Annals of Statistics
- Ann. Statist.
- Volume 42, Number 6 (2014), 2301-2339.
Confidence sets for persistence diagrams
Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, and Aarti Singh
Full-text: Open access
Abstract
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.
Article information
Source
Ann. Statist., Volume 42, Number 6 (2014), 2301-2339.
Dates
First available in Project Euclid: 20 October 2014
Permanent link to this document
https://projecteuclid.org/euclid.aos/1413810729
Digital Object Identifier
doi:10.1214/14-AOS1252
Mathematical Reviews number (MathSciNet)
MR3269981
Zentralblatt MATH identifier
1310.62059
Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62H12: Estimation
Keywords
Persistent homology topology density estimation
Citation
Fasy, Brittany Terese; Lecci, Fabrizio; Rinaldo, Alessandro; Wasserman, Larry; Balakrishnan, Sivaraman; Singh, Aarti. Confidence sets for persistence diagrams. Ann. Statist. 42 (2014), no. 6, 2301--2339. doi:10.1214/14-AOS1252. https://projecteuclid.org/euclid.aos/1413810729
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Supplemental materials
- Supplementary material: Supplement to “Confidence sets for persistence diagrams”. In the supplementary material we give a brief introduction to persistence homology and provide additional details about homology, simplicial complexes and stability of persistence diagrams.Digital Object Identifier: doi:10.1214/14-AOS1252SUPP

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