Distance Functions for Reproducing Kernel Hilbert Spaces

TL;DR

This paper explores various distance functions derived from the structure of reproducing kernel Hilbert spaces, discussing their interpretations, interrelations, and computational aspects.

Contribution

It introduces and analyzes different distance functions on X based on RKHS structure, highlighting their properties and computational considerations.

Findings

Several distance functions are characterized and compared.

Interrelations between different RKHS-based distances are established.

Computational properties and examples are provided.

Abstract

Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also present some computational properties and examples.