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Persistence diagrams are common objects in the field of Topological Data Analysis.
The algebraic degree of geometric optimization problems
Chanderjit Bajaj · 1988
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Geodesic geometry and fixed point theory
William A Kirk · 2003
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Retrieval of trademark images by means of size functions
Andrea Cerri, Massimo Ferri, and Daniela Giorgi · 2006
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Functional data analysis
James O Ramsay · 2006
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Object oriented data analysis: Sets of trees
Haonan Wang, JS Marron, et al · 2007
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Computing robustness and persistence for images
Paul Bendich, Herbert Edelsbrunner, and Michael Kerber · 2010
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Statistical topology via morse theory persistence and nonparametric estimation
Peter Bubenik, Gunnar Carlsson, Peter T Kim, and Zhi-Ming Luo · 2010
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Computational Topology: An Introduction
H. Edelsbrunner and J. L. Harer · 2010
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Exploring uses of persistent homology for statistical analysis of landmark-based shape data
Jennifer Gamble and Giseon Heo · 2010
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Distance functions, critical points, and topology for some random complexes
Omer Bobrowski and Robert J Adler · 2011
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Random geometric complexes
Matthew Kahle · 2011
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Probability measures on the space of persistence diagrams
Yuriy Mileyko, Sayan Mukherjee, and John Harer · 2011
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Barycenters in alexandrov spaces of curvature bounded below
Shin-ichi Ohta · 2012
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A persistence landscapes toolbox for topological statistics
Peter Bubenik and Pawel Dlotko · 2013
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On the bootstrap for persistence diagrams and landscapes
Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Aarti Singh, and Larry Wasserman · 2013
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Optimal rates of convergence for persistence diagrams in topological data analysis
Frédéric Chazal, Marc Glisse, Catherine Labruère, and Bertrand Michel · 2013
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Overview of object oriented data analysis
J Steve Marron and Andrés M Alonso · 2014
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Object oriented data analysis: a few methodological challenges
Laura M Sangalli, Piercesare Secchi, and Simone Vantini · 2014
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Fréchet means for distributions of persistence diagrams
Katharine Turner, Yuriy Mileyko, Sayan Mukherjee, and John Harer · 2014
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Persistent homology transform for modeling shapes and surfaces
Katharine Turner, Sayan Mukherjee, and Doug M Boyer · 2014
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Random geometric complexes in the thermodynamic regime
D Yogeshwaran, Eliran Subag, and Robert J Adler · 2014
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Decomposition of pointwise finite-dimensional persistence modules
William Crawley-Boevey · 2015
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Limit the theorems for betti numbers of random simplicial complexes
Matthew Kahle, Elizabeth Meckes, et al · 2013
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Crackle: The homology of noise
Robert J Adler, Omer Bobrowski, and Shmuel Weinberger · 2014
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Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces
Andrew J Blumberg, Itamar Gal, Michael A Mandell, and Matthew Pancia · 2014
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Confidence sets for persistence diagrams
Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, Aarti Singh, et al · 2014
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Object-oriented data analysis of cell images
Xiaosun Lu, JS Marron, and Perry Haaland · 2014
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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
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Functional data analysis of amplitude and phase variation
JS Marron, James O Ramsay, Laura M Sangalli, Anuj Srivastava, et al · 2015
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Probabilistic fréchet means for time varying persistence diagrams
Elizabeth Munch, Katharine Turner, Paul Bendich, Sayan Mukherjee, Jonathan Mattingly, John Harer, et al · 2015
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On the topology of random complexes built over stationary point processes
D Yogeshwaran, Robert J Adler, et al · 2015
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Geometry helps to compare persistence diagrams
Michael Kerber, Dmitriy Morozov, and Arnur Nigmetov · 2017
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