Title: Modeling longitudinal compositional data as trajectories on Riemannian manifolds
Authors: Xiongtao Dai - University of California Davis (United States)
Hans-Georg Mueller - University of California Davis (United States) [presenting]
Abstract: Longitudinal compositional data exhibit dependencies over time as well as among the $p$ components of the compositional vectors, as these are constrained to be non-negative and to sum to 1. Such data are encountered in various applications, including the longitudinal modeling of behaviors for samples of individuals and in many other contexts, for example in metabolomics. This type of data can be represented as trajectories on the positive quadrant of a $(p-1)$-dimensional sphere. This motivates the study of functional data with trajectories on smooth Riemannian manifolds, with spheres as a special case. Of particular interest is the associated Riemannian functional principal component analysis. The proposed methods are supported by theory and will be illustrated with samples of trajectories consisting of compositional as well as other types of data.