Medians and means in riemannian geometry: existence, uniqueness and computation, Matrix Information Geometry, pp.169-197, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00640626
Riemannian medians and means with applications to radar signal processing, IEEE Journal of Selected Topics in Signal Processing, vol.7, issue.4, pp.595-604, 2013. ,
On the performance of clustering in hilbert spaces, IEEE Transactions on Information Theory, vol.54, issue.2, pp.781-790, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00290855
Geodesic pca in the wasserstein space by convex pca, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, vol.53, pp.1-26, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01978864
Stochastic gradient descent on riemannian manifolds, IEEE Transactions on Automatic Control, vol.58, issue.9, pp.2217-2229, 2013. ,
Asymptotic analysis of a class of optimal location problems, Journal de mathématiques pures et appliquées, vol.95, issue.4, pp.382-419, 2011. ,
The kantorovich metric for probability measures on the circle, Journal of Computational and Applied Mathematics, vol.57, issue.3, pp.345-361, 1995. ,
An explicit solution of information geodesic equations for the multivariate normal model, Statistics & Risk Modeling, vol.9, issue.1-2, pp.119-138, 1991. ,
Riemannian geometry. Birkhäuser, 1992. ,
Persistence-based clustering in riemannian manifolds, Journal of the ACM (JACM), vol.60, issue.6, p.41, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01094872
Comparison theorems in Riemannian geometry, vol.365, 2008. ,
Applying complexity science to air traffic management, Journal of Air Transport Management, vol.42, pp.149-158, 2015. ,
Air traffic complexity based on dynamical systems, Proceedings of the 49th CDC conference, 2010. ,
DOI : 10.1109/cdc.2010.5718004
URL : https://hal.archives-ouvertes.fr/hal-00938405
Riemannian geometry for the statistical analysis of diffusion tensor data, Signal Processing, vol.87, issue.2, pp.250-262, 2007. ,
Principal geodesic analysis for the study of nonlinear statistics of shape, IEEE transactions on medical imaging, vol.23, issue.8, pp.995-1005, 2004. ,
Les éléments aléatoires de nature quelconque dans un espace distancié, Ann. Inst. H. Poincaré, vol.10, issue.3, pp.215-310, 1948. ,
Foundations of quantization for probability distributions, 2007. ,
Asymptotic quantization for probability measures on riemannian manifolds, vol.22, pp.770-785, 2016. ,
Riemannian geometry and geometric analysis, vol.42005, 2008. ,
DOI : 10.1007/978-3-662-22385-7
URL : http://cds.cern.ch/record/1666885/files/9783540773405_TOC.pdf
Riemannian center of mass and mollifier smoothing, Communications on pure and applied mathematics, vol.30, issue.5, pp.509-541, 1977. ,
Shape manifolds, procrustean metrics, and complex projective spaces, Bulletin of the London Mathematical Society, vol.16, issue.2, pp.81-121, 1984. ,
DOI : 10.1112/blms/16.2.81
URL : http://image.diku.dk/imagecanon/material/kendall-shapes.pdf
Approximation by finitely supported measures. ESAIM: Control, Optimisation and Calculus of Variations, vol.18, pp.343-359, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00461329
Dynamic density: An air traffic management metric, 1998. ,
Computing distances and geodesics between manifold-valued curves in the srv framework, Journal of Geometric Mechanics, vol.9, issue.2, pp.131-156, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01253495
Air traffic complexity : An input-output approach, Proceedings of the US Europe ATM Seminar, pp.2-9, 2007. ,
DOI : 10.1109/acc.2007.4282989
Multivariate normal distributions parametrized as a riemannian symmetric space, Journal of Multivariate Analysis, vol.74, issue.1, pp.36-48, 2000. ,
Discrete optimal transport: complexity, geometry and applications. Discrete & Computational Geometry, vol.55, pp.263-283, 2016. ,
A new representation of air traffic data adapted to complexity assessment, Proceedings of ALLDATA2018, pp.28-33, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01799373
On estimating regression, Theory of Probability & Its Applications, vol.9, pp.141-142, 1964. ,
Quadratic optimal functional quantization of stochastic processes and numerical applications. In Monte Carlo and Quasi-Monte Carlo Methods, pp.101-142, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00158846
Introduction to vector quantization and its applications for numerics. ESAIM: proceedings and surveys, vol.48, pp.29-79, 2015. ,
Optimal quantization methods and applications to numerical problems in finance, Handbook of computational and numerical methods in finance, pp.253-297, 2004. ,
Intrinsic statistics on riemannian manifolds: Basic tools for geometric measurements, Journal of Mathematical Imaging and Vision, vol.25, issue.1, p.127, 2006. ,
URL : https://hal.archives-ouvertes.fr/inria-00614994
A riemannian framework for tensor computing, International Journal of computer vision, vol.66, issue.1, pp.41-66, 2006. ,
URL : https://hal.archives-ouvertes.fr/inria-00070743
Toward air traffic complexity assessment in new generation air traffic management systems, IEEE Transactions on Intelligent Transportation Systems, vol.12, issue.3, pp.809-818, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-01020894
Transportation distances on the circle, Journal of Mathematical Imaging and Vision, vol.41, issue.1-2, p.147, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00399832
Silhouettes: A graphical aid to the interpretation and validation of cluster analysis, Journal of Computational and Applied Mathematics, vol.20, pp.53-65, 1987. ,
Riemannian gaussian distributions on the space of symmetric positive definite matrices, IEEE Transactions on Information Theory, vol.63, issue.4, pp.2153-2170, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01710191
Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations, European conference on computer vision, pp.43-56, 2010. ,
Nonlinear mean shift over riemannian manifolds, International journal of computer vision, vol.84, issue.1, p.1, 2009. ,
Statistical computations on grassmann and stiefel manifolds for image and video-based recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.33, issue.11, pp.2273-2286, 2011. ,
Smooth regression analysis, The Indian Journal of Statistics, Series A, pp.359-372, 1964. ,
Nonparametric covariance model, Statistica Sinica, vol.20, p.469, 2010. ,
, Efficient clustering on riemannian manifolds: A kernelised random projection approach