Persistence weighted Gaussian kernel for topological data analysis

TL;DR

This paper introduces a new kernel method for persistence diagrams in topological data analysis, offering stability, explicit persistence control, and fast approximation, demonstrated on protein and glass data.

Contribution

It proposes a novel kernel for persistence diagrams that enhances stability, control, and computational efficiency in topological data analysis.

Findings

The kernel satisfies stability properties.

It provides explicit control over persistence effects.

Applied to protein and glass data with improved results.

Abstract

Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy topological properties. This paper proposes a kernel method on persistence diagrams to develop a statistical framework in TDA. The proposed kernel satisfies the stability property and provides explicit control on the effect of persistence. Furthermore, the method allows a fast approximation technique. The method is applied into practical data on proteins and oxide glasses, and the results show the advantage of our method compared to other relevant methods on persistence diagrams.