maximum number of depths of an individual tree, (**d**) minimum number of samples required to split an internal node, and (**e**) minimum number of samples at the leaf node. every iteration, we generate an ROC of each RF. After that, the mean ROC curves are generated by interpolating the single ROCs, as illustrated in Figure 12a-e. Finally, the comparison of the mean ROCs of five RFs is shown in Figure 12f. Figure 12: Comparison of ROC curves for five RFs. (**a**) Original RF, (**b**) improved RF using RELIEFF attribute selection algorithm, (**c**) improved RF using genetic algorithm (GA) attribute selection algorithm, (**d**) improved RF using particle swarm optimization (PSO) attribute selection algorithm, (**e**) improved RF using firefly (FA) attribute selection algorithm, and (**f**) comparison of the mean ROCs of five RFs with respected to five-fold cross-validation. However, comparing the ROC curves directly from the graph is very difficult as they are not scalar values. For this reason, we add another assessment measurement called the area under the curve (AUC) to ascertain the specific differences between the ROC curves. As the name implies, AUC can be measured by calculating the area of the trapezoid region under the ROC curve. Table 3 summarizes all the assessment values of each RF with respect to the five-fold cross-validation. From this table, we can know that the optimized RF that applies the firefly attribute selection (RF+FA) can provide superior performance, as compared to its counterparts. Some example of outputs of our proposed nodule detection are demonstrated in Figure 13. Figure 13a shows the detection of a sharp solid nodule that resides inside the lung without touching other lesions. Such nodules are easy to detect, and our proposed method well-detected them. However, Figure 13b shows the results of an isolated ground glass nodule (GGO) that had a very faint intensity. This type of nodules is hard to detect due to their hazy structures. However, the proposed method can successfully detect them because we used a very low-intensity value (\(-910\) HU) during nodule candidate detection. Moreover, our method ensures the detection of juxta-pleural nodules that are connected to the lung boundary. Figure 13c represents the detection of a small juxta-pleural nodule, and Figure 13d represents the detection of a very big one, respectively. Our method can ensure