Construction of 'Support Vector' Machine Feature Spaces via Deformed Weyl-Heisenberg Algebra
This work provides a theoretical foundation for kernel methods in machine learning, but it appears incremental as it builds on existing group theories without demonstrating broad practical gains.
The paper tackled the problem of defining kernel functions for machine learning by proposing a meta-kernel function based on deformed coherent states from a deformed Weyl-Heisenberg algebra, with empirical results showing performance similar to the Radial Basis kernel.
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).