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, Harm; Weyman, Jerzy (2005). "Quiver representations" (PDF). Notices of the American Mathematical Society. 52 (2): 200–6.
Weinberger, Shmuel (2011). "What is... persistent homology?" (PDF). Notices of the American Mathematical Society. 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].
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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 and 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].
Droz, Jean-Marie (2012-10-15). "A subset of Euclidean space with large Vietoris-Rips homology". arXiv:1210.4097 [math.GT].
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].
Bubenik, Peter; Dlotko, Pawel (2014-12-31). "A persistence landscapes toolbox for topological statistics". Journal of Symbolic Computation. 78: 91–114. arXiv:1501.00179. Bibcode:2015arXiv150100179B. doi:10.1016/j.jsc.2016.03.009. S2CID 9789489.
Kurlin, V. (2014). "A Fast and Robust Algorithm to Count Topologically Persistent Holes in Noisy Clouds". 2014 IEEE Conference on Computer Vision and Pattern Recognition (PDF). pp. 1458–1463. arXiv:1312.1492. doi:10.1109/CVPR.2014.189. ISBN 978-1-4799-5118-5. S2CID 10118087.
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 of the United States of America. 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.
Gidea, Marian; Katz, Yuri (2018). "Topological data analysis of financial time series: Landscapes of crashes". Physica A: Statistical Mechanics and Its Applications. 491. Elsevier BV: 820–834. arXiv:1703.04385. Bibcode:2018PhyA..491..820G. doi:10.1016/j.physa.2017.09.028. ISSN 0378-4371. S2CID 85550367.
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berkeley.edu

events.berkeley.edu

"UC Berkeley Mathematics Department Colloquium: Persistent homology and applications from PDE to symplectic topology". events.berkeley.edu. Archived from the original on 2021-04-18. Retrieved 2021-03-27.

books.google.com

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doi.org

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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.
Cerri, Andrea; Fabio, Barbara Di; Ferri, Massimo; Frosini, Patrizio; Landi, Claudia (2013-08-01). "Betti numbers in multidimensional persistent homology are stable functions". Mathematical Methods in the Applied Sciences. 36 (12): 1543–57. Bibcode:2013MMAS...36.1543C. doi:10.1002/mma.2704. ISSN 1099-1476. S2CID 9938133.
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worldcat.org

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worldscientific.com

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zenodo.org

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zotero.org

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