论文标题
事件历史和拓扑数据分析
Event History and Topological Data Analysis
论文作者
论文摘要
当我们穿过拓扑空间的嵌套序列时，持续的同源性用于跟踪特征的外观和消失。将嵌套序列等同于过滤以及事件特征的外观和消失，我们表明可以将简单的事件历史方法用于分析拓扑数据。我们提出了众所周知的纳尔逊 - 奥伦累积危害估计器的版本，以比较随机场的拓扑特征和测试参数假设。我们建议采用COX比例危害方法，用于分析嵌入式公制树。纳尔逊 - 亚烯方法在全球分布的气候数据以及银河系中的中性氢分布上进行了说明。 COX方法用于比较健康和糖尿病性视网膜病患者眼睛眼睛的眼睛图像中的血管模式。
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.
