  We introduce a mixed-effects model to learn spatiotempo-ral patterns on a
network by considering longitudinal measures distributed on a fixed graph. The
data come from repeated observations of subjects at different time points which
take the form of measurement maps distributed on a graph such as an image or a
mesh. The model learns a typical group-average trajectory characterizing the
propagation of measurement changes across the graph nodes. The subject-specific
trajectories are defined via spatial and temporal transformations of the
group-average scenario, thus estimating the variability of spatiotemporal
patterns within the group. To estimate population and individual model
parameters, we adapted a stochastic version of the Expectation-Maximization
algorithm, the MCMC-SAEM. The model is used to describe the propagation of
cortical atrophy during the course of Alzheimer's Disease. Model parameters
show the variability of this average pattern of atrophy in terms of
trajectories across brain regions, age at disease onset and pace of
propagation. We show that the personalization of this model yields accurate
prediction of maps of cortical thickness in patients.
