CONFIDENCE SETS FOR PERSISTENCE DIAGRAMS

被引：141
作者：
Fasy, Brittany Terese [1 ]
Lecci, Fabrizio [2 ]
Rinaldo, Alessandro [2 ]
Wasserman, Larry [2 ]
Balakrishnan, Sivaraman [3 ]
Singh, Aarti [3 ]
机构：
[1] Tulane Univ, Dept Comp Sci, New Orleans, LA 70118 USA
[2] Carnegie Mellon Univ, Dept Stat, Pittsburgh, PA 15213 USA
[3] Carnegie Mellon Univ, Dept Comp Sci, Pittsburgh, PA 15213 USA
来源：
ANNALS OF STATISTICS | 2014年 / 42卷 / 06期
关键词：
Persistent homology; topology; density estimation; NONPARAMETRIC-ESTIMATION; DENSITY ESTIMATORS; TOPOLOGY; HOMOLOGY; SUPPORT;
D O I：
10.1214/14-AOS1252
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short lifetimes are informally considered to be "topological noise," and those with a long lifetime are considered to be "topological signal." In this paper, we bring some statistical ideas to persistent homology. In particular, we derive confidence sets that allow us to separate topological signal from topological noise.
引用
收藏
页码：2301 / 2339
页数：39
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