Geometry and statistics: manifolds and stratified spaces

Aasa Feragen; Mads Nielsen; Eva Bjørn Vedel Jensen; Andrew du Plessis; Francois Bernard Lauze

doi:10.1007/s10851-014-0504-5

Geometry and statistics: manifolds and stratified spaces

Aasa Feragen, Mads Nielsen, Eva Bjørn Vedel Jensen, Andrew du Plessis, Francois Bernard Lauze

Datalogisk Institut

2 Citationer (Scopus)

Abstract

Manifolds and stratified spaces are large families of nonlinear geometric spaces used for mathematical modeling of real data. Standard operations such as interpolation, averaging, principal components or hypothesis testing are no longer straightforward or even necessarily well defined when data is modeled in such spaces. Shapes are classical examples of objects whose variation exhibits nonlinear behavior. Stratified spaces lend themselves well to modeling data with variable topology, such as weighted trees or graphs.

Originalsprog	Engelsk
Tidsskrift	Journal of Mathematical Imaging and Vision
Vol/bind	50
Udgave nummer	1
Sider (fra-til)	1-4
Antal sider	4
ISSN	0924-9907
DOI	https://doi.org/10.1007/s10851-014-0504-5
Status	Udgivet - 2014

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10.1007/s10851-014-0504-5

10.1007%2Fs10851-014-0504-5.pdfForlagets udgivne version, 444 KB

https://link.springer.com/content/pdf/10.1007/s10851-014-0504-5.pdf

Citationsformater

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AU - Feragen, Aasa

AU - Nielsen, Mads

AU - Jensen, Eva Bjørn Vedel

AU - Plessis, Andrew du

AU - Lauze, Francois Bernard

PY - 2014

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AB - Manifolds and stratified spaces are large families of nonlinear geometric spaces used for mathematical modeling of real data. Standard operations such as interpolation, averaging, principal components or hypothesis testing are no longer straightforward or even necessarily well defined when data is modeled in such spaces. Shapes are classical examples of objects whose variation exhibits nonlinear behavior. Stratified spaces lend themselves well to modeling data with variable topology, such as weighted trees or graphs.

U2 - 10.1007/s10851-014-0504-5

DO - 10.1007/s10851-014-0504-5

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JO - Journal of Mathematical Imaging and Vision

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Geometry and statistics: manifolds and stratified spaces

Abstract

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