PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Nonparametric Regression between General Riemannian Manifolds
Florian Steinke, Matthias Hein and Bernhard Schölkopf
SIAM Journal on Imaging Sciences Volume 3, Number 3, pp. 527-563, 2010.


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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Brain Computer Interfaces
Theory & Algorithms
ID Code:7790
Deposited By:Bernhard Schölkopf
Deposited On:17 March 2011