 |
|
|
|
| HAL : hal-00569029, version 1 |
| arXiv : 1102.4972 |
| Fiche détaillée |  Récupérer au format |
|
|
|
|
| Witnessed k-Distance |
|
|
Leonidas J. Guibas 1Quentin Mérigot 2 |
|
|
| (30/11/2010) |
|
|
|
| Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausdorff noise, but fail in the presence of outliers. The recently introduced distance to a measure offers a solution by extending the distance function framework to reasoning about the geometry of probability measures, while maintaining theoretical guarantees about the quality of the inferred information. A combinatorial explosion hinders working with distance to a measure as an ordinary (power) distance function. In this paper, we analyze an approximation scheme that keeps the representation linear in the size of the input, while maintaining the guarantees on the inference quality close to those for the exact (but costly) representation. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Department of Computer Science |
|
|
|
Stanford University |
|
|
| 2 : | Laboratoire Jean Kuntzmann (LJK) |
|
|
|
CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
|
|
| 3 : | Lawrence Berkeley National Laboratory (LBNL) |
|
|
|
Lawrence Berkeley National Lab |
|
|
|
|
|
|
|
|
|
| Domaine | : | Informatique/Géométrie algorithmique |
|
|
| computational topology – geometric inference – outliers – power distance |
|
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| hal-00569029, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00569029 | |
| oai:hal.archives-ouvertes.fr:hal-00569029 | |
| Contributeur : Quentin Mérigot | |
| Soumis le : Jeudi 24 Février 2011, 12:33:37 | |
| Dernière modification le : Jeudi 24 Février 2011, 13:29:53 | |
