Beyond the Gegenbauer Paradigm: q-Orthogonal Kernels for Machine Learning
The performance of Support Vector Machines (SVMs) critically depends on the kernel function choice, which enables implicit mapping of data into high-dimensional feature spaces. While classical kernels like Radial Basis Function (RBF) remain popular, orthogonal polynomial kernels offer mathematically interpretable alternatives that can incorporate structured prior knowledge. This work extends the orthogonal polynomial kernel paradigm by introducing a novel family based on discrete $q$-Hermite I polynomials, a class of $q$-orthogonal polynomials that generalize classical Hermite polynomials through a deformation parameter $q$. We formally define the q-Hermite kernel and establish its validi...
| Authors | Álvaro Sánchez-Paniagua Ríos, Juan P. Llerena, Alberto Lastra et al. |
|---|---|
| Primary category | cs.LG |
| Published | 4 August 2026 |
| Last updated at source | 4 August 2026 |
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