Variably Scaled Persistence Kernels (VSPKs) for persistent homology applications

Speaker: Stefano De Marchi, University of Padova

Abstract: In recent years, various kernels have been proposed in persistent homology to deal with persistence diagrams in supervised learning approaches. In this talk, we consider the idea of Variably Scaled Kernels (VSK) for approximating functions and data and interpret them in the framework of persistent homology. We call the new kernels Variably Scaled Persistence Kernels (VSPKs). These kernels have been then tested in different classification experiments showing that they can improve the performance and efficiency of existing standard kernels.

Biography: Stefano De Marchi is a full professor of numerical analysis at the University of Padova. His research spans from theoretical aspects of multivariate polynomial approximation, kernel-based approximation, and rational approximation to applications to image reconstruction by kernels, "fake nodes" and classification by SVM with persistent kernels. He discovered the "Padua points" for bivariate polynomial interpolation and cubature on the square and, more recently, he studied the "Variably Scaled Discontinuous Kernels" for approximating discontinuous functions. He is the author of more than 130 papers, managing editor of Dolomites Research Notes on Approximation, and a member of many editorial boards. He founded the Italian Network on Approximation (RITA)  and is the Italian Mathematical Union's Coordinator of the topical group on Approximation Theory and Applications.

Host: Prof. Kai Hormann