Clustering of longitudinal shape data sets into mixtures of independent or branching trajectories
This presentation aims at introducing how we model the evolution of a population given repeated observations of several subjects over time, i.e. a longitudinal data set. Our method learns an average trajectory (or representative curve) from images, shapes or other inputs and its variance in space and time. Representative trajectories are built as the combination of pieces of curves. This enables to account for changes in dynamic for example relapse events in oncology. We also handle heterogeneous populations. For this we use mixture model which are flexible enough to handle independent trajectories for each cluster as well as fork and merge scenarios. The estimation of such non linear mixture models in high dimension is known to be difficult because of the trapping states effect that hampers the optimisation of cluster assignments during training. We address this issue by using a tempered version of the stochastic EM algorithm. We apply our algorithm on different data sets: 1D RECIST score used to monitor tumors growth and meshes of the hippocampus. In particular, we show how the method can be used to test different scenarios of hippocampus atrophy in aging by using an heterogeneous population of normal aging individuals and mild cognitive impaired subjects.
Professor of Applied Mathematics, PR[AI]RIE fellow and deputy director
Université de Paris, Ecole Polytechnique