15 citations · 22 across the 6 of their papers we have counts for
7 papers
From Dual Connections to Almost Contact Structures
E. Gnandi, S. Puechmorel
A dualistic structure on a smooth Riemaniann manifold is a triple with a Riemaniann metric and an affine connection, generally assumed to be torsion…
Adversarial attacks on neural networks through canonical Riemannian foliations
Eliot Tron, Nicolas Couellan, Stéphane Puechmorel
Deep learning models are known to be vulnerable to adversarial attacks. Adversarial learning is therefore becoming a crucial task. We propose a new vision on neural network robustn…
Classifying histograms of medical data using information geometry of beta distributions
Alice Le Brigant, Nicolas Guigui, Sana Rebbah +1
In this paper, we use tools of information geometry to compare, average and classify histograms. Beta distributions are fitted to the histograms and the corresponding Fisher inform…
Fisher-Rao geometry of Dirichlet distributions
Alice Le Brigant, Stephen Preston, Stéphane Puechmorel
In this paper, we study the geometry induced by the Fisher-Rao metric on the parameter space of Dirichlet distributions. We show that this space is geodesically complete and has ev…
Convergence of the Hesse-Koszul flow on compact Hessian manifolds
Stéphane Puechmorel, Tat Dat Tô
We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique…
The Fisher-Rao geometry of beta distributions applied to the study of canonical moments
Alice Le Brigant, Stéphane Puechmorel
This paper studies the Fisher-Rao geometry on the parameter space of beta distributions. We derive the geodesic equations and the sectional curvature, and prove that it is negative…
Optimal Riemannian quantization with an application to air traffic analysis
Alice Le Brigant, Stéphane Puechmorel
The goal of optimal quantization is to find the best approximation of a probability distribution by a discrete measure with finite support. When dealing with empirical distribution…