Diffusion Means and Heat Kernel on Manifolds

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Diffusion Means and Heat Kernel on Manifolds. / Hansen, Pernille; Eltzner, Benjamin; Sommer, Stefan.

Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. Springer, 2021. p. 111-118 (Lecture Notes in Computer Science, Vol. 12829).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Harvard

Hansen, P, Eltzner, B & Sommer, S 2021, Diffusion Means and Heat Kernel on Manifolds. in Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. Springer, Lecture Notes in Computer Science, vol. 12829, pp. 111-118, 5th conference on Geometric Science of Information - GSI2021, Paris, France, 21/07/2021. https://doi.org/10.1007/978-3-030-80209-7_13

APA

Hansen, P., Eltzner, B., & Sommer, S. (2021). Diffusion Means and Heat Kernel on Manifolds. In Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings (pp. 111-118). Springer. Lecture Notes in Computer Science Vol. 12829 https://doi.org/10.1007/978-3-030-80209-7_13

Vancouver

Hansen P, Eltzner B, Sommer S. Diffusion Means and Heat Kernel on Manifolds. In Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. Springer. 2021. p. 111-118. (Lecture Notes in Computer Science, Vol. 12829). https://doi.org/10.1007/978-3-030-80209-7_13

Author

Hansen, Pernille ; Eltzner, Benjamin ; Sommer, Stefan. / Diffusion Means and Heat Kernel on Manifolds. Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. Springer, 2021. pp. 111-118 (Lecture Notes in Computer Science, Vol. 12829).

Bibtex

@inproceedings{0136a383c53d49e2aeaa919bebe6d6a7,
title = "Diffusion Means and Heat Kernel on Manifolds",
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{\'e}chet mean exhibits finite sample smeariness.",
author = "Pernille Hansen and Benjamin Eltzner and Stefan Sommer",
year = "2021",
doi = "10.1007/978-3-030-80209-7_13",
language = "English",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "111--118",
booktitle = "Geometric Science of Information",
address = "Switzerland",
note = "5th conference on Geometric Science of Information - GSI2021 ; Conference date: 21-07-2021 Through 23-07-2021",

}

RIS

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 -

ID: 274868413