Medians and means in Finsler geometry

DOI10.1112/S1461157010000513zbMath1293.53025arXiv1011.6076MaRDI QIDQ5169623

Marc Arnaudon, Frank Nielsen

Publication date: 11 July 2014

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.6076

zbMATH Keywords

probability measureFinsler center pointstime gradient flow

Mathematics Subject Classification ID

Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

Related Items (2)

A stochastic algorithm finding generalized means on compact manifolds ⋮ Clustering in Hilbert’s Projective Geometry: The Case Studies of the Probability Simplex and the Elliptope of Correlation Matrices

Cites Work

• Comparison theorems in Finsler geometry and their applications
• Uniform convexity and smoothness, and their applications in Finsler geometry
• Simplification and hierarchical representations of mixtures of exponential families
• Riemann-Finsler geometry with applications to information geometry
• Informative barycentres in statistics
• Barycenters of measures transported by stochastic flows
• Riemannian median and its estimation
• Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
• Riemannian center of mass and mollifier smoothing
• On the Convergence of a Class of Iterative Methods for Solving the Weber Location Problem
• Convexity and the Hemisphere
• The multivariate L ₁ -median and associated data depth
• Riemannian barycentres and geodesic convexity
• Estimation of Riemannian Barycentres
• Sided and Symmetrized Bregman Centroids
• A note on Fermat's problem

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