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Title: Statistical analysis of longitudinal data on Riemannian manifolds Authors:  Zhenhua Lin - National University of Singapore (Singapore)
Hans-Georg Mueller - University of California Davis (United States)
Xiongtao Dai - Iowa State University (United States) [presenting]
Abstract: A manifold version of the principal analysis by conditional expectation (PACE) is proposed to represent sparsely observed longitudinal data that take values on a nonlinear Riemannian manifold. Typical examples of such manifold-valued data include longitudinal compositional data, as well as longitudinal shape trajectories located on a hypersphere. Compared to standard functional principal component analysis that is geared to Euclidean geometry, the proposed approach leads to improved trajectory recovery on nonlinear manifolds in simulations. As an illustration, we apply the proposed method on longitudinal emotional well-being data for unemployed workers. An R implementation of our method is available on GitHub.