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This œuvre, Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry, by Frank Nielsen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International license.

Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry


Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry
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We generalize the O(dnϵ2)-time (1 + ε)-approximation algorithm for the smallest enclosing Euclidean ball [2,10] to point sets in hyperbolic geometry of arbitrary dimension. We guarantee a O(1/ϵ2) convergence time by using a closed-form formula to compute the geodesic α-midpoint between any two points. Those results allow us to apply the hyperbolic k-center clustering for statistical location-scale families or for multivariate spherical normal distributions by using their Fisher information matrix as the underlying Riemannian hyperbolic metric.
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Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry
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