Proximity of persistence modules and their diagrams

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2009, Pages 237-246

  Chazal, Frédéric ^a   Cohen Steiner, David ^b   Glisse, Marc ^c   Guibas, Leonidas J ^d   Oudot, Steve Y ^a  

^a INRIA SACLAY   (France)

^b INRIA   (France)

^c GIPSA LAB   (France)

^d Stanford University   (United States)

Author keywords

Discretization; Persistence diagram; Stability; Topological data analysis; Topological persistence

Indexed keywords

ALGEBRA; COMPUTATION THEORY; COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS;

CONTINUOUS FUNCTIONS; DISCRETIZATIONS; FUNDAMENTAL PROPERTIES; PERSISTENCE DIAGRAM; REAL-VALUED FUNCTIONS; TOPOLOGICAL DATA ANALYSIS; TOPOLOGICAL PERSISTENCES; TOPOLOGICAL SPACES;

TOPOLOGY;

EID: 70849097151     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1542362.1542407     Document Type: Conference Paper

References (21)

1. D. Attali, M. Glisse, S. Hornus, F. Lazarus, and D. Morozov. Persistence-sensitive simplification of functions on surfaces in linear time. Presented at the workshop TopoInVis'09.
2. P. Bendich, D. Cohen-Steiner, H. Edelsbrunner, J. Harer, and D. Morozov. Inferring local homology from sampled stratiéd spaces. In Proc. 48th Annu. IEEE Sympos. Foundations of Computer Science, pages 536-546, 2007.
3. S. Biasotti, A. Cerri, P. Frosini, D. Giorgi, and C. Landi. Multidimensional size functions for shape comparison. Journal of Mathematical Imaging and Vision, 32:161-179, 2008.
4. F. Cagliari, B. Di Fabio, and M. Ferri. Title: One-dimensional reduction of multidimensional persistent homology. Research report, University of Bologna, February 2007. LANL arXiv:math/0702713v2 [Math.AT].
5. G. Carlsson and A. Zomorodian. The theory of multi-dimensional persistence. In Proc. 23rd ACM Sympos. on Comput. Geom., pages 184-193, 2007.
6. G. Carlsson, A. Zomorodian, A. Collins, and L. Guibas. Persistence barcodes for shapes. Internat. Journal of Shape Modeling, 11:149-187, 2005.
7. F. Chazal and D. Cohen-Steiner. Geometric Inference. submitted as a book chapter, 2007.
8. F. Chazal, D. Cohen-Steiner, M. Glisse, L. J. Guibas, and S. Y. Oudot. Proximity of persistence modules and their diagrams. Research Report 6568, INRIA, November 2008. http://hal.inria.fr/inria-00292566/en/.
9. F. Chazal, L. J. Guibas, S. Y. Oudot, and P. Skraba. Analysis of scalar élds over point cloud data. In Proc. 19th ACM-SIAM Sympos. on Discrete Algorithms, pages 1021-1030, 2009.
10. C. Chen and D. Freedman. Quantifying homology classes. In Proc. 25th Symposium on Theoretical Aspects of Computer Science (STACS), 2008.
11. D. Cohen-Steiner and H. Edelsbrunner. Inequalities for the curvature of curves and surfaces. In Proc. 21st Sympos. on Comput. Geom., pages 272-277, 2005.
12. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer. Stability of persistence diagrams. In Proc. 21st ACM Sympos. Comput. Geom., pages 263-271, 2005.
13. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer. Extending persistence using Poincaré and Lefschetz duality. Found. Comput. Math., 2008. To appear.
14. D. Cohen-Steiner, H. Edelsbrunner, and D. Morozov. Vines and vineyards by updating persistence in linear time. In Proc. 22nd Sympos. on Comput. Geom., pages 119-126, 2006.
15. M. d'Amico, P. Frosini, and C. Landi. Using matching distance in size theory: a survey. Internat. Journal of Imaging Systems and Technology, 16(5):154-161, 2006.
16. M. d'Amico, P. Frosini, and C. Landi. Natural pseudo-distance and optimal matching between reduced size functions. Acta Appl. Math., 2008. Online: http://www.springerlink.com/content/cj84327h4n280144/.
17. H. Edelsbrunner, D. Letscher, and A. Zomorodian. Topological persistence and simplification. Discrete Comput. Geom., 28:511-533, 2002. (Pubitemid 36161396)
18. H. Edelsbrunner, D. Morozov, and V. Pascucci. Persistence-sensitive simplification of functions on 2-manifolds. In Proc. 22nd Sympos. on Comput. Geom., pages 127-134, 2006.
19. A. Hatcher. Algebraic Topology. Cambridge University Press, 2001.
20. D. Morozov. Homological Illusions of Persistence and Stability. Ph.d. dissertation, Department of Computer Science, Duke University, August 2008.
21. A. Zomorodian and G. Carlsson. Computing persistent homology. Discrete Comput. Geom., 33(2):249-274, 2005.