Leveraging the Urysohn Lemma of Topology for an Enhanced Binary Classifier

Abstract: In this article we offer a comprehensive analysis of the Urysohn's classifier in a binary classification context. It utilizes Urysohn's Lemma of Topology to construct separating functions, providing rigorous and adaptable solutions. Numerical experiments demonstrated exceptional performance, with scores ranging from 95% to 100%. Notably, the Urysohn's classifier outperformed CatBoost and KNN in various scenarios. Despite sensitivity to the p-metric parameter, it proved robust and adaptable. The Urysohn's classifier's mathematical rigor and adaptability make it promising for binary classification, with applications in medical diagnosis, fraud detection and cyber security. Future research includes parameter optimization and combining the Urysohn's classifier with other techniques. It offers an elegant and principled approach to classification, ensuring integrity and valuable data insights.