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arXiv · 0911.3474

Riemannian Median and Its Estimation

Le Yang
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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]

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Le Yang. 2009-11-18. Riemannian Median and Its Estimation. https://doi.org/10.1112/s1461157020090531

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