The Persistent Homology of a Self-Map

Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that...

Full description

Saved in:
Bibliographic Details
Published in:Foundations of computational mathematics 2015-10, Vol.15 (5), p.1213-1244
Main Authors: Edelsbrunner, Herbert, Jabłoński, Grzegorz, Mrozek, Marian
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Computer Science
Economics
Homology theory (Mathematics)
Linear and Multilinear Algebras
Mappings (Mathematics)
Math Applications in Computer Science
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility.
ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-014-9223-y