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  Nonparametric Regression between General Riemannian Manifolds

Steinke, F., Hein, M., & Schölkopf, B. (2010). Nonparametric Regression between General Riemannian Manifolds. SIAM Journal on Imaging Sciences, 3(3), 527-563. doi:10.1137/080744189.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-BE54-5 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-6ABC-4
Genre: Journal Article

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https://epubs.siam.org/doi/10.1137/080744189 (Publisher version)
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 Creators:
Steinke, F1, 2, Author              
Hein, M1, 2, Author              
Schölkopf, B1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: 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.

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 Dates: 2010-09
 Publication Status: Published in print
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 Identifiers: DOI: 10.1137/080744189
BibTex Citekey: 6617
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Title: SIAM Journal on Imaging Sciences
Source Genre: Journal
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Pages: - Volume / Issue: 3 (3) Sequence Number: - Start / End Page: 527 - 563 Identifier: ISSN: 1936-4954