Persistence kernels for classification: A comparative study

TL;DR

This paper compares five different persistence kernels in the context of classification problems, evaluating their performance across various datasets and providing Python code for reproducibility.

Contribution

It introduces and compares five persistence kernels for classification, offering insights into their relative effectiveness and reproducibility through code.

Findings

Different persistence kernels show varying classification performance

The study provides a reproducible framework with Python code

Comparison across multiple datasets highlights kernel strengths and weaknesses

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.