# On the Schoenberg Transformations in Data Analysis: Theory and Illustrations

@article{Bavaud2011OnTS, title={On the Schoenberg Transformations in Data Analysis: Theory and Illustrations}, author={François Bavaud}, journal={Journal of Classification}, year={2011}, volume={28}, pages={297-314} }

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… Expand

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