A Methodological Framework for Analyzing and Differentiating Daily Physical Activity Across Groups Using Digital Biomarkers from the Frequency Domain

Ya-Ting Liang, Chuhsing Kate Hsiao, Amrita Chattopadhyay, Tzu-Pin Lu, Po-Hsiu Kuo and Charlotte Wang ()
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Ya-Ting Liang: Institute of Epidemiology and Preventive Medicine, College of Public Health, National Taiwan University, Taipei 100025, Taiwan
Chuhsing Kate Hsiao: Institute of Health Data Analytics and Statistics, College of Public Health, National Taiwan University, Taipei 100025, Taiwan
Amrita Chattopadhyay: Institute of Epidemiology and Preventive Medicine, College of Public Health, National Taiwan University, Taipei 100025, Taiwan
Tzu-Pin Lu: Institute of Epidemiology and Preventive Medicine, College of Public Health, National Taiwan University, Taipei 100025, Taiwan
Po-Hsiu Kuo: Institute of Epidemiology and Preventive Medicine, College of Public Health, National Taiwan University, Taipei 100025, Taiwan
Charlotte Wang: Institute of Health Data Analytics and Statistics, College of Public Health, National Taiwan University, Taipei 100025, Taiwan

Mathematics, 2025, vol. 13, issue 22, 1-22

Abstract: Human daily physical activity (PA), monitored via wearable devices, provides valuable information for real-time health assessment and disease prevention. However, analyzing time-domain PA data is challenging due to large data volumes and high inter- and intra-individual heterogeneity. Traditional PA analyses often rely on demographics, while advanced methods utilize time-domain summary statistics (e.g., L5, M10) or functional principal component analysis (FPCA). This study presents a data-efficient approach utilizing the Discrete Fourier Transform (DFT) to convert time-domain data into a compact set of frequency-domain variables. Our research suggests that adding these DFT variables can significantly enhance model performance. We demonstrate that incorporating DFT-derived variables substantially improves model performance. Specifically, (1) a small subset of DFT variables effectively captures major PA levels with effective dimensionality reduction; (2) these variables retain known associations with factors like age, sex, and weekday/weekend status; (3) they enhance the performance of classifiers. Mathematical and empirical analyses further confirm the reliability and interpretability of DFT-based features in dimension reduction. Across three mental health studies, these DFT-derived variables successfully capture key PA characteristics while retaining known associations and strengthening model performance. Overall, the proposed DFT-based framework offers a robust and scalable tool for analyzing accelerometer data, with broad applicability in health and behavioral research.

Keywords: activity level; classification; digital biomarker; dimension reduction; fast Fourier transformation; feature extraction; machine learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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