An optimization problem on the sphere

2008/05/15 by Andreas Maurer, Maurer, Andreas
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Mathematics and Applications #cs.CG #cs.LG

paper · pdf · doi:10.48550/arxiv.0805.2362

arxiv created 2008/05/15 · arxiv updated 2009/12/01

Abstract

We prove existence and uniqueness of the minimizer for the average geodesic distance to the points of a geodesically convex set on the sphere. This implies a corresponding existence and uniqueness result for an optimal algorithm for halfspace learning, when data and target functions are drawn from the uniform distribution.

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