article

Topological Persistence and Simplification

Authors:

Edelsbrunner,

Letscher,

ZomorodianAuthors Info & Claims

Discrete & Computational Geometry, Volume 28, Issue 4

Pages 511 - 533

https://doi.org/10.1007/s00454-002-2885-2

Published: 01 November 2002 Publication History

Abstract

We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.

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Cited By

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Buchet MB Dornelas BKerber M(2024)Sparse Higher Order Čech FiltrationsJournal of the ACM10.1145/366608571:4(1-23)Online publication date: 27-May-2024
https://dl.acm.org/doi/10.1145/3666085
Randolph Franklin Wde Magalhães S(2024)Implementing Simulation of Simplicity for Geometric DegeneraciesSpatial Gems, Volume 210.1145/3617291.3617299(71-84)Online publication date: 25-Jan-2024
https://dl.acm.org/doi/10.1145/3617291.3617299
Le Guillou EWill MGuillou PLukasczyk JFortin PGarth CTierny J(2024)TTK is Getting MPI-ReadyIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2024.339021930:8(5875-5892)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1109/TVCG.2024.3390219
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Topological Persistence and Simplification
1. Theory of computation

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cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 28, Issue 4

November 2002

228 pages

ISSN:0179-5376

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 November 2002

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Buchet MB Dornelas BKerber M(2024)Sparse Higher Order Čech FiltrationsJournal of the ACM10.1145/366608571:4(1-23)Online publication date: 27-May-2024
https://dl.acm.org/doi/10.1145/3666085
Randolph Franklin Wde Magalhães S(2024)Implementing Simulation of Simplicity for Geometric DegeneraciesSpatial Gems, Volume 210.1145/3617291.3617299(71-84)Online publication date: 25-Jan-2024
https://dl.acm.org/doi/10.1145/3617291.3617299
Le Guillou EWill MGuillou PLukasczyk JFortin PGarth CTierny J(2024)TTK is Getting MPI-ReadyIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2024.339021930:8(5875-5892)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1109/TVCG.2024.3390219
Guillou PVidal JTierny J(2024)Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data – An Algorithm and a BenchmarkIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.323800830:4(1897-1915)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3238008
Ballester RClemente XCasacuberta CMadadi MCorneanu CEscalera S(2024)Predicting the generalization gap in neural networks using topological data analysisNeurocomputing10.1016/j.neucom.2024.127787596:COnline publication date: 1-Sep-2024
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Gao DGao YLin H(2024)Periodic implicit representation, design and optimization of porous structures using periodic B-splinesComputer-Aided Design10.1016/j.cad.2024.103703171:COnline publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1016/j.cad.2024.103703
Kindelan RFrías JCerda MHitschfeld N(2024)A topological data analysis based classifierAdvances in Data Analysis and Classification10.1007/s11634-023-00548-418:2(493-538)Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1007/s11634-023-00548-4
Dong ZLin HZhou CZhang BLi G(2024)Persistence B-spline grids: stable vector representation of persistence diagrams based on data fittingMachine Language10.1007/s10994-023-06492-w113:3(1373-1420)Online publication date: 1-Mar-2024
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Nigmetov AMorozov D(2024)Topological Optimization with Big StepsDiscrete & Computational Geometry10.1007/s00454-023-00613-x72:1(310-344)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s00454-023-00613-x
Maria CSchreiber H(2024)Discrete Morse Theory for Computing Zigzag PersistenceDiscrete & Computational Geometry10.1007/s00454-023-00594-x71:2(708-737)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1007/s00454-023-00594-x
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Statistical topological data analysis using persistence landscapes