Publications

Preprints

• A Riemannian viewpoint on the Amari-Cencov alpha-connections and Proudman-Johnson equations, with M. Bauer and C. Maor. [arXiv]

• On the Wasserstein Geodesic Principal Components Analysis of probability measures, with N. Vesseron, E. Cazelles and T. Klein. [arXiv, HAL]

• Geodesics, curvature, and conjugate points on Lie groups, with L. Lichtenfelz and S. C. Preston. [arXiv, HAL]

• Learning from landmarks, curves, surfaces, and shapes in Geomstats, with L. F. Pereira, A. Myers, E. Hartman, A. Khan, M. Tuerkoen, T. Dold, M. Gu, P. Suárez-Serrato and N. Miolane. [arXiv]

Journal publications

• The L^p Fisher-Rao metric and Amari-Cencov alpha-connections, with M. Bauer, Y. Lu and C. Maor. 

Calculus of Variations and Partial Differential Equations, 63.2 (2024): 1-33. [doi, arXiv, HAL]

• Conjugate points along Kolmogorov flows on the torus, with S. C. Preston.

Journal of Mathematical Fluid Mechanics, 26.2 (2024): 24. [doi, arXiv, HAL, code]

• Parametric information geometry with the package Geomstats, with J. Deschamps, A. Collas and N. Miolane.

Transactions on Mathematical Software, 49.4 (2023): 1 - 26. [doi, arXiv, HAL, code]

• Fisher-Rao geometry of Dirichlet distributions, with S. C. Preston and S. Puechmorel. 

Differential Geometry and its Applications, 74 (2021): 101702. [doi, arXiv, HAL]

• Intrinsic Riemannian metrics on spaces of curves: theory and computation, with M. Bauer, N. Charon and E. Klassen.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision (2021): 1-35. [doi, arXiv]

• Geomstats: a Python package for Riemannian geometry in machine learning, with N. Miolane, N. Guigui, J. Mathe, B. Hou, Y. Thanwerdas, S. Heyder, O. Peltre, N. Koep, H. Zaatiti, H. Hajri, Y. Cabanes, T. Gerald, P. Chauchat, C. Shewmake, D. Brooks, B. Kainz, C. Donnat, S. Holmes, X. Pennec.

Journal of Machine Learning Research, 21.223 (2020): 1-9. [doi, code]

• Quantization and clustering on Riemannian manifolds with an application to air traffic analysis, with S. Puechmorel.

Journal of Multivariate Analysis, 173 (2019): 685-703. [doi, HAL]

• Approximation of densities on Riemannian manifolds, with S. Puechmorel.

Entropy, 21:1 (2019): 43. [doi, HAL]

• A discrete framework to find the optimal matching between manifold-valued curves. 

Journal of Mathematical Imaging and Vision, 61.1 (2019): 40-70. [doi, arXiv, HAL]

• Computing distances and geodesics between manifold-valued curves in the SRV framework.

Journal of Geometric Mechanics, 9.2 (2017): 131-156. [doi, arXiv, HAL]

Conference proceedings

• Classifying histograms of medical data using information geometry of beta distributions, with N. Guigui, S. Rebbah and S. Puechmorel.

IFAC-PapersOnLine 54.9 (2021): 514-520. [doi, arXiv, HAL, code]

• Optimal matching between curves in a manifold, with M. Arnaudon and F. Barbaresco.

Geometric Science of Information, Springer Lecture Notes in Computer Science 10589 (2017): 57 - 64. [doi, arXiv, HAL]

• Geometric barycenters of time/Doppler spectra for the recognition of non-stationary targets, with F. Barbaresco and M. Arnaudon.

17th International Radar Symposium (2016): 1-6. [doi]

• Reparameterization invariant metric on the space of curves, with M. Arnaudon and F. Barbaresco.

Geometric Science of Information, Springer Lecture Notes in Computer Science 9389 (2015): 140-149. [doi, arXiv, HAL]

• Reparameterization invariant distance on the space of curves in the hyperbolic plane, with M. Arnaudon and F. Barbaresco.

AIP Conference Proceedings 1641 (2015): 504. [doi]

Thesis

• Probability on the spaces of curves and the associated metric spaces using information geometry; radar applications. [HAL]