Corpus ID: 12315925

An optimization problem on the sphere

@article{Maurer2008AnOP,
  title={An optimization problem on the sphere},
  author={Andreas Maurer},
  journal={ArXiv},
  year={2008},
  volume={abs/0805.2362}
}
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. 
A Uniform Lower Error Bound for Half-Space Learning
TLDR
It is argued that the lower bound for the error of any unitarily invariant algorithm learning half-spaces against the uniform or related distributions on the unit sphere is well suited to evaluate the benefits of multi-task or transfer learning, or other cases where an expense in the acquisition of domain knowledge has to be justified. Expand

References

SHOWING 1-3 OF 3 REFERENCES
A concept of the mass center of a system of material points in the constant curvature spaces
This article demonstrates that in the Lobatchevsky space and on a sphere of arbitrary dimensions, the concept of the mass center of a system of mass points can be correctly defined. Presented are: aExpand
Spherical averages and applications to spherical splines and interpolation
TLDR
A method for computing weighted averages on spheres based on least squares minimization that respects spherical distance is introduced, and existence and uniqueness properties of the weighted averages are proved, and fast iterative algorithms with linear and quadratic convergence rates are given. Expand
Convex Analysisの二,三の進展について