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Reeb spaces, as well as their discretized versions called Mappers, are common descriptors used in Topological Data Analysis, with plenty of applications in various fields of science, such as computational biology and data visualization, among others.
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Georges Reeb · 1946
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Ronald DeVore and George Lorentz · 1993
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A course in metric geometry
Dmitri Burago, Yuri Burago, and Sergei Ivanov · 2001
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The elements of statistical learning
Trevor Hastie, Robert Tibshirani, and Jerome Friedman · 2003
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Shahar Mendelson and Roman Vershynin · 2003
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Theory of classification: A survey of some recent advances
Stéphane Boucheron, Olivier Bousquet, and Gábor Lugosi · 2005
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John Shawe-Taylor, Christopher KI Williams, Nello Cristianini, and Jaz Kandola · 2005
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Gilles Blanchard, Olivier Bousquet, and Laurent Zwald · 2007
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Conditional density estimation in a regression setting
Sam Efromovich · 2007
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Topological methods for the analysis of high dimensional data sets and 3D object recognition
Gurjeet Singh, Facundo Mémoli, and Gunnar Carlsson · 2007
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Data skeletonization via Reeb graphs
Xiaoyin Ge, Issam Safa, Mikhail Belkin, and Yusu Wang · 2011
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Manifold learning theory and applications
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Patrick Billingsley · 2013
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Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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Topological analysis of nerves, Reeb spaces, Mappers, and Multiscale Mappers
Tamal Dey, Facundo Mémoli, and Yusu Wang · 2017
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Single-cell topological RNA-seq analysis reveals insights into cellular differentiation and development
Abbas Rizvi, Pablo Cámara, Elena Kandror, Thomas Roberts, Ira Schieren, Tom Maniatis, and Raúl Rabadán · 2017
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Exposition and interpretation of the topology of neural networks
Rickard Brüel-Gabrielsson and Gunnar Carlsson · 2018
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Statistical analysis and parameter selection for Mapper
Mathieu Carrière, Bertrand Michel, and Steve Oudot · 2018
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Topological data analysis of single-cell Hi-C contact maps
Mathieu Carrière and Raúl Rabadán · 2018
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Measuring distance between Reeb graphs
Ulrich Bauer, Xiaoyin Ge, and Yusu Wang · 2014
Cited alongside, same era.
Convergence rates for persistence diagram estimation in topological data analysis
Frédéric Chazal, Marc Glisse, Catherine Labruère, and Bertrand Michel · 2015
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Categorified Reeb graphs
Vin de Silva, Elizabeth Munch, and Amit Patel · 2016
Cited alongside, same era.
Convergence between categorical representations of Reeb space and Mapper
Elizabeth Munch and Bei Wang · 2016
Cited alongside, same era.
An introduction to topological data analysis: fundamental and practical aspects for data scientists
Frédéric Chazal and Bertrand Michel · 2017
Cited alongside, same era.
Structure and stability of the one-dimensional Mapper
Mathieu Carrière and Steve Oudot · 2017
Cited alongside, same era.
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Gregory Naitzat, Namita Lokare, Jorge Silva, and Ilknur Kaynar-Kabul · 2018
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Probabilistic convergence and stability of random Mapper graphs
Adam Brown, Omer Bobrowski, Elizabeth Munch, and Bei Wang · 2019
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Rachel Jeitziner, Mathieu Carrière, Jacques Rougemont, Steve Oudot, Kathryn Hess, and Cathrin Brisken · 2019
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A k k -points-based distance for robust geometric inference
Claire Brécheteau and Clément Levrard · 2020
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Nonasymptotic upper bounds for the reconstruction error of pca
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