On geodesic exponential kernels

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

Standard

On geodesic exponential kernels. / Feragen, Aasa; Lauze, François; Hauberg, Søren.

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. ed. / Aasa Feragen; Marcello Pelillo; Marco Loog. Springer, 2015. p. 211-213.

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

Harvard

Feragen, A, Lauze, F & Hauberg, S 2015, On geodesic exponential kernels. in A Feragen, M Pelillo & M Loog (eds), Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Springer, pp. 211-213, 3rd International Workshop on Similarity-Based Pattern Recognition, SIMBAD 2015, Copenhagen, Denmark, 12/10/2015. https://doi.org/10.1007/978-3-319-24261-3

APA

Feragen, A., Lauze, F., & Hauberg, S. (2015). On geodesic exponential kernels. In A. Feragen, M. Pelillo, & M. Loog (Eds.), Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (pp. 211-213). Springer. https://doi.org/10.1007/978-3-319-24261-3

Vancouver

Feragen A, Lauze F, Hauberg S. On geodesic exponential kernels. In Feragen A, Pelillo M, Loog M, editors, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Springer. 2015. p. 211-213 https://doi.org/10.1007/978-3-319-24261-3

Author

Feragen, Aasa ; Lauze, François ; Hauberg, Søren. / On geodesic exponential kernels. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. editor / Aasa Feragen ; Marcello Pelillo ; Marco Loog. Springer, 2015. pp. 211-213

Bibtex

@inbook{93d3680be43c430c8317346953177d80,
title = "On geodesic exponential kernels",
abstract = "We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically.",
author = "Aasa Feragen and Fran{\c c}ois Lauze and S{\o}ren Hauberg",
year = "2015",
doi = "10.1007/978-3-319-24261-3",
language = "English",
isbn = "9781467369640",
pages = "211--213",
editor = "Aasa Feragen and Marcello Pelillo and Marco Loog",
booktitle = "Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition",
publisher = "Springer",
address = "Switzerland",
note = "3rd International Workshop on Similarity-Based Pattern Recognition, SIMBAD 2015 ; Conference date: 12-10-2015 Through 14-10-2015",

}

RIS

TY - ABST

T1 - On geodesic exponential kernels

AU - Feragen, Aasa

AU - Lauze, François

AU - Hauberg, Søren

PY - 2015

Y1 - 2015

N2 - We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically.

AB - We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically.

U2 - 10.1007/978-3-319-24261-3

DO - 10.1007/978-3-319-24261-3

M3 - Conference abstract in proceedings

AN - SCOPUS:84959214477

SN - 9781467369640

SP - 211

EP - 213

BT - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

A2 - Feragen, Aasa

A2 - Pelillo, Marcello

A2 - Loog, Marco

PB - Springer

T2 - 3rd International Workshop on Similarity-Based Pattern Recognition, SIMBAD 2015

Y2 - 12 October 2015 through 14 October 2015

ER -

ID: 160634529