Article: article from journal or magazin.
On the Schoenberg transformations in data analysis: theory and illustrations
Journal of Classification
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.
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
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