Universality of persistence diagrams and the bottleneck and Wasserstein distances

Computational Geometry - Tập 105 - Trang 101882 - 2022
Peter Bubenik, Alex Elchesen

Tài liệu tham khảo

Bubenik, 2015, Metrics for generalized persistence modules, Found. Comput. Math., 15, 1501, 10.1007/s10208-014-9229-5 Bubenik Bubenik, 2022, Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces, J. Appl. Comput. Topol., 10.1007/s41468-022-00091-9 Blumberg, 2014, Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces, Found. Comput. Math., 14, 745, 10.1007/s10208-014-9201-4 Bakke Bjerkevik, 2021, On the stability of interval decomposable persistence modules, Discrete Comput. Geom., 66, 92, 10.1007/s00454-021-00298-0 Blumberg Botnan, 2018, Algebraic stability of zigzag persistence modules, Algebraic Geom. Topol., 18, 3133, 10.2140/agt.2018.18.3133 Bauer, 2020, The Reeb graph edit distance is universal, Found. Comput. Math., 1 Bubenik, 2014, Categorification of persistent homology, Discrete Comput. Geom., 51, 600, 10.1007/s00454-014-9573-x Bubenik Chazal, 2009, Proximity of persistence modules and their diagrams Cochoy, 2020, Decomposition of exact pfd persistence bimodules, Discrete Comput. Geom., 63, 255, 10.1007/s00454-019-00165-z Cohen-Steiner, 2007, Stability of persistence diagrams, Discrete Comput. Geom., 37, 103, 10.1007/s00454-006-1276-5 Cohen-Steiner, 2010, Lipschitz functions have Lp-stable persistence, Found. Comput. Math., 10, 127, 10.1007/s10208-010-9060-6 Carlsson, 2004, Persistence barcodes for shapes, 124 Collins, 2004, A barcode shape descriptor for curve point cloud data, Comput. Graph., 28, 881, 10.1016/j.cag.2004.08.015 d'Amico, 2010, Natural pseudo-distance and optimal matching between reduced size functions, Acta Appl. Math., 109, 527, 10.1007/s10440-008-9332-1 Divol, 2021, Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport, J. Appl. Comput. Topol., 5, 1, 10.1007/s41468-020-00061-z Lesnick, 2015, The theory of the interleaving distance on multidimensional persistence modules, Found. Comput. Math., 15, 613, 10.1007/s10208-015-9255-y Lane, 1998, Categories for the Working Mathematician, vol. 5 Riehl, 2017 Skraba Villani, 2003, Topics in Optimal Transportation, vol. 58