A. Adcock, E. Carlsson, and G. Carlsson, The ring of algebraic functions on persistence bar codes, Homology, Homotopy and Applications, vol.18, issue.1
DOI : 10.4310/HHA.2016.v18.n1.a21

K. Pankaj, A. Agarwal, M. Efrat, and . Sharir, Vertical decomposition of shallow levels in 3-dimensional arrangements and its applications, SIAM J. Comput, vol.29, pp.39-50, 1999.

U. Bauer, M. Kerber, and J. Reininghaus, PHAT (Persistent Homology Algorithm Toolbox), accessed 11, 2013.
DOI : 10.1007/978-3-662-44199-2_24

P. Bendich, J. S. Marron, E. Miller, A. Pieloch, and S. Skwerer, Persistent homology analysis of brain artery trees, The Annals of Applied Statistics, vol.10, issue.1, p.2014
DOI : 10.1214/15-AOAS886SUPP

P. Bubenik, Statistical topological data analysis using persistence landscapes, Journal of Machine Learning Research, vol.16, pp.77-102, 2015.

P. Bubenik and J. A. Scott, Categorification of Persistent Homology, Discrete & Computational Geometry, vol.33, issue.2, pp.600-627, 2014.
DOI : 10.1007/s00454-014-9573-x

G. Carlsson, Topology and data, Bulletin of the American Mathematical Society, vol.46, issue.2, pp.255-308, 2009.
DOI : 10.1090/S0273-0979-09-01249-X

G. Carlsson, T. Ishkhanov, V. De-silva, and A. Zomorodian, On the Local Behavior of Spaces of Natural Images, International Journal of Computer Vision, vol.265, issue.4, pp.1-12, 2008.
DOI : 10.1007/s11263-007-0056-x

M. Carrire, S. Y. Oudot, and M. Ovsjanikov, Stable Topological Signatures for Points on 3D Shapes, Eurographics Symposium on Geometry Processing 2015, 2015.
DOI : 10.1111/cgf.12692

F. Chazal, B. T. Fasy, F. Lecci, B. Michel, A. Rinaldo et al., Subsampling methods for persistent homology
URL : https://hal.archives-ouvertes.fr/hal-01073073

F. Chazal, B. T. Fasy, F. Lecci, A. Rinaldo, A. Singh et al., On the bootstrap for persistence diagrams and landscapes. Modeling and Analysis of Information Systems, pp.96-105, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00879982

F. Chazal, M. Vin-de-silva, S. Glisse, and . Oudot, The structure and stability of persistence modules. arXiv:1207, pp.3674-2012
URL : https://hal.archives-ouvertes.fr/hal-01107617

S. Chepushtanova, T. Emerson, E. Hanson, M. Kirby, F. Motta et al., Persistence images: An alternative persistent homology representation

M. K. Chung, P. Bubenik, and P. T. Kim, Persistence Diagrams of Cortical Surface Data, Information Processing in Medical Imaging (IPMI) 2009, pp.386-397, 2009.
DOI : 10.1007/s00454-004-1146-y

D. Cohen-steiner, H. Edelsbrunner, and J. Harer, Stability of Persistence Diagrams, Discrete & Computational Geometry, vol.37, issue.1, pp.103-120, 2007.
DOI : 10.1007/s00454-006-1276-5

D. Cohen-steiner, H. Edelsbrunner, and J. Harer, Extending Persistence Using Poincar?? and Lefschetz Duality, Foundations of Computational Mathematics, vol.33, issue.1, pp.79-103, 2009.
DOI : 10.1007/s10208-008-9027-z
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.538.5795

D. Cohen-steiner, H. Edelsbrunner, J. Harer, and Y. Mileyko, Lipschitz Functions Have L p -Stable Persistence, Foundations of Computational Mathematics, vol.33, issue.2, pp.127-139, 2010.
DOI : 10.1007/s10208-010-9060-6

C. Cortes and V. Vapnik, Support-vector networks, Machine Learning, 1995.
DOI : 10.1007/BF00994018

V. De-silva and R. Ghrist, Coverage in sensor networks via persistent homology, Algebraic & Geometric Topology, vol.7, issue.1, pp.339-358, 2007.
DOI : 10.2140/agt.2007.7.339

B. , D. Fabio, and M. Ferri, Comparing persistence diagrams through complex vectors, 2015.

P. Donatini, P. Frosini, and A. Lovato, Size functions for signature recognition Vision Geometry VII, Proceedings of the SPIE's Workshop, pp.178-183, 1998.

H. Edelsbrunner and J. Harer, Computational Topology, 2010.
DOI : 10.1090/mbk/069

H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological persistence and simplification, Discrete & Computational Geometry, issue.28, pp.511-533, 2002.

A. Efrat, A. Itai, and M. J. Katz, Geometry Helps in Bottleneck Matching and Related Problems, Algorithmica, vol.31, issue.1, 2001.
DOI : 10.1007/s00453-001-0016-8

B. T. Fasy, J. Kim, F. Lecci, and C. Maria, Introduction to the r package tda, p.2014
URL : https://hal.archives-ouvertes.fr/hal-01113028

B. T. Fasy, F. Lecci, A. Rinaldo, L. Wasserman, S. Balakrishnan et al., Confidence sets for persistence diagrams, The Annals of Statistics, vol.42, issue.6, pp.2301-2339, 2014.
DOI : 10.1214/14-AOS1252SUPP
URL : http://arxiv.org/abs/1303.7117

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, pp.329-337, 1998.
DOI : 10.1007/3-540-63930-6_138

J. Gamble and G. Heo, Exploring uses of persistent homology for statistical analysis of landmark-based shape data, Journal of Multivariate Analysis, vol.101, issue.9, pp.2184-2199, 2010.
DOI : 10.1016/j.jmva.2010.04.016

R. Ghrist, Barcodes: The persistent topology of data, Bulletin of the American Mathematical Society, vol.45, issue.01, pp.61-75, 2008.
DOI : 10.1090/S0273-0979-07-01191-3

J. Hershberger, Finding the upper envelope of n line segments in O(n log n) time, Information Processing Letters, vol.33, issue.4, p.169174, 1989.
DOI : 10.1016/0020-0190(89)90136-1

J. Hershberger, Upper envelope onion peeling, Lecture Notes in Computer Science, vol.447, pp.368-379, 1990.
DOI : 10.1007/3-540-52846-6_105

M. Kahle and E. Meckes, Limit theorems for Betti numbers of random simplicial complexes, Homology, Homotopy and Applications, vol.15, issue.1, 2015.
DOI : 10.4310/HHA.2013.v15.n1.a17

C. Maria, GUDHI, Simplicial Complexes and Persistent Homology Packages, 2014.

K. Mischaikow and V. Nanda, Morse Theory for Filtrations and Efficient Computation of Persistent Homology, Discrete & Computational Geometry, vol.37, issue.10, pp.330-353, 2013.
DOI : 10.1007/s00454-013-9529-6

D. Morozov, The Dionysus software project, 2013.

V. Nanda, The Perseus software project, 2013.

M. Nicolau, A. J. Levine, and G. Carlsson, Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival, Proc. Nat. Acad. Sci, pp.7265-7270, 2011.
DOI : 10.1073/pnas.1102826108

V. K. Nikolic, G. Heo, D. Nikoli´cnikoli´c, and P. Bubenik, Using cycles in high dimensional data to analyze protein binding

J. Perea and J. Harer, Sliding windows and persistence: An application of topological methods to signal analysis. arXiv:1307, p.6188

J. Reininghaus, S. Huber, U. Bauer, and R. Kwitt, A stable multi-scale kernel for topological machine learning, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), p.2014
DOI : 10.1109/CVPR.2015.7299106
URL : http://arxiv.org/abs/1412.6821

V. Robins and K. Turner, Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids, Physica D: Nonlinear Phenomena, vol.334
DOI : 10.1016/j.physd.2016.03.007

A. Robinson and K. Turner, Hypothesis testing for topological data analysis

K. Turner, Y. Mileyko, S. Mukherjee, and J. Harer, Fr??chet Means for Distributions of Persistence Diagrams, Discrete & Computational Geometry, vol.11, issue.4, 2014.
DOI : 10.1007/s00454-014-9604-7

L. Wasserman, All of statistics Springer Texts in Statistics, 2004.

T. Williams and C. Kelley, Gnuplot 4.5: an interactive plotting program, 2011.

A. Zomorodian and G. Carlsson, Computing persistent homology, Discrete & Computational Geometry, issue.33, pp.249-274, 2005.
DOI : 10.1145/997817.997870
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5064