Medians and means in Finsler geometryReport as inadecuate

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* Corresponding author 1 LMA-Poitiers - Laboratoire de Mathématiques et Applications 2 LIX - Laboratoire d-informatique de l-École polytechnique Palaiseau

Abstract : We investigate existence and uniqueness of p-means and the median of a probability measure on a Finsler manifold, in relation with the convexity of the support of the measure. We prove that the p-mean is the limit point of a continuous time gradient flow. Under some additional condition which is always satisfied for larger than or equal to 2, a discretization of this path converges to the p-mean. This provides an algorithm for determining those Finsler center points.

Keywords : mean median barycenter convexity Finsler geometry algorithm gradient descent

Author: Marc Arnaudon - Frank Nielsen -



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