14h00-15h00 – Salle du conseil (L2S)
Riemannian geometry for data analysis: illustration on blind source separation and low-rank structured covariance matrices
Florent Bouchard (Chargé de recherche CNRS, L2S, CentraleSupélec)
Abstract. In this presentation, Riemannian geometry for data analysis is introduced. In particular, it is applied on two specific statistical signal processing problems: blind source separation and low-rank structured covariance matrices. Blind source separation can be solved by jointly diagonalizing some covariance matrices. We show here how geometry can be exploited in order to provide original joint diagonalization criteria and ways to compare them theoretically. These results are illustrated with numerical experiments both on simulated and real data. Concerning low-rank structured covariance matrices, an intrinsic Cramér-Rao bound of the corresponding estimation problem is presented, illustrating the interest of geometry for performance analysis. These results are validated with simulations.
Biography. I am currently a CNRS researcher (chargé de recherche) in the Signal department of L2S, Université Paris-Saclay, CNRS, CentraleSupélec. I am interested in robust learning methods with Riemannian geometry, especially in the context of structured covariance matrices. I work both on models and optimization techniques. Before my position at L2S, I was postdoc from 2018 to 2020 with Guillaume Ginolhac in LISTIC, Université Savoie Mont Blanc. I obtained my PhD degree from Université Grenoble Alpes in 2018. It took place from 2015 to 2018 at Gipsa-lab under the supervision of Marco Congedo and Jérôme Malick.