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.

翻译：Garside等人使用事件历史方法分析地形数据,我们提供了关于持久性同系物的更多背景,以对比Garside等人使用的危险估计数据,并采用传统的地形数据分析方法,特别是前者是一种局部方法,具有优缺点,而同系物则是全球性的。我们还提供了更多关于持久性地貌的背景,并展示了更全面地使用这一统计数据如何改善它的性能。