refs.bib

@article{Robinson2017,
	author = {Robinson, Andrew and Turner, Katharine},
	journal = {Journal of Applied and Computational Topology},
	pages = {241--261},
	publisher = {Springer},
	title = {{Hypothesis testing for topological data analysis}},
	year = {2017}
}

@inproceedings{Zomorodian2004,
	author = {Zomorodian, Afra and Carlsson, Gunnar},
	booktitle = {Proceedings of the Annual Symposium on Computational Geometry},
	keywords = {Computational topology,Persistent homology},
	pages = {347--356},
	title = {{Computing persistent homology}},
	volume = {33},
	year = {2004}
}


@article{Fasy2014a,
	author = {Fasy, Brittany Terese and Lecci, Fabrizio and Rinaldo, Alessandro and Wasserman, Larry and Balakrishnan, Sivaraman and Singh, Aarti},
	journal = {Annals of Statistics},
	pages = {2301--2339},
	title = {{Confidence sets for persistence diagrams}},
	year = {2014}
}

@article{Bendich2013,
	author = {Bendich, Paul and Edelsbrunner, Herbert and Morozov, Dmitriy and Patel, Amit},
	journal = {Homology, Homotopy and Applications},
	pages = {51--72},
	title = {{Homology and robustness of level and interlevel sets}},
	year = {2013}
}


@article{Mileyko2011,
	author = {Mileyko, Yuriy and Mukherjee, Sayan and Harer, John},
	journal = {Inverse Problems},
	publisher = {Institute of Physics Publishing},
	title = {{Probability measures on the space of persistence diagrams}},
	year = {2011}
}
@article{Chazal2015,
	author = {Chazal, Fr{\'{e}}d{\'{e}}ric and Glisse, Marc and Labru{\'{e}}re, Catherine and Michel, Bertrand},
	journal = {Journal of Machine Learning Research},
	pages = {3603--3635},
	title = {{Convergence rates for persistence diagram estimation in topological data analysis}},
	year = {2015}
}

@incollection{Edelsbrunner2008,
author = {Edelsbrunner, Herbert and Harer, John},
booktitle = {Contemporary mathematics},
pages = {257--282},
publisher = {American Mathematical Society},
title = {{Persistent homology — a survey}},
volume = {453},
year = {2008}
}

@article{Barrett1962,
	author = {Barrett, Lida K. and Hilton, P. J. and Wylie, S.},
	journal = {The American Mathematical Monthly},
	publisher = {Academic Press},
	title = {{Homology Theory, An Introduction to Algebraic Topology.}},
	year = {1962}
}
@article{Futagami2019,
	author = {Futagami, Rentaro and Yamada, Noritaka and Shibuya, Takeshi},
	journal = {Lecture Notes in Computer Science},
	title = {{Inferring underlying manifold of data by the use of persistent homology analysis}},
	year = {2019}
}

@article{Cohen-Steiner2010,
	author = {Cohen-Steiner, David and Edelsbrunner, Herbert and Harer, John and Mileyko, Yuriy},
	journal = {Foundations of Computational Mathematics},
	pages = {127--139},
	publisher = {Springer},
	title = {{Lipschitz functions have Lp-stable persistence}},
	volume = {10},
	year = {2010}
}

@article{Edelsbrunner2002a,
	author = {Edelsbrunner, Herbert and Letscher, David and Zomorodian, Afra},
	journal = {Discrete and Computational Geometry},
	title = {{Topological persistence and simplification}},
	year = {2002}
}

@article{DeSilva2011,
	author = {{De Silva}, Vin and Morozov, Dmitriy and Vejdemo-Johansson, Mikael},
	journal = {Inverse Problems},
	pages = {1--16},
	title = {{Dualities in persistent (co)homology}},
	year = {2011}
}

@article{Bauer2016,
	author = {Bauer, Ulrich and Edelsbrunner, Herbert},
	journal = {Transactions of the American Mathematical Society},
	title = {{The Morse theory of {\v{C}}ech and Delaunay complexes}},
	volume = {369},
	year = {2016}
}

@article{Bubenik2015,
	author = {Bubenik, Peter},
	journal = {Journal of Machine Learning Research},
	pages = {77--102},
	title = {{Statistical topological data analysis using persistence landscapes}},
	volume = {16},
	year = {2015}
}

@article{Cerri2016,
	author = {Cerri, Andrea and Landi, Claudia},
	journal = {Foundations of Computational Mathematics},
	pages = {343--367},
	title = {{Hausdorff Stability of Persistence Spaces}},
	year = {2016}
}

@book{Carlsson2009,
	author = {Carlsson, Gunnar},
	publisher = {Bulletin of the American Mathematical Society},
	pages = {255--308},
	title = {{Topology and data}},
	year = {2009}
}

@article{Carlsson2009a,
	author = {Carlsson, Gunnar and Zomorodian, Afra},
	journal = {Discrete and Computational Geometry},
	pages = {71--93},
	title = {{The theory of multidimensional persistence}},
	year = {2009}
}

@article{Steiner2007,
author = {Cohen-Steiner, David and Edelsbrunner, Herbert and Harer, John},
doi = {10.1007/s00454-006-1276-5},
issn = {14320444},
journal = {Discrete and Computational Geometry},
number = {1},
pages = {103--120},
title = {{Stability of persistence diagrams}},
volume = {37},
year = {2007}
}
@inproceedings{Zomorodian2010,
author = {Zomorodian, Afra},
booktitle = {Computers and Graphics (Pergamon)},
doi = {10.1016/j.cag.2010.03.007},
issn = {00978493},
keywords = {Clique complex,Topological data analysis,Vietoris-Rips complex},
pages = {263--271},
title = {{Fast construction of the Vietoris-Rips complex}},
year = {2010}
}
@book{Boissonnat2018,
author = {Boissonnat, Jean Daniel and Chazal, Fr{\'{e}}d{\'{e}}ric and Yvinec, Mariette},
booktitle = {Geometric and Topological Inference},
doi = {10.1017/9781108297806},
publisher = {Cambridge University Press},
title = {{Geometric and Topological Inference}},
volume = {57},
year = {2018}
}
@article{Edelsbrunner2002,
author = {Edelsbrunner, Herbert and Letscher, David and Zomorodian, Afra},
doi = {10.1007/s00454-002-2885-2},
issn = {01795376},
journal = {Discrete and Computational Geometry},
number = {4},
pages = {511--533},
title = {{Topological persistence and simplification}},
volume = {28},
year = {2002}
}
@inproceedings{Reem2011a,
author = {Reem, Daniel},
booktitle = {Proceedings of the Annual Symposium on Computational Geometry},
doi = {10.1145/1998196.1998234},
pages = {254--263},
title = {{The geometric stability of Voronoi diagrams with respect to small changes of the sites}},
year = {2011}
}
@inproceedings{Carriere2017,
author = {Carri{\`{e}}re, Mathieu and Cuturi, Marco and Oudot, Steve},
booktitle = {34th International Conference on Machine Learning, ICML 2017},
pages = {1092--1101},
title = {{Sliced Wasserstein kernel for persistence diagrams}},
volume = {2},
year = {2017}
}
@article{Kim2018,
author = {Kim, Kwangho and Kim, Jisu and Rinaldo, Alessandro},
journal = {arXiv:1812.02987},
pages = {1--28},
title = {{Time Series Featurization via Topological Data Analysis}},
year = {2018}
}
@article{Morozov2008a,
author = {Morozov, Dmitriy},
journal = {PhD Thesis},
title = {{Homological Illusions of Persistence and Stability}},
year = {2008}
}
@article{Kerber2017,
author = {Kerber, Michael and Morozov, Dmitriy and Nigmetov, Arnur},
doi = {10.1145/3064175},
journal = {ACM Journal of Experimental Algorithmics},
pages = {1--4},
publisher = {Association of Computing Machinery},
title = {{Geometry helps to compare persistence diagrams}},
volume = {22},
year = {2017}
}
@article{Silva2004,
author = {Silva, Vin De and Carlsson, Gunnar},
journal = {Symposium on Point-Based Graphics},
pages = {157--166},
title = {{Topological estimation using witness complexes}},
year = {2004}
}
@book{janich2013topologie,
title={Topologie},
author={J{\"a}nich, Klaus},
year={2013},
publisher={Springer-Verlag}
}