Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry
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چکیده
We generalize the O( dn 2 )-time (1 + )-approximation algorithm for the smallest enclosing Euclidean ball [2, 10] to point sets in hyperbolic geometry of arbitrary dimension. We guarantee a O ( 1/ 2 ) 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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تاریخ انتشار 2015