| ID Serval |
serval:BIB_A642660C70E1 |
| Type de publication |
Article: article d'un périodique ou d'un magazine. |
| Collection |
Publications |
| Fonds |
UNIL/CHUV |
| Auteur(s) |
Bavaud F. |
| Titre |
On the Schoenberg transformations in data analysis: theory and illustrations |
| Périodique |
Journal of Classification |
| Statut éditorial |
Publié |
| Année |
2011 |
| Peer-reviewed |
oui |
| Volume |
28 |
| Numéro |
3 |
| Pages |
297-314 |
| Langue |
anglais |
| Résumé |
The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented,
and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths,
angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional
scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely
connected to the Gaussian kernels of Machine Learning.
|
| ISBN/ISSN |
1432-1343 |
| Mots-clé |
Bernstein functions - Conditionally negative definite matrices - Discriminant analysis - Euclidean distances - Huygens principle
- Isometric embedding - helix - Kernels - Menger curvature - Multidimensional scaling - Rectifiable curves - Robust centroids
- Robust PCA
|
| URN |
urn:nbn:ch:serval-BIB_A642660C70E16 |
| OAI |
oai:serval.unil.ch:BIB_A642660C70E1 |
| DOI |
10.1007/s00357-011-9092-x |
| Texte intégral PDF |
Voir - Télécharger |
| Dernière modification |
2012-11-26 |
