## 3 Results
### Classification Performance Comparison over the Testing Data Set
Looking at the detailed performance of the proposed GMM model and the rule-based classifier over different apnea severity conditions, we can notice that the best performance for the rule-based threshold classifier is in severe apnea patients and that the performance significantly degrades over less severe cases. On other hand, the GMM based classifier maintains a high ability to detect apnea events in severe patients, but more importantly, it has a significantly higher ability to detect apneic events in less severe apnea patients which can be clearly seen through the \(TPR\) of these detections. Moreover, looking at the \(AUC\) values, we can also notice an excellent overall ability to detect apnea events in severe patients for the GMM modeling framework as well as a significantly improved overall ability to detect apnea in less severe patients compared to the rule-based classification model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**AICPVwGMM** & & \(TPR\) **(\%)** & \(TNR\) **(\%)** & \(PPV\) **(\%)** & \(ACC\) **(\%)** & \(F_{1}\) **(\%)** & \(AUC\) **(\%)** \\ \hline \multirow{6}{*}{Type of Apnea} & MSA & 97.2 & 80.6 & 9.9 & 80.9 & 18.0 & 88.9 \\  & CSA & 88.7 & 80.6 & 41.8 & 81.7 & 56.8 & 84.6 \\  & OSA & 92.7 & 80.6 & 25.3 & 81.4 & 39.8 & 86.7 \\ \hline \multirow{6}{*}{AHI Severity} & Severe & 96.4 & 77.3 & 68.7 & 83.8 & 80.3 & 86.7 \\  & Moderate & 98.1 & 77.5 & 32.6 & 79.5 & 48.9 & 87.8 \\ \cline{1-1}  & Mild & 100.0 & 84.8 & 12.2 & 85.2 & 21.7 & 92.4 \\ \cline{1-1}  & None/Minimal & 27.3 & 71.8 & 0.0 & 83.4 & 0.0 & 86.7 \\ \hline All & & 88.5 & 82.5 & 46.6 & 83.4 & 42.7 & 86.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Test performance of AICPV with GMM classifier over different types of apnea and different apnea severities. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & \(TPR\) **(\%)** & \(TNR\) **(\%)** & \(PPV\) **(\%)** & \(ACC\) **(\%)** & \(F_{1}\) **(\%)** & \(AUC\) **(\%)** \\ \hline AICPVwTH & 88.3 & 79.4 & 28.2 & 80.2 & 42.7 & 83.9 \\ AICPVwGMM & 88.5 & 82.5 & 46.6 & 83.4 & 61.1 & 86.7 \\ \cline{1-1} \cline{3-7} \cl  
Finally, we performed a comprehensive analysis for the performance per class of apnea types among different patient severity levels. Table 6 evaluates how the proposed model performs on detecting different apnea types in each of apnea severity classes. As it can be seen in the table, the proposed model AIPCVwGMM maintains a high ability to detect different apnea types regardless disease severity in the test patients. MSA events are very rare in mild patients which caused low and skewed detection rates for these patients. Also, the final row in Table 6 was left empty since there are no MSA events in the class of none/minimal apnea patients. In general, the class of none/minimal apnea reflects patients that are healthy or with few significant apnea events and so it a class of less interest compared to other disease states. Nevertheless, we kept performance results on all disease severity classes to report comprehensive assessment of the modeling framework. It is worthy to be mentioned that the implemented algorithms were trained and tested using full overnight PS records. Our goal is to test the proposed framework and to compare it with existing works in a more practical setting as opposed to many previous studies that considered shorter records avoiding the class imbalance problem and excluding segments with low signal to noise ratio (SNR). False positives were affected by the class imbalance problem, segments of low airflow signal quality, and irregular breathing patterns and artifacts. High airflow peak amplitudes resulting from increased respiratory effort after the end of apnea events may affect false positives by contributing falsely to the respiratory baseline. Future work may consider adding more advanced signal filtration algorithms that can allow more accurate detection of artifacts as well as to reject airflow segments with very low SNR.