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A comparison framework for interleaved persistence modules

A comparison framework for interleaved persistence modules We present a generalization of the induced matching theorem of as reported by Bauer and Lesnick (in: Proceedings of the thirtieth annual symposium computational geometry 2014) and use it to prove a generalization of the algebraic stability theorem for $${\mathbb {R}}$$ R -indexed pointwise finite-dimensional persistence modules. Via numerous examples, we show how the generalized algebraic stability theorem enables the computation of rigorous error bounds in the space of persistence diagrams that go beyond the typical formulation in terms of bottleneck (or log bottleneck) distance. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied and Computational Topology Springer Journals

A comparison framework for interleaved persistence modules

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Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Mathematics; Algebraic Topology; Computational Science and Engineering; Mathematical and Computational Biology
ISSN
2367-1726
eISSN
2367-1734
DOI
10.1007/s41468-019-00026-x
Publisher site
See Article on Publisher Site

Abstract

We present a generalization of the induced matching theorem of as reported by Bauer and Lesnick (in: Proceedings of the thirtieth annual symposium computational geometry 2014) and use it to prove a generalization of the algebraic stability theorem for $${\mathbb {R}}$$ R -indexed pointwise finite-dimensional persistence modules. Via numerous examples, we show how the generalized algebraic stability theorem enables the computation of rigorous error bounds in the space of persistence diagrams that go beyond the typical formulation in terms of bottleneck (or log bottleneck) distance.

Journal

Journal of Applied and Computational Topology – Springer Journals

Published: May 16, 2019

References

  • Approximating persistent homology in euclidean space through collapses
    Botnan, M; Spreemann, G
  • Categorification of persistent homology
    Bubenik, P; Scott, JA
  • Metrics for generalized persistence modules
    Bubenik, P; Silva, V; Scott, J
  • Efficient and robust persistent homology for measures
    Buchet, M; Chazal, F; Oudot, SY; Sheehy, DR
  • The Structure and Stability of Persistence Modules (SpringerBriefs in Mathematics)
    Chazal, F; Silva, V; Glisse, M; Oudot, S
  • Stability of persistence diagrams
    Cohen-Steiner, D; Edelsbrunner, H; Harer, J
  • Decomposition of pointwise finite-dimensional persistence modules
    Crawley-Boevey, W
  • Introduction to Lattices and Order
    Davey, BA; Priestley, HA
  • Computational Topology : an Introduction
    Edelsbrunner, H; Harer, JL
  • Survey article: an elementary illustrated introduction to simplicial sets
    Friedman, G
  • Analysis of Kolmogorov flow and Rayleigh–Bénard convection using persistent homology
    Kramár, M; Levanger, R; Tithof, J; Suri, B; Xu, M; Paul, M; Schatz, MF; Mischaikow, K
  • Persistence Theory: from Quiver Representations to Data Analysis, Mathematical Surveys and Monographs
    Oudot, SY
  • Linear-size approximations to the vietoris? rips filtration
    Sheehy, D
  • An Introduction to Homological Algebra
    Weibel, C
  • Computing persistent homology
    Zomorodian, A; Carlsson, G