A coherent framework for learning spatiotemporal piecewise- geodesic trajectories from longitudinal manifold-valued data

Juliette Chevallier (1) , Stéphane Oudard (2) , Stéphanie Allassonnière (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Department of Medical Oncology
3 CRC - Centre de Recherche des Cordeliers

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

Mots clés: EM like algorithm; Longitudinal data; Bayesian estimation; Nonlinear mixed-effects model; MCMC methods; Spatio-temporal analysis

Domaines: Mathématiques [math]; Statistiques [math.ST]; Modélisation et simulation; Méthodologie [stat.ME]

Juliette Chevallier, Stéphane Oudard, Stéphanie Allassonnière. A coherent framework for learning spatiotemporal piecewise- geodesic trajectories from longitudinal manifold-valued data. 2017. ⟨hal-01646298v1⟩