## 6 Results and Discussion
### PVA Detection  
We again begin with the normal model. Table 10 presents the RMSE for each normal model candidate based on the test partition within the training data (the final 10%). The 1D CNN is substantially superior, and so we again select it as the normal model.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **GRU** & **Dropout GRU** & **Bidirectional** & **1D CNN** \\ \hline
**Test error (RMSE)** & 0.1691 & 0.2406 & 0.1697 & 0.0970 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Out-of-sample test error for the normal model candidates.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Model** & **Accuracy** & **TPR** & **FPR** \\ \hline Isolation Forest (proposed) & 0.9959 & 0.9949 & 0.0006 \\ \hline OC-SVM (proposed) & 0.9927 & 0.9911 & 0.0012 \\ \hline Soft-bound Deep SVDD & 0.9859 & 0.9885 & 0.0239 \\ \hline Once-class Deep SVDD & 0.9826 & 0.9843 & 0.0239 \\ \hline OC-NN & 0.9923 & 0.9914 & 0.0047 \\ \hline OCAN & 0.7826 & 0.6859 & 0.1208 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Computer generated data: comparison against the literature.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Model** & **Accuracy** & **TPR** & **FPR** \\ \hline Isolation Forest (proposed) & 0.9995 & 0.9949 & 0.0006 \\ \hline OC-SVM (proposed) & 0.9927 & 0.9911 & 0.0012 \\ \hline Soft-bound Deep SVDD & 0.9859 & 0.9885 & 0.0239 \\ \hline Once-class Deep SVDD & 0.9826 & 0.9843 & 0.0239 \\ \hline OC-NN & 0.9923 & 0.9914 & 0.0047 \\ \hline OCAN & 0.7826 & 0.6859 & 0.1208 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Computer generated data: comparison against the literature.  
We next examine the OC-SVM AD. The first column of Table 11 presents our classification results without resampling. The overall accuracy of 87.6% is not competitive with current machine-learning approaches to PVA. Examining the results, we see that the specificity (true negative rate) of our AD is strong, but the sensitivity is low. This is what we expect to find when the class boundary for OC-SVM is drawn too narrowly. Accordingly, we apply our proposed resampling technique, obtaining the results in the second column.  
In Table 12, we compare our results against existing PVA-diagnosis algorithms. Note that these latter examples are all based on supervised classification, rather than semi-supervised anomaly detection, meaning that examples of both normal and asynchronous breaths were presented to the learning algorithm. This is in keeping with the objective of a _diagnosis_, which is a multi-class problem that seeks identification of the particular form of PVA being presented. Our algorithm, as an anomaly detector, only identifies the _presence_ of PVA. In addition, except for [39] (reported in the first row and marked by an \"*\") the experiments were conducted based on different PVA datasets collected from different locations and using different equipment. The results for the algorithms were usually reported as sensitivity and specificity for individual PVA types, as well as the \"normal\" class. We reconstruct the sensitivity and specificity of detecting PVA _in general_ by reversing the sensitivity and specificity from the \"normal\" class in Table 12.  
What we find from Table 12 is that our semi-supervised AD approach, when combined with oversampling, is competitive with the existing supervised techniques, even though we are training the AD only on normal data. In addition, while [PERSON] et al. [69] build their model directly from the flow and pressure data streams, the other two extract additional metadata from it, in the form of derived quantities (tidal volume, etc. [39]) or shape features extracted from the waveforms [56]. Ref. [39] also used SMOTE resampling to further improve the performance of their supervised algorithm. Thus, our semi-supervised AD approach is competitive with supervised algorithms using far more information.