On the Schoenberg Transformations in Data Analysis: Theory and Illustrations
By François Bavaud. 2010
26 citations recorded by the source corpus.
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.
Subfields: Computer Vision and Pattern Recognition, Geometry and Topology, Statistics and Probability, Signal Processing
How researchers see this paper
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In Computer Vision and Pattern Recognition
- Bharath K. Sriperumbudur
- Kenji Fukumizu
- Krikamol Muandet
- Bernhard Schölkopf
- Luc Van Gool
- David Lopez-Paz
- Arthur Gretton
- Dacheng Tao
In Geometry and Topology
In Statistics and Probability
- Krikamol Muandet
- Kenji Fukumizu
- Bharath K. Sriperumbudur
- Bernhard Schölkopf
- Arthur Gretton
- Dino Sejdinovic
- Le Song
- Jan Peters
In Signal Processing
- Kenji Fukumizu
- Bharath K. Sriperumbudur
- Krikamol Muandet
- Bernhard Schölkopf
- Arthur Gretton
- Dominik Janzing
- David Lopez-Paz
- Jan Peters
Citations in the corpus
- Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “, Bavaud (2011), Wendland (2005; Ch. 7), and Rasmussen and Williams (2005) for a detailed exposition on radial kernels and Schoenberg’s theorem.”