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On Fréchet means in simplex shape spaces

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Alfred Kume  and
Huiling Le
Alfred Kume*
Affiliation:
University of Nottingham
Huiling Le*
Affiliation:
University of Nottingham
*
∗ Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
∗ Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
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Abstract

By making use of the geometric properties of simplex shape spaces, this paper investigates the problems relating to the estimation of the Fréchet means of the random shapes of simplices in Euclidean spaces and also, for the random shapes induced by certain normally distributed simplices, the problems relating to the location of these Fréchet means. In particular, we obtain an algorithm for computing sample mean shapes in simplex shape spaces which converges reasonably fast.

Keywords

Fréchet mean shapessimplex shape spaces

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 885 - 897
Copyright
Copyright © Applied Probability Trust 2003 

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