%0 Journal Article
%T Riemannian Median and Its Estimation
%A Le Yang
%J Mathematics
%D 2009
%I arXiv
%R 10.1112/S1461157020090531
%X 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]
%U http://arxiv.org/abs/0911.3474v1