22 citations · 46 across the 9 of their papers we have counts for
11 papers
On the Wasserstein Geodesic Principal Component Analysis of probability measures
Nina Vesseron, Elsa Cazelles, Alice Le Brigant +1
This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesi…
Conjugate points on Lie groups with left-invariant metrics
Alice Le Brigant, Leandro Lichtenfelz, Stephen C. Preston
We prove sufficient conditions for the existence of conjugate points along geodesics of a left-invariant metric on a Lie group, using a reformulation of the index form in terms of…
Learning from landmarks, curves, surfaces, and shapes in Geomstats
Luís F. Pereira, Alice Le Brigant, Adele Myers +7
We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves and surfaces across fields of natural sciences and engin…
Optimal matching between curves in a manifold
Alice Le Brigant, Marc Arnaudon, Frédéric Barbaresco
This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared…
The -Fisher-Rao metric and Amari-Cencov -connections
Martin Bauer, Alice Le Brigant, Yuxiu Lu +1
We introduce a family of Finsler metrics, called the -Fisher-Rao metrics , for , which generalizes the classical Fisher-Rao metric , both on the spa…
Conjugate points along Kolmogorov flows on the torus
Alice Le Brigant, Stephen C. Preston
The geodesics in the group of volume-preserving diffeomorphisms (volumorphisms) of a manifold , for a Riemannian metric defined by the kinetic energy, can be used to model the m…
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…
A discrete framework to find the optimal matching between manifold-valued curves
Alice Le Brigant
The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the act…
Computing distances and geodesics between manifold-valued curves in the SRV framework
Alice Le Brigant
This paper focuses on the study of open curves in a Riemannian manifold M, and proposes a reparametrization invariant metric on the space of such paths. We use the square root velo…
Reparameterization invariant metric on the space of curves
Alice Le Brigant, Marc Arnaudon, Frédéric Barbaresco
This paper focuses on the study of open curves in a manifold M, and proposes a reparameterization invariant metric on the space of such paths. We use the square root velocity funct…