Fast Generalized Longitudinal Functional Principal Components Analysis with Applications to Population-Level Neuronal Dynamics
- 1University of Minnesota
Abstract
Functional data are widely collected across many fields. One approach for modeling functional data collected across repeated measures is longitudinal functional PCA (LFPCA), which allows for the decomposition of variability at multiple levels. However, existing estimation approaches for LFPCA can be computationally demanding for large or high-dimensional datasets. Here, we propose fast generalized LFPCA, a novel estimation technique that bins data along the functional domain and fits a marginal mixed model at each bin. Simulation results show that the proposed method is orders of magnitude faster than existing techniques while achieving similar accuracy, making LFPCA scalable to datasets with more densely sampled observations and larger sample sizes. We apply the proposed technique to model neuronal firing rate data both on and off deep brain stimulation (DBS) to investigate how the intervention modulates population-level neuronal activity. Our results suggest that the vast majority of between-neuron variation can be explained by four principal components, which relate to individual differences in neuronal firing as well as the arm manipulation paradigm under study. We also find that DBS significantly increases the variability of firing activity, likely driven by increased firing from a subset of neurons in response to DBS, a novel insight not obtained in previous analyses. Code to implement the proposed method and run simulation studies is included in the supplement.
Related
- Beyond phosphate uptake: PT4/PT11 as key functional components linking phosphate acquisition, nutrient exchange, and arbuscule maintenance in arbuscular mycorrhizal symbiosis
- Functional and biochemical characterization of Alyftrek® components reveals high-potency rescue of F508del-CFTR
- Association between diabetes mellitus and hearing impairment in the adult Canadian population: data from the Canadian longitudinal study on aging
- Selenium Biofortification Enhances Functional Bioactive Components and Nutritional Quality of Edible Mung Bean Sprouts During Germination.
- Longitudinal Subject Pairing in Cross-Sectional Neonatal Data Reveals Asynchronous Structural and Functional Brain Maturation
BibTeX
@misc{duffy2026fast,
title = {{Fast Generalized Longitudinal Functional Principal Components Analysis with Applications to Population-Level Neuronal Dynamics}},
author = {K. A. Duffy and N. Pai and D. Schneck and G. Kozienko and L. Zheng and A. Xenopoulos-Oddsson and J. Wang and L. A. Johnson and J. Vitek and M. Fiecas and E. Cui},
howpublished = {bioRxiv},
year = {2026},
month = oct,
doi = {10.64898/2026.10.12.758639},
url = {https://www.biorxiv.org/content/10.64898/2026.10.12.758639v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Fast Generalized Longitudinal Functional Principal Components Analysis with Applications to Population-Level Neuronal Dynamics
AU - K. A. Duffy
AU - N. Pai
AU - D. Schneck
AU - G. Kozienko
AU - L. Zheng
AU - A. Xenopoulos-Oddsson
AU - J. Wang
AU - L. A. Johnson
AU - J. Vitek
AU - M. Fiecas
AU - E. Cui
PY - 2026
DA - 2026/10/12
PB - bioRxiv
DO - 10.64898/2026.10.12.758639
UR - https://www.biorxiv.org/content/10.64898/2026.10.12.758639v1
AB - Functional data are widely collected across many fields. One approach for modeling functional data collected across repeated measures is longitudinal functional PCA (LFPCA), which allows for the decomposition of variability at multiple levels. However, existing estimation approaches for LFPCA can be computationally demanding for large or high-dimensional datasets. Here, we propose fast generalized LFPCA, a novel estimation technique that bins data along the functional domain and fits a marginal mixed model at each bin. Simulation results show that the proposed method is orders of magnitude faster than existing techniques while achieving similar accuracy, making LFPCA scalable to datasets with more densely sampled observations and larger sample sizes. We apply the proposed technique to model neuronal firing rate data both on and off deep brain stimulation (DBS) to investigate how the intervention modulates population-level neuronal activity. Our results suggest that the vast majority of between-neuron variation can be explained by four principal components, which relate to individual differences in neuronal firing as well as the arm manipulation paradigm under study. We also find that DBS significantly increases the variability of firing activity, likely driven by increased firing from a subset of neurons in response to DBS, a novel insight not obtained in previous analyses. Code to implement the proposed method and run simulation studies is included in the supplement.
ER -