The Annals of Statistics
- Ann. Statist.
- Volume 42, Number 6 (2014), 2301-2339.
Confidence sets for persistence diagrams
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.
Ann. Statist., Volume 42, Number 6 (2014), 2301-2339.
First available in Project Euclid: 20 October 2014
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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
- 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.