## 5 Experimental Results and Simulations
### Evaluation of Classification Algorithms  
Initially, we examine the performance of different classification methods for sleep apnea classification. In this paper, we employed 13 other classification methods to predict the occurrence of OSA from ECG extracted features. To evaluate the performance of all \begin{table}
\begin{tabular}{c c c} \hline \hline
**Preset Classifier** & **Parameter** & **Value** \\ \hline Medium DT & Maximum number of splits & 20 \\ \cline{2-3}  & split criterion & [PERSON]’s diversity index \\ \hline LDA & discriminant type & linear \\ \hline Gaussian NB & Distribution & Gaussian \\ \hline Medium KNN & Number of neighbors & 10 \\ \hline  & Distance metric & Euclidean \\ \cline{2-3}  & Distance weight & Equal \\ \cline{2-3}  & standardize data & TRUE \\ \hline Boosted Trees & Ensemble method & AdaBoost \\ \hline  & Learner type & DT \\ \cline{2-3}  & Maximum number of splits & 20 \\ \cline{2-3}  & Number of learners & 30 \\ \cline{2-3}  & Learning rate & 0.1 \\ \hline Coarse Gaussian SVM & Kernel function & Gaussian \\ \hline  & Kernel scale & 22 \\ \cline{2-3}  & standardize data & TRUE \\ \cline{2-3}  & Box constraint level & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The parameter settings of preset classifiers. \begin{table}
\begin{tabular}{c l l c} \hline \hline
**Optimized Classifier** & **Parameter** & **Hyperparameters Search Range** & **Optimized Hyperparameters** \\ \hline DT\({}^{*}\) & Maximum number of splits & 1-14,756 & 56 \\ \cline{2-3}  & split criterion & Gini’s diversity index, Maximum deviance reduction & Gini’s diversity index \\ \hline NB\({}^{*}\) & Distribution & Gaussian, kernal & Gaussian \\ \cline{2-3}  & kernel type & Gaussian, Box, Triangle, Epanechnikov & Box \\ \hline KNN\({}^{*}\) & Number of neighbors & 1 to 7379 & 10 \\ \cline{2-3}  & Distance metric & city block, Chebyshev, cosine, & Euclidean \\  & & eculidean, hamming, & \\  & & Jaccard, Minkowski (cubic), & \\  & & spearman, Mahalanobis & \\ \cline{2-3}  & Distance weight & equal, inverse, squared inverse & Equal \\ \cline{2-3}  & standardize data & true, false & TRUE \\ \hline DA\({}^{*}\) & discriminant type & linear, quadratic, diagonal linear & linear \\  & & ear, & diagonal quadratic \\ \hline Ensemble DT\({}^{*}\) & Ensemble method & bag, gentleboost,logitboost, & bag \\  & adaboost,RUSboost & & \\ \cline{2-3}  & max no of splits & 1-14,756 & 355 \\ \cline{2-3}  & no of learners & 10–500 & 389 \\ \cline{2-3}  & no of predictors to sample & 1–9 & 6 \\ \cline{2-3}  & learning rate & 0.001–1 & 0.1 \\ \cline{2-3}  & learner type & - & DT \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Details of optimized hyperparametersclassifiers, we measure accuracy, True Positive Rate (TPR), True Negative Rate (TNR), Area under the curve (AUC), Precision, F-score, and G-mean criteria. Table 6 outlines the results obtained by all tested classifiers. The results show that ensemble DT* outperformed other classifiers with accuracy equals 77.26%, followed by KNN* (76.50%). The ensemble DT* and KNN* scored the highest AUC performances of 68.21% and 68.24%, respectively. G-mean, Precision, and F-score's findings reveal the superiority of ensemble DT* and KNN* classifiers in this work. On the one hand, the worst performance is achieved by the NB classifier with accuracy equals 69.97%. Based on the results obtained, the optimized classifiers can usually work better than those predefined parameter classifiers, which leads to satisfactory performance. Figure 5 illustrates the minimum classification error for four classifiers (DT*, Ensemble DT*, KNN*, and DA*). The convergence curve (i.e., dark blue points) refers to the observed minimum classification error computed so far by the optimization process. While the light blue convergence curve refers to minimum classification error when examining all hyper-parameter values tried so far. Figure 5 shows that the classifiers accelerated to find the global minimum error. Accordingly, tuning internal parameters can affect the overall performance of the classifier.