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We define a new topological summary for data that we call the persistence landscape.
On the imbedding of systems of compacta in simplicial complexes
Karol Borsuk · 1948
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The law of large numbers and the central limit theorem in Banach spaces
J. Hoffmann-Jørgensen and G. Pisier · 1976
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Probability in Banach Spaces
Michel Ledoux and Michel Talagrand · 1991
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Simulation of stationary Gaussian processes in [ 0 , 1 ] d [0,1]^{d}
Andrew T. A. Wood and Grace Chan · 1994
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Topological persistence and simplification
Herbert Edelsbrunner, David Letscher, and Afra Zomorodian · 2001
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Algebraic Topology
Allen Hatcher · 2002
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Topological estimation using witness complexes
Vin de Silva and Gunnar Carlsson · 2004
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Computing persistent homology
Afra Zomorodian and Gunnar Carlsson · 2005
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Random Fields and Geometry
Robert J. Adler and Jonathan E. Taylor · 2007
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Stability of persistence diagrams
David Cohen-Steiner, Herbert Edelsbrunner, and John Harer · 2007
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On the local behavior of spaces of natural images
Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, and Afra Zomorodian · 2008
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Comparison of pattern detection methods in microarray time series of the segmentation clock
Mary-Lee Dequéant, Sebastian Ahnert, Herbert Edelsbrunner, Thomas M. A. Fink, Earl F. Glynn, Gaye Hattem, Andrzej Kudlicki, Yuriy Mileyko, Jason Morton, Arcady R. Mushegian, Lior Pachter, Maga Rowicka, Anne Shiu, Bernd Sturmfels, and Olivier Pourquié · 2008
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Barcodes: the persistent topology of data
Robert Ghrist · 2008
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Topology and data
Gunnar Carlsson · 2009
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Proximity of persistence modules and their diagrams
Frédéric Chazal, David Cohen-Steiner, Marc Glisse, Leonidas J. Guibas, and Steve Y. Oudot · 2009
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Persistence diagrams in cortical surface data
Moo K. Chung, Peter Bubenik, and Peter T. Kim · 2009
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Extending persistence using Poincaré and Lefschetz duality
David Cohen-Steiner, Herbert Edelsbrunner, and John Harer · 2009
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Persistent homology for random fields and complexes
Robert J. Adler, Omer Bobrowski, Matthew S. Borman, Eliran Subag, and Shmuel Weinberger · 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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Lipschitz functions have L p L_{p} -stable persistence
David Cohen-Steiner, Herbert Edelsbrunner, John Harer, and Yuriy Mileyko · 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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Quantifying transversality by measuring the robustness of intersections
Topological analysis of variance and the maxillary complex
Giseon Heo, Jennifer Gamble, and Peter T. Kim · 2012
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Dionysus: a C++ library with various algorithms for computing persistent homology
Dimitriy Morozov · 2012
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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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An output-sensitive algorithm for persistent homology
Chao Chen and Michael Kerber · 2013
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Limit theorems for Betti numbers of random simplicial complexes
Matthew Kahle and Elizabeth Meckes · 2013
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Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel · 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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Zigzag persistent homology in matrix multiplication time
Nikola Milosavljević, Dmitriy Morozov, and Primož Škraba · 2011
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Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival
Monica Nicolau, Arnold J. Levine, and Gunnar Carlsson · 2011
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Javaplex: a research software package for persistent (co)homology
Andrew Tausz, Mikael Vejdemo-Johansson, and Henry Adams · 2011
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Euler integration of Gaussian random fields and persistent homology
Omer Bobrowski and Matthew Strom Borman · 2012
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Elizabeth Munch, Paul Bendich, Katharine Turner, Sayan Mukherjee, Jonathan Mattingly, and John Harer · 2013
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Perseus: the persistent homology software
Vidit Nanda · 2013
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Hypothesis testing for topological data analysis
Andrew Robinson and Katharine Turner · 2013
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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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Categorification of persistent homology
Peter Bubenik and Jonathan A. Scott · 2014
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Stochastic convergence of persistence landscapes and silhouettes
Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, and Larry Wasserman · 2014
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Confidence sets for persistence diagrams
Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, and Aarti Singh · 2014
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Using cycles in high dimensional data to analyze protein binding
Violeta Kovacev-Nikolic, Giseon Heo, Dragan Nikolić, and Peter Bubenik · 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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Graph induced complex on point data
Tamal Krishna Dey, Fengtao Fan, and Yusu Wang · 2031
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