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      On the Schoenberg Transformations in Data Analysis: Theory and Illustrations

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          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 simple distance-based discriminant algorithm illustrates the theory, intimately connected to the Gaussian kernels of Machine Learning.

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          Journal
          2010-04-01
          2010-04-01
          Article
          1004.0089

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          stat.ML

          Machine learning

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