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diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index d1b2f558..d8472ad0 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -7,11 +7,14 @@ } @article{Carriere17c, - author = {Carri\`ere, Mathieu and Michel, Bertrand and Oudot, Steve}, - title = {{Statistical Analysis and Parameter Selection for Mapper}}, - journal = {CoRR}, - volume = {abs/1706.00204}, - year = {2017} +author = {Carri{\`{e}}re, Mathieu and Michel, Bertrand and Oudot, Steve}, +journal = {Journal of Machine Learning Research}, +pages = {1--39}, +publisher = {JMLR.org}, +title = {{Statistical analysis and parameter selection for Mapper}}, +volume = {19}, +year = {2018}, +url = {https://jmlr.org/papers/v19/17-291.html}, } @inproceedings{Dey13, @@ -20,14 +23,19 @@ booktitle = {Proceedings of the Twenty-ninth Annual Symposium on Computational Geometry}, year = {2013}, pages = {107--116}, + doi = {10.1145/2462356.2462387} } @article{Carriere16, - title={{Structure and Stability of the 1-Dimensional Mapper}}, - author={Carri\`ere, Mathieu and Oudot, Steve}, - journal={CoRR}, - volume= {abs/1511.05823}, - year={2015} +author = {Carri{\`{e}}re, Mathieu and Oudot, Steve}, +journal = {Foundations of Computational Mathematics}, +number = {6}, +pages = {1333--1396}, +publisher = {Springer-Verlag}, +doi = {10.1007/s10208-017-9370-z}, +title = {{Structure and stability of the one-dimensional Mapper}}, +volume = {18}, +year = {2017} } @inproceedings{zigzag_reflection, @@ -36,6 +44,18 @@ year = {2014 $\ \ \ \ \ \ \ \ \ \ \ $ \emph{In Preparation}}, } +@article{Cohen-Steiner2009, +author = {Cohen-Steiner, David and Edelsbrunner, Herbert and Harer, John}, +journal = {Foundations of Computational Mathematics}, +number = {1}, +pages = {79--103}, +publisher = {Springer-Verlag}, +doi = {10.1007/s10208-008-9027-z}, +title = {{Extending persistence using Poincar{\'{e}} and Lefschetz duality}}, +volume = {9}, +year = {2009} +} + @misc{gudhi_stpcoh, author = {Cl\'ement Maria}, title = "\textsc{Gudhi}, Simplex Tree and Persistent Cohomology Packages", @@ -131,10 +151,10 @@ language={English}, %% hal-00922572, version 2 -%% http://hal.inria.fr/hal-00922572 +%% https://hal.inria.fr/hal-00922572 @techreport{boissonnat:hal-00922572, hal_id = {hal-00922572}, - url = {http://hal.inria.fr/hal-00922572}, + url = {https://hal.inria.fr/hal-00922572}, title = {Computing Persistent Homology with Various Coefficient Fields in a Single Pass}, author = {Boissonnat, Jean-Daniel and Maria, Cl{\'e}ment}, abstract = {{In this article, we introduce the multi-field persistence diagram for the persistence homology of a filtered complex. It encodes compactly the superimposition of the persistence diagrams of the complex with several field coefficients, and provides a substantially more precise description of the topology of the filtered complex. Specifically, the multi-field persistence diagram encodes the Betti numbers of integral homology and the prime divisors of the torsion coefficients of the underlying shape. Moreover, it enjoys similar stability properties as the ones of standard persistence diagrams, with the appropriate notion of distance. These properties make the multi-field persistence diagram a useful tool in computational topology.}}, @@ -147,7 +167,7 @@ language={English}, number = {RR-8436}, year = {2013}, month = Dec, - pdf = {http://hal.inria.fr/hal-00922572/PDF/RR-8436.pdf}, + pdf = {https://hal.inria.fr/hal-00922572v5/document}, } @@ -303,7 +323,7 @@ language={English}, %------------------------------------------------------------------ @article{rips2012, hal_id = {hal-00785072}, - url = {http://hal.archives-ouvertes.fr/hal-00785072}, + url = {https://hal.archives-ouvertes.fr/hal-00785072}, title = {{Vietoris-Rips Complexes also Provide Topologically Correct Reconstructions of Sampled Shapes}}, author = {Attali, Dominique and Lieutier, Andr{\'e} and Salinas, David}, keywords = {Shape reconstruction \sep Rips complexes \sep clique complexes \sep \v Cech complexes ; homotopy equivalence ; collapses ; high dimensions}, @@ -555,6 +575,15 @@ note = "http://gmplib.org/", %TEMPORARY %------------------------------------------------------------------ +@misc{royer2019atol, + title={ATOL: Measure Vectorisation for Automatic Topologically-Oriented Learning}, + author={Martin Royer and Frédéric Chazal and Clément Levrard and Yuichi Ike and Yuhei Umeda}, + year={2019}, + eprint={1909.13472}, + archivePrefix={arXiv}, + primaryClass={cs.CG} +} + @inproceedings{deSilva:2013:GSP:2493132.2462402, author = {de Silva, Vin and Nanda, Vidit}, title = {Geometry in the space of persistence modules}, @@ -814,6 +843,7 @@ book{hatcher2002algebraic, number = {4}, year = {2010}, pages = {367-405}, + doi = {10.1007/s10208-010-9066-0}, ee = {http://dx.doi.org/10.1007/s10208-010-9066-0}, bibsource = {DBLP, http://dblp.uni-trier.de} } @@ -909,6 +939,7 @@ language={English} booktitle = {Symposium on Computational Geometry}, year = {2014}, pages = {345}, + doi = {10.1145/2582112.2582165}, ee = {http://doi.acm.org/10.1145/2582112.2582165}, bibsource = {DBLP, http://dblp.uni-trier.de} } @@ -1059,7 +1090,7 @@ language={English} @ARTICLE{Reininghaus_Huber_ALL_PSSK, author = {J. Reininghaus and S. Huber and U. Bauer and R. Kwitt}, title = {A Stable Multi-Scale Kernel for Topological Machine Learning.}, - journal = {Proc. 2015 IEEE Conf. Comp. Vision & Pat. Rec. (CVPR '15)}, + journal = {Proc. 2015 IEEE Conf. Comp. Vision \& Pat. Rec. (CVPR '15)}, year = {2015} } @@ -1076,7 +1107,7 @@ language={English} journal = {Computational Geometry: Theory and Applications}, volume = {58}, pages = {70--96}, - doi = "https://doi.org/10.1016/j.comgeo.2016.07.001", + doi = "10.1016/j.comgeo.2016.07.001", year = {2016} } @@ -1084,7 +1115,7 @@ language={English} author = {Nicholas J. Cavanna and Mahmoodreza Jahanseir and Donald R. Sheehy}, booktitle = {Proceedings of the Canadian Conference on Computational Geometry}, title = {A Geometric Perspective on Sparse Filtrations}, - url = {http://research.cs.queensu.ca/cccg2015/CCCG15-papers/01.pdf}, + url = {https://research.cs.queensu.ca/cccg2015/CCCG15-papers/01.pdf}, year = {2015} } @@ -1120,7 +1151,7 @@ language={English} editor = {Lars Arge and J{\'a}nos Pach}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, - URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5098}, + URL = {https://drops.dagstuhl.de/opus/volltexte/2015/5098/}, URN = {urn:nbn:de:0030-drops-50981}, doi = {10.4230/LIPIcs.SOCG.2015.642}, annote = {Keywords: Simplicial complex, Compact data structures, Automaton, NP-hard} @@ -1133,7 +1164,7 @@ language={English} journal = {CoRR}, volume = {abs/1607.08449}, year = {2016}, - url = {http://arxiv.org/abs/1607.08449}, + url = {https://arxiv.org/abs/1607.08449}, archivePrefix = {arXiv}, eprint = {1607.08449}, timestamp = {Mon, 13 Aug 2018 16:46:26 +0200}, @@ -1180,3 +1211,159 @@ language={English} booktitle = {In Neural Information Processing Systems}, year = {2007} } +@inproceedings{10.5555/3327546.3327645, +author = {Lacombe, Th\'{e}o and Cuturi, Marco and Oudot, Steve}, +title = {Large Scale Computation of Means and Clusters for Persistence Diagrams Using Optimal Transport}, +year = {2018}, +publisher = {Curran Associates Inc.}, +address = {Red Hook, NY, USA}, +booktitle = {Proceedings of the 32nd International Conference on Neural Information Processing Systems}, +pages = {9792–9802}, +numpages = {11}, +location = {Montr\'{e}al, Canada}, +series = {NIPS’18} +} +@article{tomato, +author = {Chazal, Fr\'{e}d\'{e}ric and Guibas, Leonidas J. and Oudot, Steve Y. and Skraba, Primoz}, +title = {Persistence-Based Clustering in Riemannian Manifolds}, +year = {2013}, +issue_date = {November 2013}, +publisher = {Association for Computing Machinery}, +address = {New York, NY, USA}, +volume = {60}, +number = {6}, +issn = {0004-5411}, +url = {https://doi.org/10.1145/2535927}, +doi = {10.1145/2535927}, +journal = {J. ACM}, +month = nov, +articleno = {Article 41}, +numpages = {38}, +keywords = {mode seeking, Unsupervised learning, computational topology, clustering, Morse theory, topological persistence} +} +@Article{dtm, +author={Chazal, Fr{\'e}d{\'e}ric +and Cohen-Steiner, David +and M{\'e}rigot, Quentin}, +title={Geometric Inference for Probability Measures}, +journal={Foundations of Computational Mathematics}, +year={2011}, +volume={11}, +number={6}, +pages={733-751}, +abstract={Data often comes in the form of a point cloud sampled from an unknown compact subset of Euclidean space. The general goal of geometric inference is then to recover geometric and topological features (e.g., Betti numbers, normals) of this subset from the approximating point cloud data. It appears that the study of distance functions allows one to address many of these questions successfully. However, one of the main limitations of this framework is that it does not cope well with outliers or with background noise. In this paper, we show how to extend the framework of distance functions to overcome this problem. Replacing compact subsets by measures, we introduce a notion of distance function to a probability distribution in Rd. These functions share many properties with classical distance functions, which make them suitable for inference purposes. In particular, by considering appropriate level sets of these distance functions, we show that it is possible to reconstruct offsets of sampled shapes with topological guarantees even in the presence of outliers. Moreover, in settings where empirical measures are considered, these functions can be easily evaluated, making them of particular practical interest.}, +issn={1615-3383}, +doi={10.1007/s10208-011-9098-0}, +url={https://doi.org/10.1007/s10208-011-9098-0} +} +@article{dtmdensity, +author = "Biau, Gérard and Chazal, Frédéric and Cohen-Steiner, David and Devroye, Luc and Rodríguez, Carlos", +doi = "10.1214/11-EJS606", +fjournal = "Electronic Journal of Statistics", +journal = "Electron. J. Statist.", +pages = "204--237", +publisher = "The Institute of Mathematical Statistics and the Bernoulli Society", +title = "A weighted k-nearest neighbor density estimate for geometric inference", +url = "https://doi.org/10.1214/11-EJS606", +volume = "5", +year = "2011" +} +@article{turner2014frechet, + title={Fr{\'e}chet means for distributions of persistence diagrams}, + author={Turner, Katharine and Mileyko, Yuriy and Mukherjee, Sayan and Harer, John}, + journal={Discrete \& Computational Geometry}, + doi={10.1007/s00454-014-9604-7}, + volume={52}, + number={1}, + pages={44--70}, + year={2014}, + publisher={Springer} +} + +@inproceedings{dtmfiltrationsconf, + author = {Hirokazu Anai and + Fr{\'{e}}d{\'{e}}ric Chazal and + Marc Glisse and + Yuichi Ike and + Hiroya Inakoshi and + Rapha{\"{e}}l Tinarrage and + Yuhei Umeda}, + editor = {Gill Barequet and + Yusu Wang}, + title = {DTM-Based Filtrations}, + booktitle = {35th International Symposium on Computational Geometry, SoCG 2019, + June 18-21, 2019, Portland, Oregon, {USA}}, + series = {LIPIcs}, + volume = {129}, + pages = {58:1--58:15}, + publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik}, + year = {2019}, + url = {https://doi.org/10.4230/LIPIcs.SoCG.2019.58}, + doi = {10.4230/LIPIcs.SoCG.2019.58}, + timestamp = {Tue, 11 Feb 2020 15:52:14 +0100}, + biburl = {https://dblp.org/rec/conf/compgeom/AnaiCGIITU19.bib}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + +@InProceedings{dtmfiltrations, +author="Anai, Hirokazu +and Chazal, Fr{\'e}d{\'e}ric +and Glisse, Marc +and Ike, Yuichi +and Inakoshi, Hiroya +and Tinarrage, Rapha{\"e}l +and Umeda, Yuhei", +editor="Baas, Nils A. +and Carlsson, Gunnar E. +and Quick, Gereon +and Szymik, Markus +and Thaule, Marius", +title="DTM-Based Filtrations", +booktitle="Topological Data Analysis", +year="2020", +publisher="Springer International Publishing", +address="Cham", +pages="33--66", +isbn="978-3-030-43408-3", +doi="10.1007/978-3-030-43408-3_2", +} + +@InProceedings{edgecollapsesocg2020, + author = {Jean-Daniel Boissonnat and Siddharth Pritam}, + title = {{Edge Collapse and Persistence of Flag Complexes}}, + booktitle = {36th International Symposium on Computational Geometry (SoCG 2020)}, + pages = {19:1--19:15}, + series = {Leibniz International Proceedings in Informatics (LIPIcs)}, + ISBN = {978-3-95977-143-6}, + ISSN = {1868-8969}, + year = {2020}, + volume = {164}, + editor = {Sergio Cabello and Danny Z. Chen}, + publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik}, + address = {Dagstuhl, Germany}, + URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12177/}, + URN = {urn:nbn:de:0030-drops-121777}, + doi = {10.4230/LIPIcs.SoCG.2020.19}, + annote = {Keywords: Computational Topology, Topological Data Analysis, Edge Collapse, Simple Collapse, Persistent homology} +} + +@misc{edgecollapsearxiv, + author = {Marc Glisse and Siddharth Pritam}, + title = {{Swap, Shift and Trim to Edge Collapse a Filtration}}, + url = {https://arxiv.org/abs/2203.07022}, +} + +@phdthesis{KachanovichThesis, + TITLE = {{Meshing submanifolds using Coxeter triangulations}}, + AUTHOR = {Kachanovich, Siargey}, + URL = {https://hal.inria.fr/tel-02419148}, + NUMBER = {2019AZUR4072}, + SCHOOL = {{COMUE Universit{\'e} C{\^o}te d'Azur (2015 - 2019)}}, + YEAR = {2019}, + MONTH = Oct, + KEYWORDS = {Mesh generation ; Coxeter triangulations ; Simplex quality ; Triangulations of the Euclidean space ; Freudenthal-Kuhn triangulations ; G{\'e}n{\'e}ration de maillages ; Triangulations de Coxeter ; Qualit{\'e} des simplexes ; Triangulations de l'espace euclidien ; Triangulations de Freudenthal-Kuhn}, + TYPE = {Theses}, + PDF = {https://hal.inria.fr/tel-02419148v2/file/2019AZUR4072.pdf}, + HAL_ID = {tel-02419148}, + HAL_VERSION = {v2}, +} |