Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces

被引：0
作者：
Andrew J. Blumberg
Itamar Gal
Michael A. Mandell
Matthew Pancia
机构：
[1] University of Texas at Austin,Department of Mathematics
[2] Indiana University,Department of Mathematics
来源：
Foundations of Computational Mathematics | 2014年 / 14卷
关键词：
Persistent homology; Stability; Robustness; Barcode space; Bottleneck metric; Gromov–Prohorov metric ; Hypothesis testing; Confidence interval; Metric measure space; 55U10; 68U05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces and illustrate their use in hypothesis testing and providing confidence intervals for topological data analysis.
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页码：745 / 789
页数：44
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