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.

翻译：睡眠分期是一项具有挑战性的任务，通常由睡眠技师根据患者夜间睡眠研究中采集的脑电图及其他生物信号手动完成。近期研究致力于利用自动化算法，不基于脑电图信号，而是基于受试者的气流信号进行睡眠分期。先前的研究采用了拓扑数据分析（TDA）的思想，特别是持久性曲线的埃尔米特函数展开（HEPC）来对气流信号进行特征化。然而，有限阶的HEPC仅能捕获部分信息。在本研究中，我们提出了持久性曲线的傅里叶逼近（FAPC），并利用该技术基于气流信号进行睡眠分期。我们使用XGBoost模型对来自全国儿童医院睡眠数据库（NCHSDB）的1155项儿科睡眠研究进行了性能分析，发现FAPC方法为HEPC方法提供了补充信息，相较于基线方法，性能提升了4.9%。