The analysis of longitudinal trajectories is a longstanding problem in medical imaging which is often tackled in the context of Riemannian geometry: the set of observations is assumed to lie on an a priori known Riemannian manifold. When dealing with high-dimensional or complex data, it is in general not possible to design a Riemannian geometry of relevance. In this paper, we perform Riemannian manifold learning in association with the statistical task of longitudinal trajectory analysis. After inference, we obtain both a submanifold of observations and a Riemannian metric so that the observed progressions are geodesics. This is achieved using a deep generative network, which maps trajectories in a low-dimensional Euclidean space to the observation space.
CITATION STYLE
Louis, M., Couronné, R., Koval, I., Charlier, B., & Durrleman, S. (2019). Riemannian Geometry Learning for Disease Progression Modelling. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11492 LNCS, pp. 542–553). Springer Verlag. https://doi.org/10.1007/978-3-030-20351-1_42
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