Persistence Symmetric Kernels for Classification: A Comparative Study

Abstract

The aim of the present work is a comparative study of different persistence kernels applied to various classification problems. After some necessary preliminaries on homology and persistence diagrams, we introduce five different kernels that are then used to compare their performances of classification on various datasets. We also provide the Python codes for the reproducibility of results and, thanks to the symmetry of kernels, we can reduce the computational costs of the Gram matrices.

Keywords

• TDA
• persistent homology
• support vector machine
• classification
• kernel