事件历史和拓扑数据分析
Event History and Topological Data Analysis
摘要：
持久同调是用来跟踪的出现和消失的功能，因为我们通过一个嵌套序列的拓扑空间。将嵌套序列等同于过滤和事件特征的出现和消失，我们证明了简单的事件历史方法可以用于拓扑数据的分析。我们提出了一个版本的著名的Nelson-Aalen累积风险估计比较的拓扑特征的随机场和检验参数假设。我们提出了一个Cox比例风险的嵌入式度量树的分析方法。纳尔逊-阿伦方法说明全球分布的气候数据和中性氢分布在银河系。Cox方法用于比较健康和糖尿病视网膜病变患者眼睛的眼底图像中的血管模式。
英文摘要：
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 use to compare vascular patterns in fundus images of the eyes of healthy and diabetic retinopathy patients.
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