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An algorithm for computing Frechet means on the sphere

Gabriele Eichfelder(Gabriele.Eichfelder***at***tu-ilmenau.de)
Thomas Hotz(thomas.hotz***at***tu-ilmenau.de)
Johannes Wieditz(johannes.wieditz***at***uni-goettingen.de)

Abstract: For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special global problem over the sphere, namely the determination of Frechet means, which are points minimising the mean distance to a given set of points. The Branch and Bound method derived needs no further assumptions on the input data, but is able to cope with this objective function which is neither convex nor differentiable. The algorithmís performance is tested on simulated and real data.

Keywords: Branch and Bound, Frechet means, Global optimisation

Category 1: Global Optimization

Category 2: Applications -- Science and Engineering (Statistics )

Citation:

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Entry Submitted: 02/26/2018
Entry Accepted: 02/26/2018
Entry Last Modified: 02/26/2018

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