Gaussian RBF-kernels via Fock spaces: quaternionic and several complex variables settings

TL;DR

This paper explores extensions of Gaussian RBF kernels into quaternionic and multivariable complex settings, connecting them with Fock spaces and slice hyperholomorphic functions for advanced kernel methods.

Contribution

It introduces quaternionic Gaussian RBF kernels via slice hyperholomorphic functions and extends Gaussian RBF kernels to several complex variables, linking them with Fock space theory.

Findings

Quaternionic Gaussian RBF kernel constructed using slice hyperholomorphic functions

Extension of Gaussian RBF kernels to several complex variables

Connections established between kernels and Fock spaces in both settings

Abstract

In this paper we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock spaces in two different settings. First, we introduce the quaternonic Gaussian RBF kernel constructed using the theory of slice hyperholomorphic functions. Then, we consider the case of Gaussian RBF kernels in several complex variables.