# A Gentle Introduction to the Kernel Distance

@article{Phillips2011AGI, title={A Gentle Introduction to the Kernel Distance}, author={J. M. Phillips and Suresh Venkatasubramanian}, journal={ArXiv}, year={2011}, volume={abs/1103.1625} }

This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning, functional analysis and geometric measure theory. The key aspect of the kernel distance developed here is its interpretation as an L2 distance between probability measures or various shapes (e.g. point sets, curves, surfaces) embedded in a vector space (specifically…

## 71 Citations

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- 2011

This paper presents fast approximation algorithms for computing the kernel distance between two point sets P and Q that runs in near-linear time in the size of P ∪ Q (an explicit calculation would take quadratic time).

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This paper proposes kernels for data sets that provide a metrization of the set of points sets (the power set) that rely on the estimation of density level sets of the underlying distribution and can be extended from data sets to probability measures.

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This work provides a careful analysis of the iterative Frank-Wolfe algorithm adapted to this context, an algorithm called kernel herding, which unites a broad line of work that spans statistics, machine learning, and geometry.

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This thesis presents a distance that generalizes the Mahalanobis distance to the case where the distribution of the data is not Gaussian and is able to solve hypothesis tests and classification problems in general contexts, obtaining better results than other standard methods in statistics.

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