Summary

Persistent homology is used to track the appearance and disappearance of features as we move through a nested sequence of topological spaces. Equating the nested sequence to a filtration and the appearance and disappearance of features to events, we show that simple event history methods can be used for the analysis of topological data. We propose a version of the well-known Nelson–Aalen cumulative hazard estimator for the comparison of topological features of random fields and for testing parametric assumptions. We suggest a Cox proportional hazards approach for the analysis of embedded metric trees. The Nelson–Aalen method is illustrated on globally distributed climate data and on neutral hydrogen distribution in the Milky Way. The Cox method is used to compare vascular patterns in fundus images of the eyes of healthy and diabetic retinopathy patients.

中文翻译：

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事件历史和拓扑数据分析

概括

当我们在嵌套的拓扑空间序列中移动时，持久同源性用于跟踪特征的出现和消失。将嵌套序列等同于过滤，将特征的出现和消失等同于事件，我们表明简单的事件历史方法可用于分析拓扑数据。我们提出了一个著名的 Nelson-Aalen 累积风险估计器版本，用于比较随机场的拓扑特征和测试参数假设。我们建议使用 Cox 比例风险方法来分析嵌入式度量树。Nelson-Aalen 方法在全球分布的气候数据和银河系中的中性氢分布中得到了说明。