Diffusion Means and Heat Kernel on Manifolds
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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.
Originalsprog | Engelsk |
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Titel | Geometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings |
Forlag | Springer |
Publikationsdato | 2021 |
Sider | 111-118 |
DOI | |
Status | Udgivet - 2021 |
Begivenhed | 5th conference on Geometric Science of Information - GSI2021 - Paris, Frankrig Varighed: 21 jul. 2021 → 23 jul. 2021 |
Konference
Konference | 5th conference on Geometric Science of Information - GSI2021 |
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Land | Frankrig |
By | Paris |
Periode | 21/07/2021 → 23/07/2021 |
Navn | Lecture Notes in Computer Science |
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Vol/bind | 12829 |
ISSN | 0302-9743 |
Links
- https://arxiv.org/pdf/2103.00588.pdf
Indsendt manuskript
ID: 274868413