Please note that eDoc will be permanently shut down in the first quarter of 2021!      Home News About Us Contact Contributors Disclaimer Privacy Policy Help FAQ

Home
Search
Quick Search
Advanced
Fulltext
Browse
Collections
Persons
My eDoc
Session History
Login
Name:
Password:
Documentation
Help
Support Wiki
Direct access to
document ID:


          Institute: MPI für biologische Kybernetik     Collection: Biologische Kybernetik     Display Documents



ID: 548451.0, MPI für biologische Kybernetik / Biologische Kybernetik
Nonparametric Regression between General Riemannian Manifolds
Authors:Steinke, F.; Hein, M.; Schölkopf, B.
Date of Publication (YYYY-MM-DD):2010-09
Title of Journal:SIAM Journal on Imaging Sciences
Volume:3
Issue / Number:3
Start Page:527
End Page:563
Audience:Not Specified
Intended Educational Use:No
Abstract / Description:We study nonparametric regression between Riemannian manifolds based on regularized empirical risk minimization. Regularization functionals for mappings between manifolds should respect the geometry of input and output manifold and be independent of the chosen parametrization of the manifolds. We define and analyze the three most simple regularization functionals with these properties and present a rather general scheme for solving the resulting optimization problem. As application examples we discuss interpolation on the sphere, fingerprint processing, and correspondence computations between three-dimensional surfaces. We conclude with characterizing interesting and sometimes counterintuitive implications and new open problems that are specific to learning between Riemannian manifolds and are not encountered in multivariate regression in Euclidean space.
External Publication Status:published
Document Type:Article
Communicated by:Holger Fischer
Affiliations:MPI für biologische Kybernetik/Empirical Inference (Dept. Schölkopf)
Identifiers:LOCALID:6617
The scope and number of records on eDoc is subject to the collection policies defined by each institute - see "info" button in the collection browse view.