Evolution equations with anisotropic distributions and diffusion PCA

Stefan Horst Sommer

doi:10.1007/978-3-319-25040-3_1

Evolution equations with anisotropic distributions and diffusion PCA

Stefan Horst Sommer

Datalogisk Institut

4 Citationer (Scopus)

Abstract

This paper presents derivations of evolution equations for the family of paths that in the Diffusion PCA framework are used for approximating data likelihood. The paths that are formally interpreted as most probable paths generalize geodesics in extremizing an energy functional on the space of differentiable curves on a manifold with connection. We discuss how the paths arise as projections of geodesics for a (non bracket-generating) sub-Riemannian metric on the frame bundle. Evolution equations in coordinates for both metric and cometric formulations of the sub-Riemannian geometry are derived. We furthermore show how rank-deficient metrics can be mixed with an underlying Riemannian metric, and we use the construction to show how the evolution equations can be implemented on finite dimensional LDDMM landmark manifolds.

Originalsprog	Engelsk
Titel	Geometric science of information : Second International Conference, GSI 2015, Palaiseau, France, October 28–30, 2015, Proceedings
Redaktører	Frank Nielsen, Frédéric Barbaresco
Antal sider	9
Forlag	Springer Science+Business Media
Publikationsdato	2015
Sider	3-11
ISBN (Trykt)	978-3-319-25039-7
ISBN (Elektronisk)	978-3-319-25040-3
DOI	https://doi.org/10.1007/978-3-319-25040-3_1
Status	Udgivet - 2015
Begivenhed	International Conference, GSI 2015 - Palaiseau, Frankrig Varighed: 28 okt. 2015 → 30 okt. 2015 Konferencens nummer: 2

Konference

Konference	International Conference, GSI 2015
Nummer	2
Land/Område	Frankrig
By	Palaiseau
Periode	28/10/2015 → 30/10/2015

Navn	Lecture notes in computer science
Vol/bind	9389
ISSN	0302-9743

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10.1007/978-3-319-25040-3_1

Citationsformater

Evolution equations with anisotropic distributions and diffusion PCA. / Sommer, Stefan Horst.
Geometric science of information: Second International Conference, GSI 2015, Palaiseau, France, October 28–30, 2015, Proceedings. red. / Frank Nielsen; Frédéric Barbaresco. Springer Science+Business Media, 2015. s. 3-11 (Lecture notes in computer science, Bind 9389).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

Sommer, SH 2015, Evolution equations with anisotropic distributions and diffusion PCA. i F Nielsen & F Barbaresco (red), Geometric science of information: Second International Conference, GSI 2015, Palaiseau, France, October 28–30, 2015, Proceedings. Springer Science+Business Media, Lecture notes in computer science, bind 9389, s. 3-11, International Conference, GSI 2015, Palaiseau, Frankrig, 28/10/2015. https://doi.org/10.1007/978-3-319-25040-3_1

Sommer SH. Evolution equations with anisotropic distributions and diffusion PCA. I Nielsen F, Barbaresco F, red., Geometric science of information: Second International Conference, GSI 2015, Palaiseau, France, October 28–30, 2015, Proceedings. Springer Science+Business Media. 2015. s. 3-11. (Lecture notes in computer science, Bind 9389). doi: 10.1007/978-3-319-25040-3_1

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Evolution equations with anisotropic distributions and diffusion PCA

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