## 3 Results
### Classification Performance Comparison over the Testing Data Set  
We performed an overall evaluation for the proposed model (AICPV with GMM--AICPVwGMM) over the 30 patient test data and we compared the performance results with the rule-based classification model that uses the same input features (AICPV with Threshold - AICPVwTH). Also, we considered performance comparison with two well known published algorithms for automated apnea detection using the oronasal thermal airflow signal and similar time-domain based features [39; 45]. The first algorithm implements a classical threshold based classification model [39] while the other one uses an artificial neural network classification model [45]. Note that [39] includes an additional module for classifying the type of detected apnea using a neural network classifier trained on the thoracic effort signal. Nevertheless, we just included the apnea detection module from this study since the proposed algorithm uses only a single channel of oronasal airflow. In order to do a fair comparison, the four algorithms AICPVwGMM, AICPVwTH, Refs. [39; 45] were all trained, evaluated, and tested on identical data within our data set. Table 3 comprehensively compares classification performance over the test data between these four algorithms. First, it can be noticed that the AICPVwGMM and the AICPVwTH outperform the two previously published algorithms in all performance measures of this paper. The AICPV algorithms demonstrate a higher ability to detect apnea events (reflected by their \(TPR\)) as well a higher ability to detect normal respiration patterns (reflected by their \(TNR\)) as opposed to [39; 45]. An overall better classification performance of the AICPV algorithms can be demonstrated with the \(F_{1}\) and \(AUC\) values compared to [39; 45]. The improvement achieved with AICPV algorithms is mainly caused by the dynamic approach considered in these algorithms such that apneic events are characterized based on relative changes in airflow breath amplitudes and inter-breath intervals with respect to local respiration baseline. Comparing the performance obtained with the proposed GMM based classifier (AICPVwGMM) and the rule-based classifier (AICPVwTH), we can notice a 65.2% increase in the \(PPV\) of the apnea detections obtained with the GMM based classifier as opposed to the rule-based threshold classifier. Recognizing \(TPR/PPV\) tradeoff, and that \(TPR\) and \(PPV\) are performance metrics of competing natures, it can be noticed that using a GMM-based classifier, we can achieve a high \(TPR\) with a significantly improved \(PPV\) compared to the rule-based classifier. This can be also noticed by observing the significant increase in the \(F_{1}\) score for the detections with the proposed GMM model as opposed to the rule-based one. Also, higher \(TNR\) and \(ACC\) are obtained with the proposed algorithm reflecting a higher ability to detect normal respiratory patterns. The overall classification performance indicated by \(AUC\) also shows an improved detection with the proposed GMM modeling framework. To provide an in-depth analysis and understand the sources of improvement with the proposed model as opposed to the rule-based classification model, we did a comprehensive analysis for the test performance of the proposed algorithms over different apnea types and different apnea severity conditions. Tables 4 and 5 provide a detailed comparison between the GMM-based classifier and the rule based classifier over different apnea types and different apnea severity levels. A clear increase in the ability to detect OSA and CSA events can be noticed in the \(TPR\) of these detections using the proposed algorithm along with a significant increase in the \(PPV\) of all types of apnea detections. It can be also noticed that the \(TPR\) of the MSA detections is superior with both algorithms and that it didn't change between them which is mainly due to the fact the MSA events are minority compared to OSA and CSA events.