Learning spatio-temporal trajectories from manifold-valued longitudinal data

Abstract

International audienceWe propose a Bayesian mixed-effects model to learn typical scenarios of changesfrom longitudinal manifold-valued data, namely repeated measurements of thesame objects or individuals at several points in time. The model allows to estimatea group-average trajectory in the space of measurements. Random variations ofthis trajectory result from spatiotemporal transformations, which allow changes inthe direction of the trajectory and in the pace at which trajectories are followed.The use of the tools of Riemannian geometry allows to derive a generic algorithmfor any kind of data with smooth constraints, which lie therefore on a Riemannianmanifold. Stochastic approximations of the Expectation-Maximization algorithmis used to estimate the model parameters in this highly non-linear setting. Themethod is used to estimate a data-driven model of the progressive impairments ofcognitive functions during the onset of Alzheimer’s disease. Experimental resultsshow that the model correctly put into correspondence the age at which each in-dividual was diagnosed with the disease, thus validating the fact that it effectivelyestimated a normative scenario of disease progression. Random effects provideunique insights into the variations in the ordering and timing of the succession ofcognitive impairments across different individuals