Construction of 'Support Vector' Machine Feature Spaces via Deformed Weyl-Heisenberg Algebra

TL;DR

This paper introduces a novel theoretical framework for kernel functions in machine learning using deformed Weyl-Heisenberg algebra, unifying several groups and providing new feature space constructions.

Contribution

It develops a meta-kernel function based on deformed coherent states, unifying multiple algebraic groups and enabling new kernel function definitions in machine learning.

Findings

Deformed SU(2) and SU(1,1) kernels perform similarly to RBF kernels.

The approach offers new theoretical insights into kernel function design.

The framework unifies several algebraic groups through a common parameter.

Abstract

This paper uses deformed coherent states, based on a deformed Weyl-Heisenberg algebra that unifies the well-known SU(2), Weyl-Heisenberg, and SU(1,1) groups, through a common parameter. We show that deformed coherent states provide the theoretical foundation of a meta-kernel function, that is a kernel which in turn defines kernel functions. Kernel functions drive developments in the field of machine learning and the meta-kernel function presented in this paper opens new theoretical avenues for the definition and exploration of kernel functions. The meta-kernel function applies associated revolution surfaces as feature spaces identified with non-linear coherent states. An empirical investigation compares the deformed SU(2) and SU(1,1) kernels derived from the meta-kernel which shows performance similar to the Radial Basis kernel, and offers new insights (based on the deformed Weyl-Heisenberg algebra).