On the Schoenberg transformations in data analysis: theory and illustrations

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State: Public
Version: Final published version
Serval ID
serval:BIB_A642660C70E1
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
On the Schoenberg transformations in data analysis: theory and illustrations
Journal
Journal of Classification
Author(s)
Bavaud F.
ISSN
1432-1343
Publication state
Published
Issued date
2011
Peer-reviewed
Oui
Volume
28
Number
3
Pages
297-314
Language
english
Abstract
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.
Keywords
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
Create date
08/10/2010 18:59
Last modification date
20/08/2019 16:11
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