On approximating the Riemannian 1-center

Authors:
Marc Arnaudon;Frank Nielsen
Affiliations:
Laboratoire de Mathématiques et Applications, CNRS: UMR 7348, Université de Poitiers, Téléport 2, BP 30179, F-86962 Futuroscope Chasseneuil Cedex, France;Ecole Polytechnique, Computer Science Department (LIX), Palaiseau, France and Sony Computer Science Laboratories, Inc. (FRL), 3-14-13 Higashi Gotanda 3F, Shinagawa-Ku, Tokyo 141-0022, Japan
Venue:
Computational Geometry: Theory and Applications
Year:
2013

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Abstract

We generalize the Euclidean 1-center approximation algorithm of Badoiu and Clarkson (2003) [6] to arbitrary Riemannian geometries, and study the corresponding convergence rate. We then show how to instantiate this generic algorithm to two particular settings: (1) the hyperbolic geometry, and (2) the Riemannian manifold of symmetric positive definite matrices.