Stochastic gradient descent on Riemannian manifolds
S Bonnabel - IEEE Transactions on Automatic Control, 2013 - ieeexplore.ieee.org
Stochastic gradient descent is a simple approach to find the local minima of a cost function
whose evaluations are corrupted by noise. In this paper, we develop a procedure extending …
whose evaluations are corrupted by noise. In this paper, we develop a procedure extending …
Riemannian medians and means with applications to radar signal processing
M Arnaudon, F Barbaresco… - IEEE Journal of Selected …, 2013 - ieeexplore.ieee.org
We develop a new geometric approach for high resolution Doppler processing based on the
Riemannian geometry of Toeplitz covariance matrices and the notion of Riemannian p …
Riemannian geometry of Toeplitz covariance matrices and the notion of Riemannian p …
Riemannian Gaussian distributions on the space of symmetric positive definite matrices
Data, which lie in the space P m, of m× m symmetric positive definite matrices,(sometimes
called tensor data), play a fundamental role in applications, including medical imaging …
called tensor data), play a fundamental role in applications, including medical imaging …
Information geometry of covariance matrix: Cartan-Siegel homogeneous bounded domains, Mostow/Berger fibration and Frechet median
F Barbaresco - Matrix information geometry, 2012 - Springer
Abstract Information Geometry has been introduced by Rao, and axiomatized by Chentsov,
to define a distance between statistical distributions that is invariant to non-singular …
to define a distance between statistical distributions that is invariant to non-singular …
On the convergence of gradient descent for finding the Riemannian center of mass
We study the problem of finding the global Riemannian center of mass of a set of data points
on a Riemannian manifold. Specifically, we investigate the convergence of constant step …
on a Riemannian manifold. Specifically, we investigate the convergence of constant step …
Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm
H Cardot, P Cénac, PA Zitt - 2013 - projecteuclid.org
With the progress of measurement apparatus and the development of automatic sensors, it
is not unusual anymore to get large samples of observations taking values in high …
is not unusual anymore to get large samples of observations taking values in high …
Total variation regularization for manifold-valued data
We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic
proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals …
proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals …
Empirical arithmetic averaging over the compact Stiefel manifold
The aim of the present research work is to investigate algorithms to compute empirical
averages of finite sets of sample-points over the Stiefel manifold by extending the notion of …
averages of finite sets of sample-points over the Stiefel manifold by extending the notion of …
Online estimation of the geometric median in Hilbert spaces: Nonasymptotic confidence balls
H Cardot, P Cénac, A Godichon-Baggioni - 2017 - projecteuclid.org
Online estimation of the geometric median in Hilbert spaces: Nonasymptotic confidence balls
Page 1 The Annals of Statistics 2017, Vol. 45, No. 2, 591–614 DOI: 10.1214/16-AOS1460 © …
Page 1 The Annals of Statistics 2017, Vol. 45, No. 2, 591–614 DOI: 10.1214/16-AOS1460 © …
Medians and means in Riemannian geometry: existence, uniqueness and computation
M Arnaudon, F Barbaresco, L Yang - Matrix Information Geometry, 2012 - Springer
This paper is a short summary of our recent work on the medians and means of probability
measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local …
measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local …