H. Adams, S. Chepushtanova, T. Emerson, E. Hanson, M. Kirby, F. Motta, R. Neville, C. Peterson, P. Shipman, and L. Ziegelmeier. Persistence images: A stable vector representation of persistent homology. Journal of Machine Learning Research, 2017.
Dominique Attali, André Lieutier, and David Salinas. Efficient data structure for representing and simplifying simplicial complexes in high dimensions. In Proceedings of the 27th annual ACM symposium on Computational geometry, SoCG '11, pages 501–509, 2011.
Dominique Attali, André Lieutier, and David Salinas. Efficient data structure for representing and simplifying simplicial complexes in high dimensions. Int. J. Comput. Geometry Appl., 22(4):279–304, 2012.
Jean-Daniel Boissonnat and Arijit Ghosh. Manifold reconstruction using tangential delaunay complexes. Discrete & Computational Geometry, 51(1):221–267, 2014.
Jean-Daniel Boissonnat and Karthik C. S. An efficient representation for filtrations of simplicial complexes. CoRR, abs/1607.08449, 2016.
Jean-Daniel Boissonnat and Clément Maria. Computing persistent homology with various coefficient fields in a single pass. Rapport de recherche RR-8436, INRIA, December 2013.
Jean-Daniel Boissonnat and Clément Maria. The simplex tree: An efficient data structure for general simplicial complexes. Algorithmica, pages 1–22, 2014.
Jean-Daniel Boissonnat, Tamal K. Dey, and Clément Maria. The compressed annotation matrix: An efficient data structure for computing persistent cohomology. In ESA, pages 695–706, 2013.
Jean-Daniel Boissonnat, Karthik C. S., and Sébastien Tavenas. Building Efficient and Compact Data Structures for Simplicial Complexes. In Lars Arge and János Pach, editors, 31st International Symposium on Computational Geometry (SoCG 2015), volume 34 of Leibniz International Proceedings in Informatics (LIPIcs), pages 642–656, Dagstuhl, Germany, 2015. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik.
P. Bubenik and P. Dlotko. A persistence landscapes toolbox for topological statistics. Journal of Symbolic Computation., 2016.
P. Bubenik. Statistical topological data analysis using persistence landscapes. Journal of Machine Learning Research, 2015.
Mickaël Buchet, Frédéric Chazal, Steve Y. Oudot, and Donald Sheehy. Efficient and robust persistent homology for measures. Computational Geometry: Theory and Applications, 58:70–96, 2016.
Gunnar E. Carlsson and Vin de Silva. Zigzag persistence. Foundations of Computational Mathematics, 10(4):367–405, 2010.
Mathieu Carrière and Steve Oudot. Structure and stability of the one-dimensional Mapper. Foundations of Computational Mathematics, 18(6):1333–1396, 2017.
M. Carrière, S. Oudot, and M. Ovsjanikov. Stable topological signatures for points on 3d shapes. Proc. Sympos. on Geometry Processing, 2015.
Mathieu Carrière, Marco Cuturi, and Steve Oudot. Sliced Wasserstein kernel for persistence diagrams. In Doina Precup and Yee Whye Teh, editors, Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pages 664–673, International Convention Centre, Sydney, Australia, 06–11 Aug 2017. PMLR.
Mathieu Carrière, Bertrand Michel, and Steve Oudot. Statistical analysis and parameter selection for Mapper. Journal of Machine Learning Research, 19:1–39, 2018.
Nicholas J. Cavanna, Mahmoodreza Jahanseir, and Donald R. Sheehy. A geometric perspective on sparse filtrations. In Proceedings of the Canadian Conference on Computational Geometry, 2015.
Nicholas J. Cavanna, Mahmoodreza Jahanseir, and Donald R. Sheehy. Visualizing sparse filtrations. In Proceedings of the 31st International Symposium on Computational Geometry, 2015.
Oliver A. Chubet, Paul Macnichol, Parth Parikh, Donald R. Sheehy, and Siddharth S. Sheth. Greedy Permutations and Finite Voronoi Diagrams. In Erin W. Chambers and Joachim Gudmundsson, editors, 39th International Symposium on Computational Geometry (SoCG 2023), volume 258 of Leibniz International Proceedings in Informatics (LIPIcs), pages 64:1–64:5, Dagstuhl, Germany, 2023. Schloss Dagstuhl – Leibniz-Zentrum für Informatik.
David Cohen-Steiner, Herbert Edelsbrunner, and Dmitriy Morozov. Vines and vineyards by updating persistence in linear time. In Symposium on Computational Geometry, pages 119–126, 2006.
David Cohen-Steiner, Herbert Edelsbrunner, and John Harer. Extending persistence using Poincaré and Lefschetz duality. Foundations of Computational Mathematics, 9(1):79–103, 2009.
Vin De Silva and Gunnar Carlsson. Topological estimation using witness complexes. Proc. Sympos. Point-Based Graphics, pages 157–166, 2004.
Vin de Silva, Dmitriy Morozov, and Mikael Vejdemo-Johansson. Persistent cohomology and circular coordinates. Discrete & Computational Geometry, 45(4):737–759, 2011.
Olivier Devillers, Samuel Hornus, and Clément Jamin. dD triangulations. In CGAL User and Reference Manual. CGAL Editorial Board, 5.0 edition, 2019.
Tamal Dey, Fengtao Fan, and Yusu Wang. Graph induced complex on point data. In Proceedings of the Twenty-ninth Annual Symposium on Computational Geometry, pages 107–116, 2013.
Tamal K. Dey, Fengtao Fan, and Yusu Wang. Computing topological persistence for simplicial maps. In Symposium on Computational Geometry, page 345, 2014.
P. Donatini, P. Frosini, and A. Lovato. Size functions for signature recognition. Proceedings of SPIE, Vision Geometry VII, vol. 3454, 1998.
Herbert Edelsbrunner and John Harer. Computational Topology - an Introduction. American Mathematical Society, 2010.
Alon Efrat, Alon Itai, and Matthew J. Katz. Geometry helps in bottleneck matching and related problems. Algorithmica, 31(1):1–28, 2001.
B. Fasy, J. Kim, F. Lecci, and C. Maria. Introduction to the r package tda. arXiv:1411.1830., 2016.
M. Ferri, P. Frosini, A. Lovato, and C. Zambelli. Point selection: A new comparison scheme for size functions (with an application to monogram recognition). Proceedings Third Asian Conference on Computer Vision, Lecture Notes in Computer Science 1351., 1998.
Michael Garland and Paul S. Heckbert. Surface simplification using quadric error metrics. In Proceedings of the 24th annual conference on Computer graphics and interactive techniques, SIGGRAPH '97, pages 209–216, New York, NY, USA,
Marc Glisse and Siddharth Pritam. Swap, Shift and Trim to Edge Collapse a Filtration.
Marc Glisse. Fast persistent homology computation for functions on mathbb R, 2023.
Siargey Kachanovich. Meshing submanifolds using Coxeter triangulations. Theses, COMUE Université Côte d'Azur (2015 - 2019), October 2019.
T. Kaczynski, K. Mischaikow, and M. Mrozek. Computational Homology. Applied Mathematical Sciences. Springer New York, 2004.
Michael Kerber, Dmitriy Morozov, and Arnur Nigmetov. Geometry helps to compare persistence diagrams. J. Exp. Algorithmics, 22:1.4:1–1.4:20, September 2017.
G. Kusano, K. Fukumizu, and Y. Hiraoka. Persistence weighted gaussian kernel for topological data analysis. ICML'16 Proceedings of the 33rd International Conference on International Conference on Machine Learning - Volume 48, 2016.
Peter Lindstrom and Greg Turk. Fast and memory efficient polygonal simplification. In Proceedings of the Conference on Visualization '98, VIS '98, pages 279–286, Los Alamitos, CA, USA, 1998. IEEE Computer Society Press.
Clément Maria and Steve Y. Oudot. Zigzag persistence via reflections and transpositions. In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4-6, 2015, pages 181–199. SIAM, 2015.
James R. Munkres. Elements of algebraic topology. Addison-Wesley, 1984.
J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt. A stable multi-scale kernel for topological machine learning. Proc. 2015 IEEE Conf. Comp. Vision & Pat. Rec. (CVPR '15), 2015.
Michael Seel. dD geometry kernel. In CGAL User and Reference Manual. CGAL Editorial Board, 5.0 edition, 2019.
Donald R. Sheehy. Linear-size approximations to the Vietoris-Rips filtration. Discrete & Computational Geometry, 49(4):778–796, 2013.
The CGAL Project. CGAL User and Reference Manual. CGAL Editorial Board, 5.0 edition, 2019.
Hubert Wagner, Chao Chen, and Erald Vucini. Efficient Computation of Persistent Homology for Cubical Data, pages 91–106. Mathematics and Visualization. Springer Berlin Heidelberg, 2012.
Afra Zomorodian and Gunnar E. Carlsson. Computing persistent homology. Discrete & Computational Geometry, 33(2):249–274, 2005.