Pepijn Roos Hoefgeest: Christoffel polynomials for Topological Data Analysis

Abstract

 In topological data analysis, persistent homology has been widely used to study the geometry of point clouds in \(\mathbf{R}^n\). Unfortunately, standard methods are very sensitive to outliers, and their computational complexity depends badly on the number of data points. In this talk we will present a novel persistence module, based on recent applications of Christoffel-Darboux kernels in the context of statistical data analysis and geometric inference. Our approach is robust to outliers and can be computed in time linear in the number of data points. We illustrate the benefits and limitations of our new module with various numerical examples in \(\mathbf{R}^n\), \(n = 1, 2, 3\).