# Estimation and classification of location and covariance matrix using Riemannian geometry: application to remote sensing

#### Séminaire Données et Aléatoire Théorie & Applications

23/02/2023 - 14:00
Antoine Collas *(INRIA)*
Salle 106

Remote sensing systems offer an increased opportunity to record multi-temporal and multi-dimensional images of the earth’s surface. This opportunity significantly increases the interest in data processing tools based on multivariate image time series. In this presentation, we propose a clustering-classification pipeline to segment these data. To do so, robust statistics are estimated, clustered, or classified to obtain a segmentation of the original multivariate image time series. A significant part of the presentation is devoted to the theory of Riemannian geometry and its subfield, the information geometry, which studies Riemannian manifolds whose points are probability distributions. It allows for estimating robust statistics very quickly, even on large-scale problems, and for computing Riemannian centers of mass. Indeed, divergences are developed to measure the proximities between the estimated statistics. Then, groups of statistics are averaged by computing their Riemannian mass centers associated with these divergences. Thus, we adapt classical machine learning algorithms such as the K-means++ or the Nearest centroid classifier to Riemannian manifolds. These algorithms have been implemented for many different combinations of statistics, divergences, and Riemannian centers of mass and tested on real datasets such as the Indian pines image and the large crop type mapping dataset Breizhcrops.