Riemannian Median and Its Estimation
Differential Geometry
2019-02-20 v1 Optimization and Control
Probability
Abstract
In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also propose a subgradient algorithm and prove its convergence as well as estimating the error of approximation and the rate of convergence. The convergence property of this subgradient algorithm, which is a generalization of the classical Weiszfeld algorithm in Euclidean spaces to the context of Riemannian manifolds, also answers a recent question in P. T. Fletcher et al. [13]
Cite
@article{arxiv.0911.3474,
title = {Riemannian Median and Its Estimation},
author = {Le Yang},
journal= {arXiv preprint arXiv:0911.3474},
year = {2019}
}