论文标题
使用矢量持久图的形状测试假设测试
Hypothesis Testing for Shapes using Vectorized Persistence Diagrams
论文作者
论文摘要
拓扑数据分析涉及数据形状的统计表征。持续性同源性是拓扑数据分析的主要工具，可用于分析拓扑特征并执行统计推断。在本文中，我们为矢量持续图提出了两阶段的假设检验。第一阶段过滤矢量持续图中的向量元素以增强测试的功能。第二阶段由多个假设检验组成，误报由错误的发现率控制。我们通过将其应用于各种模拟和现实世界数据类型来证明我们的方法的灵活性。我们的结果表明，与现有的持续同源性假设测试方法相比，提出的假设检验可以对数据形状进行准确和信息的推论。
Topological data analysis involves the statistical characterization of the shape of data. Persistent homology is a primary tool of topological data analysis, which can be used to analyze topological features and perform statistical inference. In this paper, we present a two-stage hypothesis test for vectorized persistence diagrams. The first stage filters vector elements in the vectorized persistence diagrams to enhance the power of the test. The second stage consists of multiple hypothesis tests, with false positives controlled by false discovery rates. We demonstrate the flexibility of our method by applying it to a variety of simulated and real-world data types. Our results show that the proposed hypothesis test enables accurate and informative inferences on the shape of data compared to the existing hypothesis testing methods for persistent homology.
