  Objective: Breathing pattern variability (BPV), as a universal physiological
feature, encodes rich health information. We aim to show that, a high-quality
automatic sleep stage scoring based on a proper quantification of BPV
extracting from the single airflow signal can be achieved.
  Methods: Topological data analysis (TDA) is applied to characterize BPV from
the intrinsically nonstationary airflow signal, where the extracted features
are used to train an automatic sleep stage scoring model using the XGBoost
learner. The noise and artifacts commonly present in the airflow signal are
recycled to enhance the performance of the trained system. The state-of-the-art
approach is implemented for a comparison.
  Results: When applied to 30 whole night polysomnogram signals with standard
annotations, the leave-one-subject-out cross-validation shows that the proposed
features (overall accuracy 78.8\%$\pm$8.7\% and Cohen's kappa 0.56$\pm 0.15$)
outperforms those considered in the state-of-the-art work (overall accuracy
75.0\%$\pm$9.6\% and Cohen's kappa 0.50$\pm 0.15$) when applied to
automatically score wake, rapid eyeball movement (REM) and non-REM (NREM). The
TDA features are shown to contain complementary information to the traditional
features commonly used in the literature via examining the feature importance.
The respiratory quality index is found to be essential in the trained system.
  Conclusion: The proposed TDA-assisted automatic annotation system can
accurately distinguish wake, REM and NREM from the airflow signal.
  Significance: Since only one single airflow channel is needed and BPV is
universal, the result suggests that the TDA-assisted signal processing has
potential to be applied to other biomedical signals and homecare problems other
than the sleep stage annotation.
