On Approximating the Riemannian 1-Center
Abstract
In this paper, we generalize the simple Euclidean 1-center approximation algorithm of Badoiu and Clarkson (2003) to Riemannian geometries and study accordingly the convergence rate. We then show how to instantiate this generic algorithm to two particular cases: (1) hyperbolic geometry, and (2) Riemannian manifold of symmetric positive definite matrices.
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