Name
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1137/080744189 | SIAM J. Imaging Sciences |
Keywords | Field | DocType |
general riemannian manifolds,simple regularization functionals,riemannian manifold,correspondence computation,counterintuitive implication,regularization functionals,multivariate regression,chosen parametrization,nonparametric regression,application example,euclidean space,brain computer interfaces | Mathematical optimization,Harmonic map,Mathematical analysis,Nonparametric regression,Empirical risk minimization,Euclidean space,Riemannian geometry,Statistical manifold,Manifold,Mathematics,Curvature of Riemannian manifolds | Journal |
Volume | Issue | ISSN |
3 | 3 | 1936-4954 |
Citations | PageRank | References |
7 | 0.50 | 15 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Florian Steinke | 1 | 269 | 19.19 |
| Matthias Hein | 2 | 663 | 62.80 |
| Bernhard Schölkopf | 3 | 23120 | 3091.82 |