Modeling sparse longitudinal data on Riemannian manifolds

Xiongtao Dai, Zhenhua Lin and Hans‐Georg Müller

Biometrics, 2021, vol. 77, issue 4, 1328-1341

Abstract: Modern data collection often entails longitudinal repeated measurements that assume values on a Riemannian manifold. Analyzing such longitudinal Riemannian data is challenging, because of both the sparsity of the observations and the nonlinear manifold constraint. Addressing this challenge, we propose an intrinsic functional principal component analysis for longitudinal Riemannian data. Information is pooled across subjects by estimating the mean curve with local Fréchet regression and smoothing the covariance structure of the linearized data on tangent spaces around the mean. Dimension reduction and imputation of the manifold‐valued trajectories are achieved by utilizing the leading principal components and applying best linear unbiased prediction. We show that the proposed mean and covariance function estimates achieve state‐of‐the‐art convergence rates. For illustration, we study the development of brain connectivity in a longitudinal cohort of Alzheimer's disease and normal participants by modeling the connectivity on the manifold of symmetric positive definite matrices with the affine‐invariant metric. In a second illustration for irregularly recorded longitudinal emotion compositional data for unemployed workers, we show that the proposed method leads to nicely interpretable eigenfunctions and principal component scores. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database.

Date: 2021
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1111/biom.13385

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:biomet:v:77:y:2021:i:4:p:1328-1341

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0006-341X

Access Statistics for this article

More articles in Biometrics from The International Biometric Society
Bibliographic data for series maintained by Wiley Content Delivery ().