Functional-SVD for Heterogeneous Trajectories: Case Studies in Health

• 成果类型: Article; Early Access
• 署名作者: Tan, Jianbin; Shi, Pixu; Zhang, Anru R.
• 署名单位: Duke University; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2625441
• 发表日期: 2026-05-26
• 关键词: alternating minimization; factor model; Functional principal component analysis; Functional singular value decomposition; Heterogeneous functional data; principal-components; linear-regression; convergence-rates; number; DECOMPOSITION; models

摘要

Trajectory data, including time series and longitudinal measurements, are increasingly common in health-related domains such as biomedical research and epidemiology. Real-world trajectory data frequently exhibit heterogeneity across subjects such as patients, sites, and subpopulations, yet many traditional methods are not designed to accommodate such heterogeneity in data analysis. To address this, we propose a unified framework, termed Functional Singular Value Decomposition (FSVD), for statistical learning with heterogeneous trajectories. We establish the theoretical foundations of FSVD and develop a corresponding estimation algorithm that accommodates noisy and irregular observations. We further adapt FSVD to a wide range of trajectory-learning tasks, including dimension reduction, factor modeling, regression, clustering, and data completion, while preserving its ability to account for heterogeneity, leverage inherent smoothness, and handle irregular sampling. Through extensive simulations, we demonstrate that FSVD-based methods consistently outperform existing approaches across these tasks. Finally, we apply FSVD to a COVID-19 case-count dataset and electronic health record datasets, showcasing its effective performance in global and subgroup pattern discovery and factor analysis. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.