Variably Scaled Persistence Kernels (VSPKs) for persistent homology applications

TL;DR

This paper introduces Variably Scaled Persistence Kernels (VSPKs), a new class of kernels for persistent homology, which improve classification performance and efficiency in supervised learning tasks involving persistence diagrams.

Contribution

The paper proposes VSPKs, a novel kernel framework for persistent homology, demonstrating their effectiveness in enhancing classification accuracy and computational efficiency.

Findings

VSPKs outperform standard kernels in classification tasks.

VSPKs improve computational efficiency.

VSPKs enhance the accuracy of persistent homology-based methods.

Abstract

In recent years, various kernels have been proposed in the context of persistent homology to deal with persistence diagrams in supervised learning approaches. In this paper, we consider the idea of variably scaled kernels, for approximating functions and data, and we interpret it in the framework of persistent homology. We call them Variably Scaled Persistence Kernels (VSPKs). These new kernels are then tested in different classification experiments. The obtained results show that they can improve the performance and the efficiency of existing standard kernels.