On the Schoenberg Transformations in Data Analysis: Theory and\n Illustrations

2010/04/01 by François Bavaud, Bavaud, François · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (stat.ML) #Morphological variations and asymmetry #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.1004.0089

openalex publication_date 2010/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The class of Schoenberg transformations, embedding Euclidean distances into\nhigher dimensional Euclidean spaces, is presented, and derived from theorems on\npositive definite and conditionally negative definite matrices. Original\nresults on the arc lengths, angles and curvature of the transformations are\nproposed, and visualized on artificial data sets by classical multidimensional\nscaling. A simple distance-based discriminant algorithm illustrates the theory,\nintimately connected to the Gaussian kernels of Machine Learning.\n

Citations

• Some distance properties of latent root and vector methods used in multivariate analysis

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