Exploring the Essential Spectrum Extensions of Weyl's Theorem and Their Applications in Machine Learning

Abstract

This paper examines the extensions of Weyl’s theorem and their relevance in machine learning. By ensuring the stability of the essential spectrum under perturbations, Weyl’s theorem provides a theoretical foundation for robust algorithms, including spectral clustering, kernel methods, and graph-based learning. We present key theorems, illustrative examples, and computational experiments to demonstrate the practical impact of spectral stability on data-driven models.