# Sleep Apnea Classification Using the Mean Euler-Poincare Characteristic and AI Techniques
## 5 Results and Discussion
We used a 15 th-order polynomial EPC model to obtain the FNN classifier model because it had better results compared to the 21 st-order polynomial. The next step is to compare the two approaches with several cases in the literature. Table 5 compares our approach with various cases from the 2000 challenge to modern techniques that employ deep learning machines. The heart rate variability (HRV) analysis has been employed in the literature. For example, [26] used domain time features of the HRV, achieving a performance of 92.6%. In [34], the authors analyzed the frequency domain features from the T-wave, using the wavelet transform, and reached 92.3% accuracy. In [32], the spectral analysis of HRV features achieved an accuracy of 89.36%. Other works used oxygen saturation (\(S_{p}O_{2}\)) data to classify OSA. In [29], three different algorithms using the wavelet transform were compared, and the results yielded an accuracy of 88%. The decision methods can vary by work. The most used classifiers include random forest, support vector machines, linear or quadratic regression, neural networks, and KNN. In [50], a linear discriminant using frequency domain features extracted from the Hilbert transform achieved 90% accuracy. In [30], a decision tree combined with blood oxygen saturation levels classified the OSA and achieved an accuracy of 93.03%, a sensitivity of 92.35%, and a specificity of 93.52%. In [36], a neural network was used to classify RR interval data and multi-frequency filters, achieving a specificity of 99%. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Phase** & **Accuracy** & **Sensitivity** & **Specificity** & **F1 Score** \\ \hline Training & 100\% & 96\% & 100\% & 98\% \\ \hline Test & 97\% & 93\% & 100\% & 95\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Table presenting the accuracy, sensitivity, specificity, and F1 score results of the FNN classifier. Figure 14: Results of the confusion matrix for the test set using a 15 th-order polynomial and FNN. Figure 13: Confusion matrix for the training phase using a 15 th-order polynomial and FNN. In [51], a random forest classifier used features from the power spectrum and discrete wavelet transform. The best features were selected as inputs with the aid of the particle swarm optimization method. The reported accuracy was 99.22%. The authors of [35] and [17] used deep neural networks. A multi-layer feed-forward neural network (FNN) using information from the ECG, \(S_{p}\)O\({}_{2}\), and BMI yielded an accuracy of 97.8% [35]. In [17], the authors proposed an algorithm that used deep learning layers (convolutional neural networks and long short-term memory) to extract features and classify the OSA. It achieved an accuracy of 97.21%, a sensitivity of 94.41%, and a specificity of 98.94% on the Apnea-ECG database. The related works and each study's performance measures, signals used, techniques, and decision methods are summarized in Table 5. Our approach stands out in terms of performance measures (sensitivity, specificity, and accuracy); we also employed a geometrical approach, which is unique among the studies reviewed. We used a different multi-layer FNN and the EPC model as features, obtaining a similar performance to [PERSON] et al. [35]. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline  
**EKNN approach** & \
\begin{tabular}{c} Accu = 89\% \\ Sens = 89\% \\ Spec = 86\% \\ \end{tabular} & ECG &
\begin{tabular}{c} Random Field \\ Euler–Poincaré characteristic \\ \end{tabular} & EKNN classifier \\ \hline
**FNN approach** & \
\begin{tabular}{c} Accu = 98.5\% \\ Sens = 94.5\% \\ Spec = 100\% \\ \end{tabular} & ECG &
\begin{tabular}{c} Random Field \\ Euler–Poincaré characteristic \\ \end{tabular} & Multi-layer FNN \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison between our approach and the approaches used in the literature. Appendix A outlines our application of the Synthetic Minority Oversampling Technique (SMOTE) to address dataset imbalance in the database used.