On the stability of interval decomposable persistence modules
type: Item
instance of: scholarly article
title: On the stability of interval decomposable persistence modules
zbMATH Open document ID: 1471.55006
author: Håvard Bakke Bjerkevik
published in: Discrete \& Computational Geometry
publication date: 2021-07-02T00:00:00Z
review text: The authors focus on the classical algebraic stability theorem for persistence modules which is a central result in the theory of stability for persistent homology. In particular they prove that \[d_B(\mathcal{B}(M), \mathcal{B}(N)) \leq (2n - 1)d_I (M, N ), \] for rectangle decomposable \(\mathbb{R}^n\)-modules. That \[d_B(\mathcal{B}(M), \mathcal{B}(N)) \leq (n - 1)d_I (M, N ), \] for free \(\mathbb{R}^n\)-modules, and finally that equality holds for block decomposable modules.
reviewed by: My Ismail Mamouni
Mathematics Subject Classification ID: 55N31
zbMATH DE Number: 7367365
zbMATH Keywords: persistent homology
zbMATH Keywords: stability
zbMATH Keywords: multiparameter persistence
zbMATH Keywords: Reeb graphs
zbMATH Keywords: zigzag modules
MaRDI profile type: Publication
full work available at URL: s00454-021-00298-0
OpenAlex ID: W3162451511
cites work: Proofs from THE BOOK
cites work: Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem
cites work: Induced Matchings and the Algebraic Stability of Persistence Barcodes
cites work: Strong Equivalence of the Interleaving and Functional Distortion Metrics for Reeb Graphs
cites work: Homology and robustness of level and interlevel sets
cites work: Computational Complexity of the Interleaving Distance
cites work: Computing the interleaving distance is NP-hard
cites work: Interval decomposition of infinite zigzag persistence modules
cites work: Decomposition of persistence modules
cites work: Algebraic stability of zigzag persistence modules
cites work: Zigzag persistent homology and real-valued functions
cites work: The theory of multidimensional persistence
cites work: Proximity of persistence modules and their diagrams
cites work: The Structure and Stability of Persistence Modules
cites work: Decomposition of exact pfd persistence bimodules
cites work: Stability of persistence diagrams
cites work: Decomposition of pointwise finite-dimensional persistence modules
cites work: Q5115800
cites work: Q5845505
cites work: Categorified Reeb graphs
DOI: 10.1007/S00454-021-00298-0
description: scientific article; zbMATH DE number 7367365