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 both a group-representative piecewise-geodesic trajectory in the Riemannian space of shape and inter-individual variability. Following the approach of Schiratti et al. (NIPS, 2015), we estimate a representative piecewise-geodesic trajectory of the global progression and together with spacial and temporal inter-individual variabilities. We first introduce our model in its most generic formulation and then make it explicit for RECIST (Therasse et al., JNCI, 2000) score monitoring, i.e. for one-dimension manifolds and piecewise-logistically distributed data.

Domaines: Statistiques [math.ST]; Méthodologie [stat.ME]; Modélisation et simulation

Juliette Chevallier, Stéphane Oudard, Stéphanie Allassonnière. Learning spatiotemporal piecewise-geodesic trajectories from longitudinal manifold-valued data. Neural Information Processing Systems 2017, Dec 2017, Long Beach, CA, United States. . ⟨hal-01646617v2⟩