Diffusion Means and Heat Kernel on Manifolds

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

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 Fréchet mean exhibits finite sample smeariness.
OriginalsprogEngelsk
TitelGeometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings
ForlagSpringer
Publikationsdato2021
Sider111-118
DOI
StatusUdgivet - 2021
Begivenhed5th conference on Geometric Science of Information - GSI2021 - Paris, Frankrig
Varighed: 21 jul. 202123 jul. 2021

Konference

Konference5th conference on Geometric Science of Information - GSI2021
LandFrankrig
ByParis
Periode21/07/202123/07/2021
NavnLecture Notes in Computer Science
Vol/bind12829
ISSN0302-9743

ID: 274868413