Universal kernels via harmonic analysis on Riemannian symmetric spaces

• URL: http://arxiv.org/abs/2506.19245v1
• Date: Tue, 24 Jun 2025 02:03:25 GMT
• Title: Universal kernels via harmonic analysis on Riemannian symmetric spaces
• Authors: Franziskus Steinert, Salem Said, Cyrus Mostajeran,
• Abstract summary: kernels are of fundamental importance in the theoretical underpinning of kernel methods in machine learning.<n>We establish tools for investigating universality properties of kernels in symmetric spaces.<n>We provide theoretical justification for their use in applications involving manifold-valued data.
• Score: 3.7141182051230914
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in machine learning. In this work, we establish fundamental tools for investigating universality properties of kernels in Riemannian symmetric spaces, thereby extending the study of this important topic to kernels in non-Euclidean domains. Moreover, we use the developed tools to prove the universality of several recent examples from the literature on positive definite kernels defined on Riemannian symmetric spaces, thus providing theoretical justification for their use in applications involving manifold-valued data.

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