Title: Modeling Longitudinal Data on Riemannian Manifolds
We are interested in analyzing Riemannian manifold-valued data that are generated longitudinally. Typical examples include movement trajectories lying on the surface of the earth as well as longitudinally recorded brain connectivity network inferred from MRI scans. In the latter scenario the sparsity and irregularity of the visit time points induces additional methodological difficulties. Representations and estimation methods for longitudinal Riemannian trajectories intrinsic to the manifold are developed in our work by extending the functional principal component analysis framework that is geared toward the Euclidean geometry. Data applications and simulations demonstrate that the proposed intrinsic method is superior in terms of trajectory recovery and predictive power in comparison to an unrestricted method.