A Coherent Framework for Learning Spatiotemporal Piecewise-Geodesic Trajectories from Longitudinal Manifold-Valued Data

This paper provides a coherent framework for studying longitudinal manifold-valued data for which the dynamic changes over time. We introduce a Bayesian mixed-effects model that allows estimating both a group-representative piecewise-geodesic trajectory in the Riemannian space of shape and interindividual variability. We prove the existence of the maximum a posteriori estimate and its asymptotic consistency under reasonable assumptions. Due to the nonlinearity of the proposed model, we use a stochastic version of the expectation-maximization algorithm to estimate the model parameters. Our simulations show that our model is not noise-sensitive and succeeds in explaining various paths of progression.