TY - GEN
T1 - Diffusion Means and Heat Kernel on Manifolds
AU - Hansen, Pernille
AU - Eltzner, Benjamin
AU - Sommer, Stefan
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
U2 - 10.1007/978-3-030-80209-7_13
DO - 10.1007/978-3-030-80209-7_13
M3 - Article in proceedings
T3 - Lecture Notes in Computer Science
SP - 111
EP - 118
BT - Geometric Science of Information
PB - Springer
T2 - 5th conference on Geometric Science of Information - GSI2021
Y2 - 21 July 2021 through 23 July 2021
ER -