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hal-00540625, version 2

Medians and means in Finsler geometry

Marc Arnaudon (Author to contact preferably) 1, Frank Nielsen () 2

(2010-11-28)

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.

  • 1:  Laboratoire de Mathématiques et Applications (LMA-Poitiers)
  • CNRS : UMR6086 – Université de Poitiers
  • 2:  Laboratoire d'informatique de l'école polytechnique (LIX)
  • CNRS : UMR7161 – Polytechnique - X
  • Domain : Mathematics/Differential Geometry
    Computer Science/Computational Geometry
  • Keywords : mean – median – barycenter – convexity – Finsler geometry – algorithm – gradient descent
  • Available versions :  v1 (2010-11-28) v2 (2011-06-25)
 
  • hal-00540625, version 2
  • http://hal.archives-ouvertes.fr/hal-00540625
  • oai:hal.archives-ouvertes.fr:hal-00540625
  • From: Marc Arnaudon <>
  • Submitted on: Friday, 24 June 2011 22:19:37
  • Updated on: Saturday, 25 June 2011 08:47:44