Modeling Physical Activity Change as Smooth Transformations: Temporal and Amplitude Patterns Associated with Physical Function in Older Women

2026-04-23

AI Summary

Traditional summary metrics derived from accelerometry struggle to capture clinically meaningful temporal and intensity dynamics in older adults’ daily physical activity. This study proposes a novel approach that integrates a Riemannian deformation framework with multivariate functional principal component analysis (MFPCA) to model longitudinal activity trajectories as smooth transformations incorporating time warping and amplitude scaling, thereby yielding interpretable phenotypes of physical activity change. Using smoothed accelerometry curves within a linear mixed-effects modeling framework, the dominant mode of variation (PC1) was found to be significantly positively associated with physical function (p < 0.0001). Moreover, deformation energy exhibited a stronger association in later follow-ups (p = 0.003), outperforming conventional metrics and revealing dynamic activity patterns of greater clinical relevance.

Technology Category

• Planning, Routing, and Scheduling: Activity and Plan Recognition
• Computer Vision: Video Understanding & Activity Analysis
• Machine Learning: Active Learning

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Background: Minute-level accelerometer data capture rich diurnal physical activity (PA) patterns, but conventional summary metrics obscures clinically meaningful changes accumulated across a day. Building on Riemannian framework, we integrate multivariate functional principal component analysis (MFPCA) to identify main modes of PA change in older women and examine associations with physical function (PF). Method: A subset participant from OPACH as baseline and two WHISH follow-ups (W1, W2), yielded 3 accelerometer measurements; each participant's diurnal PA at each visit was represented as a smooth curve. Change between consecutive visits (defined as periods: baseline-W1, W1-W2) was modeled as a Riemannian deformation (RD) jointly capturing changes in PA timing and magnitude. Deformations were parameterized by initial momenta and summarized using MFPCA; participant-level changes were characterized by principal component (PC) scores and deformation energy (DE), a metric of overall pattern change. Associations with PF were assessed using linear mixed models. Results: Mean deformation in both periods showed overall downward shifts in PA magnitude with temporal redistribution between 10am and 7pm. Top 15 PCs explained >= 90% of variability in both periods; PC1 represented a pattern of PA increase/decrease throughout the day, explaining 22.4% (baseline-W1) and 20.8% (W1-W2). Among complete data (N=1157), an increase in PA in the mode of PC1 was positively associated with PF (p <0.0001). The interaction between DE and period was significantly associated with PF (p=0.003). Conclusions: Modeling longitudinal PA change as RDs and summarizing variability via MFPCA produced clinically interpretable phenotypes of diurnal PA change beyond standard metrics. The leading deformation mode was significantly associated with PF, and DE showed a stronger association with PF in the later period.

Problem

• physical activity change
• diurnal patterns
• physical function
• older women
• longitudinal analysis

Innovation

• Riemannian deformation
• multivariate functional principal component analysis
• physical activity patterns
• longitudinal modeling
• accelerometer data