Discussion of 'Event History and Topological Data Analysis'

TL;DR

This paper compares event history methods and persistent homology in topological data analysis, highlighting their differences, advantages, and how to improve the use of persistence landscapes for better analysis.

Contribution

It provides a detailed comparison of local hazard estimators and global homology methods, and enhances the application of persistence landscapes in topological data analysis.

Findings

Hazard estimators are local, while homology is global.

Using persistence landscapes more fully improves their performance.

Provides background contrasting traditional TDA approaches with event history methods.

Abstract

Garside et al. use event history methods to analyze topological data. We provide additional background on persistent homology to contrast the hazard estimators used by Garside et al. with traditional approaches in topological data analysis. In particular, the former is a local method, which has advantages and disadvantages, while homology is a global. We also provide more background on persistence landscapes and show how a more complete use of this statistic improves its performance.