An optimization problem on the sphere
classification
💻 cs.LG
cs.CG
keywords
existencesphereuniquenessalgorithmaverageconvexcorrespondingdata
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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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