Topological data analysis (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Topological data analysis" in English language version.

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van de Weygaert, Rien; Vegter, Gert; Edelsbrunner, Herbert; Jones, Bernard J. T.; Pranav, Pratyush; Park, Changbom; Hellwing, Wojciech A.; Eldering, Bob; Kruithof, Nico (2011-01-01). Gavrilova, Marina L.; Tan, C. Kenneth; Mostafavi, Mir Abolfazl (eds.). Transactions on Computational Science XIV. Berlin, Heidelberg: Springer-Verlag. pp. 60–101. ISBN 978-3-642-25248-8.

ams.org

Derksen, H.; Weyman, J. (2005). "Quiver representations" (PDF). Notices of the AMS. 52 (2): 200–6.
Weinberger, S. (2011). "What is... persistent homology?" (PDF). Notices of the AMS. 58 (1): 36–39.
Edelsbrunner, Herbert; Harer, John (2008). "Persistent homology — a survey". Surveys on Discrete and Computational Geometry: Twenty Years Later. Contemporary Mathematics. Vol. 453. AMS. pp. 15–18. CiteSeerX 10.1.1.87.7764. doi:10.1090/conm/453/08802. ISBN 9780821842393. Section 5
Giunti, B., Lazovskis, J., & Rieck, B. (2023). DONUT: Creation, Development, and Opportunities of a Database. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 70(10), 1640–1644. https://doi.org/10.1090/noti2798

arxiv.org

Epstein, Charles; Carlsson, Gunnar; Edelsbrunner, Herbert (2011-12-01). "Topological data analysis". Inverse Problems. 27 (12): 120201. arXiv:1609.08227. Bibcode:2011InvPr..27a0101E. doi:10.1088/0266-5611/27/12/120201. S2CID 250913810.
Chazal, Frédéric; Glisse, Marc; Labruère, Catherine; Michel, Bertrand (2013-05-27). "Optimal rates of convergence for persistence diagrams in Topological Data Analysis". arXiv:1305.6239 [math.ST].
Henselman, Gregory; Ghrist, Robert (2016). "Matroid Filtrations and Computational Persistent Homology". arXiv:1606.00199 [math.AT].
Otter, Nina; Porter, Mason A.; Tillmann, Ulrike; Grindrod, Peter; Harrington, Heather A. (2015-06-29). "A roadmap for the computation of persistent homology". EPJ Data Science. 6 (1): 17. arXiv:1506.08903. Bibcode:2015arXiv150608903O. doi:10.1140/epjds/s13688-017-0109-5. PMC 6979512. PMID 32025466.
Fasy, Brittany Terese; Kim, Jisu; Lecci, Fabrizio; Maria, Clément (2014-11-07). "Introduction to the R package TDA". arXiv:1411.1830 [cs.MS].
Dey, Tamal K.; Memoli, Facundo; Wang, Yusu (2015-04-14). "Mutiscale Mapper: A Framework for Topological Summarization of Data and Maps". arXiv:1504.03763 [cs.CG].
Curry, Justin (2013-03-13). "Sheaves, Cosheaves and Applications". arXiv:1303.3255 [math.AT].
Curry, Justin (2014-11-03). "Topological Data Analysis and Cosheaves". arXiv:1411.0613 [math.AT].
Harrington, H.; Otter, N.; Schenck, H.; Tillman, U. (2019). "Stratifying multiparameter persistent homology". SIAM Journal on Applied Algebra and Geometry. 3 (3): 439–471. arXiv:1708.07390. doi:10.1137/18M1224350. S2CID 119689059.
Cerri A, Di Fabio B, Ferri M, et al. Multidimensional persistent homology is stable[J]. arXiv:0908.0064, 2009.
Cagliari, Francesca; Landi, Claudia (2011-04-01). "Finiteness of rank invariants of multidimensional persistent homology groups". Applied Mathematics Letters. 24 (4): 516–8. arXiv:1001.0358. doi:10.1016/j.aml.2010.11.004. S2CID 14337220.
Cagliari, Francesca; Di Fabio, Barbara; Ferri, Massimo (2010-01-01). "One-dimensional reduction of multidimensional persistent homology". Proceedings of the American Mathematical Society. 138 (8): 3003–17. arXiv:math/0702713. doi:10.1090/S0002-9939-10-10312-8. ISSN 0002-9939. S2CID 18284958.
Skryzalin, Jacek; Carlsson, Gunnar (2014-11-14). "Numeric Invariants from Multidimensional Persistence". arXiv:1411.4022 [cs.CG].
Allili, Madjid; Kaczynski, Tomasz; Landi, Claudia (2013-10-30). "Reducing complexes in multidimensional persistent homology theory". arXiv:1310.8089 [cs.CG].
Cavazza, N.; Ferri, M.; Landi, C. (2010). "Estimating multidimensional persistent homology through a finite sampling". International Journal of Computational Geometry & Applications. 25 (3): 187–205. arXiv:1507.05277. doi:10.1142/S0218195915500119. S2CID 4803380.
de Silva, Vin; Morozov, Dmitriy; Vejdemo-Johansson, Mikael (2011). "Dualities in persistent (co)homology". Inverse Problems. 27 (12): 124003. arXiv:1107.5665. Bibcode:2011InvPr..27l4003D. doi:10.1088/0266-5611/27/12/124003. S2CID 5706682.
Silva, Vin de; Morozov, Dmitriy; Vejdemo-Johansson, Mikael (2011-03-30). "Persistent Cohomology and Circular Coordinates". Discrete & Computational Geometry. 45 (4): 737–759. arXiv:0905.4887. doi:10.1007/s00454-011-9344-x. ISSN 0179-5376. S2CID 31480083.
Burghelea, Dan; Dey, Tamal K. (2013-04-09). "Topological Persistence for Circle-Valued Maps". Discrete & Computational Geometry. 50 (1): 69–98. arXiv:1104.5646. doi:10.1007/s00454-013-9497-x. ISSN 0179-5376. S2CID 17407953.
Burghelea, Dan; Haller, Stefan (2015-06-04). "Topology of angle valued maps, bar codes and Jordan blocks". arXiv:1303.4328 [math.AT].
Frosini, Patrizio (2012-06-23). "Stable Comparison of Multidimensional Persistent Homology Groups with Torsion". Acta Applicandae Mathematicae. 124 (1): 43–54. arXiv:1012.4169. doi:10.1007/s10440-012-9769-0. ISSN 0167-8019. S2CID 4809929.
Lesnick, Michael (2015-03-24). "The Theory of the Interleaving Distance on Multidimensional Persistence Modules". Foundations of Computational Mathematics. 15 (3): 613–650. arXiv:1106.5305. doi:10.1007/s10208-015-9255-y. ISSN 1615-3375. S2CID 17184609.
Bubenik, Peter; Scott, Jonathan A. (2014-01-28). "Categorification of Persistent Homology". Discrete & Computational Geometry. 51 (3): 600–627. arXiv:1205.3669. doi:10.1007/s00454-014-9573-x. ISSN 0179-5376. S2CID 11056619.
d'Amico, Michele; Frosini, Patrizio; Landi, Claudia (2008-10-14). "Natural Pseudo-Distance and Optimal Matching between Reduced Size Functions". Acta Applicandae Mathematicae. 109 (2): 527–554. arXiv:0804.3500. Bibcode:2008arXiv0804.3500D. doi:10.1007/s10440-008-9332-1. ISSN 0167-8019. S2CID 1704971.
Di Fabio, B.; Frosini, P. (2013-08-01). "Filtrations induced by continuous functions". Topology and Its Applications. 160 (12): 1413–22. arXiv:1304.1268. Bibcode:2013arXiv1304.1268D. doi:10.1016/j.topol.2013.05.013. S2CID 13971804.
Lesnick, Michael (2012-06-06). "Multidimensional Interleavings and Applications to Topological Inference". arXiv:1206.1365 [math.AT].
Chazal, Frederic; de Silva, Vin; Glisse, Marc; Oudot, Steve (2012-07-16). "The structure and stability of persistence modules". arXiv:1207.3674 [math.AT].
Crawley-Boevey, William (2015). "Decomposition of pointwise finite-dimensional persistence modules". Journal of Algebra and Its Applications. 14 (5): 1550066. arXiv:1210.0819. doi:10.1142/s0219498815500668. S2CID 119635797.
Chazal, Frederic; Crawley-Boevey, William; de Silva, Vin (2014-05-22). "The observable structure of persistence modules". arXiv:1405.5644 [math.RT].
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Turner, Katharine; Mileyko, Yuriy; Mukherjee, Sayan; Harer, John (2014-07-12). "Fréchet Means for Distributions of Persistence Diagrams". Discrete & Computational Geometry. 52 (1): 44–70. arXiv:1206.2790. doi:10.1007/s00454-014-9604-7. ISSN 0179-5376. S2CID 14293062.
Robinson, Andrew; Turner, Katharine (2013-10-28). "Hypothesis Testing for Topological Data Analysis". arXiv:1310.7467 [stat.AP].
Fasy, Brittany Terese; Lecci, Fabrizio; Rinaldo, Alessandro; Wasserman, Larry; Balakrishnan, Sivaraman; Singh, Aarti (2014-12-01). "Confidence sets for persistence diagrams". The Annals of Statistics. 42 (6): 2301–39. arXiv:1303.7117. doi:10.1214/14-AOS1252. ISSN 0090-5364.
Blumberg, Andrew J.; Gal, Itamar; Mandell, Michael A.; Pancia, Matthew (2014-05-15). "Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces". Foundations of Computational Mathematics. 14 (4): 745–789. arXiv:1206.4581. doi:10.1007/s10208-014-9201-4. ISSN 1615-3375. S2CID 17150103.
Baudot, Pierre (2019). "Elements of qualitative cognition: an Information Topology Perspective". Physics of Life Reviews. 31: 263–275. arXiv:1807.04520. Bibcode:2019PhLRv..31..263B. doi:10.1016/j.plrev.2019.10.003. PMID 31679788. S2CID 207897618.
Bubenik, Peter (2012-07-26). "Statistical topological data analysis using persistence landscapes". arXiv:1207.6437 [math.AT].
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Hiraoka, Yasuaki; Nakamura, Takenobu; Hirata, Akihiko; Escolar, Emerson G.; Matsue, Kaname; Nishiura, Yasumasa (2016-06-28). "Hierarchical structures of amorphous solids characterized by persistent homology". Proceedings of the National Academy of Sciences. 113 (26): 7035–40. arXiv:1501.03611. Bibcode:2016PNAS..113.7035H. doi:10.1073/pnas.1520877113. ISSN 0027-8424. PMC 4932931. PMID 27298351.
Nakamura, Takenobu; Hiraoka, Yasuaki; Hirata, Akihiko; Escolar, Emerson G.; Nishiura, Yasumasa (2015-02-26). "Persistent Homology and Many-Body Atomic Structure for Medium-Range Order in the Glass". Nanotechnology. 26 (30): 304001. arXiv:1502.07445. Bibcode:2015Nanot..26D4001N. doi:10.1088/0957-4484/26/30/304001. PMID 26150288. S2CID 7298655.
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Taylor, D.; al, et. (2015-08-21). "Topological data analysis of contagion maps for examining spreading processes on networks". Nature Communications. 6 (6): 7723. arXiv:1408.1168. Bibcode:2015NatCo...6.7723T. doi:10.1038/ncomms8723. ISSN 2041-1723. PMC 4566922. PMID 26194875.
Li, Xiaoyun; Wu, Chenxi; Li, Ping (2020). "IVFS: Simple and Efficient Feature Selection for High Dimensional Topology Preservation". Proceedings of the AAAI Conference on Artificial Intelligence. 34 (4): 4747–4754. arXiv:2004.01299. doi:10.1609/aaai.v34i04.5908.
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Frosini, Patrizio; Landi, Claudia (2011). "Uniqueness of models in persistent homology: the case of curves". Inverse Problems. 27 (12): 124005. arXiv:1012.5783. Bibcode:2011InvPr..27l4005F. doi:10.1088/0266-5611/27/12/124005. S2CID 16636182.
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berkeley.edu

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books.google.com

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doi.org

Epstein, Charles; Carlsson, Gunnar; Edelsbrunner, Herbert (2011-12-01). "Topological data analysis". Inverse Problems. 27 (12): 120201. arXiv:1609.08227. Bibcode:2011InvPr..27a0101E. doi:10.1088/0266-5611/27/12/120201. S2CID 250913810.
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