On the Christoffel function and classification in data analysis

TL;DR

This paper introduces the empirical Christoffel function as a simple, effective tool for supervised classification, demonstrating its good generalization properties in data analysis.

Contribution

It presents a novel application of the Christoffel function for classification tasks, highlighting its potential in supervised learning.

Findings

Effective classification with good generalization

Simple computational approach

Applicable to finite point clouds

Abstract

We show that the empirical Christoffel function associated with a cloud of finitely many points sampled from a distribution, can provide a simple tool for supervised classification in data analysis, with good generalization properties.