Sleep staging is a challenging task, typically manually performed by sleep technologists based on electroencephalogram and other biosignals of patients taken during overnight sleep studies. Recent work aims to leverage automated algorithms to perform sleep staging not based on electroencephalogram signals, but rather based on the airflow signals of subjects. Prior work uses ideas from topological data analysis (TDA), specifically Hermite function expansions of persistence curves (HEPC) to featurize airflow signals. However, finite order HEPC captures only partial information. In this work, we propose Fourier approximations of persistence curves (FAPC), and use this technique to perform sleep staging based on airflow signals. We analyze performance using an XGBoost model on 1155 pediatric sleep studies taken from the Nationwide Children's Hospital Sleep DataBank (NCHSDB), and find that FAPC methods provide complimentary information to HEPC methods alone, leading to a 4.9% increase in performance over baseline methods.

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