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The stability of persistence diagrams is among the most important results in applied and computational topology.
An incremental algorithm for betti numbers of simplicial complexes
Cecil Jose A Delfinado and Herbert Edelsbrunner · 1993
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Riemannian geometry
Wilhelm Klingenberg · 1995
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Topological persistence and simplification
Herbert Edelsbrunner, David Letscher, and Afra Zomorodian · 2000
Earlier work this paper cites.
Combinatorial optimization: polyhedra and efficiency
Alexander Schrijver et al · 2003
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Computing persistent homology
Afra Zomorodian and Gunnar Carlsson · 2005
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Vines and vineyards by updating persistence in linear time
David Cohen-Steiner, Herbert Edelsbrunner, and Dmitriy Morozov · 2006
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Betti number signatures of homogeneous poisson point processes
Vanessa Robins · 2006
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Stability of persistence diagrams
David Cohen-Steiner, Herbert Edelsbrunner, and John Harer · 2007
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Real analysis: measure theory, integration, and Hilbert spaces
Elias M Stein and Rami Shakarchi · 2009
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Lipschitz functions have l p l_{p} -stable persistence
David Cohen-Steiner, Herbert Edelsbrunner, John Harer, and Yuriy Mileyko · 2010
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Computational Topology
Herbert Edelsbrunner and John Harer · 2010
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Diffusion runs low on persistence fast
Chao Chen and Herbert Edelsbrunner · 2011
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Theory and algorithms for constructing discrete morse complexes from grayscale digital images
Vanessa Robins, Peter John Wood, and Adrian P Sheppard · 2011
Earlier work this paper cites.
The structure and stability of persistence modules
Frédéric Chazal, Vin De Silva, Marc Glisse, and Steve Oudot · 2012
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Induced matchings of barcodes and the algebraic stability of persistence
Ulrich Bauer and Michael Lesnick · 2014
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Categorification of persistent homology
Peter Bubenik and Jonathan A. Scott · 2014
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Persistence stability for geometric complexes
Frédéric Chazal, Vin De Silva, and Steve Oudot · 2014
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Fréchet means for distributions of persistence diagrams
Katharine Turner, Yuriy Mileyko, Sayan Mukherjee, and John Harer · 2014
Cited alongside, same era.
Persistent homology transform for modeling shapes and surfaces
Katharine Turner, Sayan Mukherjee, and Doug M Boyer · 2014
Cited alongside, same era.
Statistical topological data analysis using persistence landscapes
Peter Bubenik · 2015
Cited alongside, same era.
Metrics for generalized persistence modules
Peter Bubenik, Vin de Silva, and Jonathan Scott · 2015
Cited alongside, same era.
Decomposition of pointwise finite-dimensional persistence modules
William Crawley-Boevey · 2015
Cited alongside, same era.
A stable multi-scale kernel for topological machine learning
Jan Reininghaus, Stefan Huber, Ulrich Bauer, and Roland Kwitt · 2015
Cited alongside, same era.
Topological function optimization for continuous shape matching
Adrien Poulenard, Primoz Skraba, and Maks Ovsjanikov · 2018
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Random čech complexes on riemannian manifolds
Omer Bobrowski and Goncalo Oliveira · 2019
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A topological regularizer for classifiers via persistent homology
Chao Chen, Xiuyan Ni, Qinxun Bai, and Yusu Wang · 2019
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Persistence curves: A canonical framework for summarizing persistence diagrams
Yu-Min Chung and Austin Lawson · 2019
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Learning representations of persistence barcodes
Christoph D Hofer, Roland Kwitt, and Marc Niethammer · 2019
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A framework for differential calculus on persistence barcodes
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The classification of endoscopy images with persistent homology
Olga Dunaeva, Herbert Edelsbrunner, Anton Lukyanov, Michael Machin, Daria Malkova, Roman Kuvaev, and Sergey Kashin · 2016
Cited alongside, same era.
Continuation of point clouds via persistence diagrams
Marcio Gameiro, Yasuaki Hiraoka, and Ippei Obayashi · 2016
Cited alongside, same era.
Persistence weighted gaussian kernel for topological data analysis
Genki Kusano, Yasuaki Hiraoka, and Kenji Fukumizu · 2016
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Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids
Vanessa Robins and Katharine Turner · 2016
Cited alongside, same era.
On time-series topological data analysis: New data and opportunities
Lee M. Seversky, Shelby Davis, and Matthew Berger · 2016
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Persistence images: A stable vector representation of persistent homology
Henry Adams, Tegan Emerson, Michael Kirby, Rachel Neville, Chris Peterson, Patrick Shipman, Sofya Chepushtanova, Eric Hanson, Francis Motta, and Lori Ziegelmeier · 2017
Cited alongside, same era.
Jacob Leygonie, Steve Oudot, and Ulrike Tillmann · 2019
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Computational optimal transport: With applications to data science
Gabriel Peyré, Marco Cuturi, et al · 2019
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Progressive wasserstein barycenters of persistence diagrams
Jules Vidal, Joseph Budin, and Julien Tierny · 2019
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Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport
Vincent Divol and Théo Lacombe · 2020
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Medians of populations of persistence diagrams
Katharine Turner · 2020
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Using persistent homology to quantify a diurnal cycle in hurricanes
Sarah Tymochko, Elizabeth Munch, Jason Dunion, Kristen Corbosiero, and Ryan Torn · 2020
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Topological detection of alzheimer’s disease using betti curves
Ameer Saadat-Yazdi, Rayna Andreeva, and Rik Sarkar · 2021
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The persistent homology of dual digital image constructions
Bea Bleile, Adélie Garin, Teresa Heiss, Kelly Maggs, and Vanessa Robins · 2022
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Topological analysis of ensembles of hydrodynamic turbulent flows an experimental study
Florent Nauleau, Fabien Vivodtzev, Thibault Bridel-Bertomeu, Heloise Beaugendre, and Julien Tierny · 2022
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Wasserstein convergence of čech persistence diagrams for samplings of submanifolds
Charles Arnal, David Cohen-Steiner, and Vincent Divol · 2024
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Altered topological structure of the brain white matter in maltreated children through topological data analysis
Moo K Chung, Tahmineh Azizi, Jamie L Hanson, Andrew L Alexander, Seth D Pollak, and Richard J Davidson · 2024
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