Learning spatiotemporal piecewise-geodesic trajectories from longitudinal manifold-valued data

Juliette Chevallier (1) , Stéphane Oudard (2) , Stéphanie Allassonnière (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Department of Medical Oncology
3 CRC - Centre de Recherche des Cordeliers

We introduce a hierarchical model which allows to estimate a group-average piecewise-geodesic trajectory in the Riemannian space of measurements and individual variability. This model falls into the well defined mixed-effect models. The subject-specific trajectories are defined through spatial and temporal transformations of the group-average piecewise-geodesic path, component by component. Thus we can apply our model to a wide variety of situations. Due to the non-linearity of the model, we use the Stochastic Approximation Expectation-Maximization algorithm to estimate the model parameters. Experiments on synthetic data validate this choice. The model is then applied to the metastatic renal cancer chemotherapy monitoring: we run estimations on RECIST scores of treated patients and estimate the time they escape from the treatment. Experiments highlight the role of the different parameters on the response to treatment.

Domaines: Statistiques [math.ST]; Méthodologie [stat.ME]; Applications [stat.AP]

Juliette Chevallier, Stéphane Oudard, Stéphanie Allassonnière. Learning spatiotemporal piecewise-geodesic trajectories from longitudinal manifold-valued data. 31st Conference on Neural Information Processing Systems (NIPS 2017), Dec 2017, Long Beach, United States. ⟨hal-01646230⟩