On the Schoenberg transformations in data analysis: theory and illustrations

Détails de la publication Détails dans Serval
ID Serval serval:BIB_A642660C70E1
Type de publication
Article: article d'un périodique ou d'un magazine.
Collection Publications
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
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Dernière modification 2012-11-26