Diffusion Means and Heat Kernel on Manifolds
Methodology
2021-03-02 v1 Statistics Theory
Statistics Theory
Abstract
We introduce diffusion means as location statistics on manifold data spaces. A diffusion mean is defined as the starting point of an isotropic diffusion with a given diffusivity. They can therefore be defined on all spaces on which a Brownian motion can be defined and numerical calculation of sample diffusion means is possible on a variety of spaces using the heat kernel expansion. We present several classes of spaces, for which the heat kernel is known and sample diffusion means can therefore be calculated. As an example, we investigate a classic data set from directional statistics, for which the sample Fr\'echet mean exhibits finite sample smeariness.
Cite
@article{arxiv.2103.00588,
title = {Diffusion Means and Heat Kernel on Manifolds},
author = {Pernille Hansen and Benjamin Eltzner and Stefan Sommer},
journal= {arXiv preprint arXiv:2103.00588},
year = {2021}
}
Comments
8 pages, 1 figure, conference paper submitted to GSI 2021