**Date - Heure / Date - Hour**

Date(s) - 14/06/2018*11h00 - 12h00*

**Emplacement / Location**

Amphi Breguet, Building Breguet

Statistics and geometry : using Riemannian geometry tools to do statistics on non-vectorial data.

In many applications in statistics, the data that we seek to process has non linear structure (shapes, images, signals), which makes it impossible to use the usual linear operations. However, the space of data can sometimes be equipped with the structure of a differential manifold, where it is possible to compute lengths, distances and angles using a Riemannian metric. In such a space, straight lines are replaced by geodesics (the shortest paths) and vectors attached to different points can no longer be compared unless they are transported to the same point beforehand. These fundamental differences with respect to Euclidean geometry are linked to curvature, and need to be taken into account when processing the data. In this talk, I will give an overview of the work of my PhD and PostDoc, where the data of interest are either curves representing plane trajectories or covariance matrices serving as indicators of air traffic complexity.

Alice Le Brigant, DEVI team, ENAC, Toulouse, France.