Medians and means in Finsler geometry
M Arnaudon, F Nielsen - LMS Journal of Computation and …, 2012 - cambridge.org
LMS Journal of Computation and Mathematics, 2012•cambridge.org
We investigate existence and uniqueness of p-means ep and the median e1 of a probability
measure μ on a Finsler manifold, in relation with the convexity of the support of μ. We prove
that ep is the limit point of a continuous time gradient flow. Under some additional condition
which is always satisfied for p≥ 2, a discretization of this path converges to ep. This
provides an algorithm for determining the Finsler center points.
measure μ on a Finsler manifold, in relation with the convexity of the support of μ. We prove
that ep is the limit point of a continuous time gradient flow. Under some additional condition
which is always satisfied for p≥ 2, a discretization of this path converges to ep. This
provides an algorithm for determining the Finsler center points.
We investigate existence and uniqueness of p-means ep and the median e1 of a probability measure μ on a Finsler manifold, in relation with the convexity of the support of μ. We prove that ep is the limit point of a continuous time gradient flow. Under some additional condition which is always satisfied for p≥2, a discretization of this path converges to ep. This provides an algorithm for determining the Finsler center points.