A sub-Riemannian model of the motor cortex with Wasserstein distance

This study aims to better understand the functional geometry of the motor cortex, starting from different sources of experimental evidence. Recent studies have proved that cells of the primary motor cortex (M1) are sensitive to short hand trajectories called fragments. Here, we propose a sub-Riemannian higher-dimensional geometry accounting for geometric and kinematic properties. Due to the constraints of the geometry, horizontal curves naturally satisfy a relation between geometric and kinematic properties experimentally observed. In the space of trajectories, we also apply a clustering algorithm based on the Wasserstein distance: we obtain a grouping which nicely fits the observed experimental data much more efficiently than the Sobolev distance.