Diffusion Means and Heat Kernel on Manifolds
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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.
Original language | English |
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Title of host publication | Geometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings |
Publisher | Springer |
Publication date | 2021 |
Pages | 111-118 |
DOIs | |
Publication status | Published - 2021 |
Event | 5th conference on Geometric Science of Information - GSI2021 - Paris, France Duration: 21 Jul 2021 → 23 Jul 2021 |
Conference
Conference | 5th conference on Geometric Science of Information - GSI2021 |
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Land | France |
By | Paris |
Periode | 21/07/2021 → 23/07/2021 |
Series | Lecture Notes in Computer Science |
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Volume | 12829 |
ISSN | 0302-9743 |
Links
- https://arxiv.org/pdf/2103.00588.pdf
Submitted manuscript
ID: 274868413