Riemannian Geometry Learning for Disease Progression Modelling
Résumé
The analysis of longitudinal trajectories is a longstandingproblem in medical imaging which is often tackled in the context ofRiemannian geometry: the set of observations is assumed to lie on an apriori known Riemannian manifold. When dealing with high-dimensionalor complex data, it is in general not possible to design a Riemanniangeometry of relevance. In this paper, we perform Riemannian manifoldlearning in association with the statistical task of longitudinal trajectoryanalysis. After inference, we obtain both a submanifold of observationsand a Riemannian metric so that the observed progressions are geodesics.This is achieved using a deep generative network, which maps trajectoriesin a low-dimensional Euclidean space to the observation space.