H. Adams, T. Emerson, M. Kirby, R. Neville, C. Peterson et al., Persistence Images: A Stable Vector Representation of Persistent Homology, Journal of Machine Learning Research, vol.18, issue.8, pp.1-35, 2017.

P. Agarwal, K. Fox, A. Nath, A. Sidiropoulos, and Y. Wang, Computing the Gromov-Hausdorff Distance for Metric Trees, Proceedings of the 26th International Symposium on Algorithms and Computation, 2015.
DOI : 10.1007/s10208-004-0145-y

M. Alagappan, From 5 to 13: Redefining the Positions in Basketball, MIT Sloan Sports Analytics Conference, 2012.

V. Barra and S. Biasotti, 3D Shape Retrieval and Classification using Multiple Kernel Learning on Extended Reeb graphs. The Visual Computer, pp.1247-1259, 2014.
DOI : 10.1007/s00371-014-0926-5
URL : https://hal.archives-ouvertes.fr/hal-01621828

H. Bauer, Measure and integration theory, 2001.
DOI : 10.1515/9783110866209

U. Bauer, B. D. Fabio, and C. Landi, An Edit Distance for Reeb Graphs, Proceedings of the Eurographics 2016 Workshop on 3D Object Retrieval, pp.27-34, 2016.

U. Bauer, X. Ge, and Y. Wang, Measuring Distance between Reeb Graphs, Annual Symposium on Computational Geometry, SOCG'14, pp.464-473, 2014.
DOI : 10.1145/2582112.2582169
URL : http://arxiv.org/pdf/1307.2839

U. Bauer, X. Ge, and Y. Wang, Measuring Distance between Reeb Graphs (v2). CoRR, abs, 1307.
DOI : 10.1145/2582112.2582169
URL : http://arxiv.org/pdf/1307.2839

U. Bauer, E. Munch, and Y. Wang, Strong Equivalence of the Interleaving and Functional Distortion Metrics for Reeb Graphs, Proceedings of the 31st Symposium on Computational Geometry, 2015.

C. Berg, J. Christensen, and P. Ressel, Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions, 1984.
DOI : 10.1007/978-1-4612-1128-0

S. Biasotti, D. Giorgi, M. Spagnuolo, and B. Falcidieno, Reeb graphs for shape analysis and applications, Theoretical Computer Science, vol.392, issue.1-3, pp.5-22, 2008.
DOI : 10.1016/j.tcs.2007.10.018
URL : https://doi.org/10.1016/j.tcs.2007.10.018

G. Biau and A. Mas, PCA-Kernel estimation Statistics and Risk Modeling with Applications in Finance and Insurance, pp.19-46, 2012.

E. Bindewald and B. Shapiro, RNA secondary structure prediction from sequence alignments using a network of k-nearest neighbor classifiers, RNA, vol.12, issue.3, pp.342-352, 2006.
DOI : 10.1261/rna.2164906

H. Bjerkevik, Stability of higher-dimensional interval decomposable persistence modules. CoRR, abs, 1609.

G. Blanchard, O. Bousquet, and L. Zwald, Statistical properties of kernel principal component analysis, Machine Learning, pp.259-294, 2007.
DOI : 10.5802/afst.729

A. Blumberg, I. Gall, M. Mandell, and M. Pancia, Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces, Foundations of Computational Mathematics, vol.33, issue.4, pp.745-789, 2014.
DOI : 10.1007/s00454-004-1146-y

M. Botnan and M. Lesnick, Algebraic Stability of Zigzag Persistence Modules. CoRR, abs, 1604.

A. Bronstein, M. Bronstein, and R. Kimmel, Numerical Geometry of Non-Rigid Shapes, 2008.
DOI : 10.1007/978-0-387-73301-2

P. Bubenik, Statistical Topological Data Analysis using Persistence Landscapes, Journal of Machine Learning Research, vol.16, pp.77-102, 2015.

M. Buchet, F. Chazal, S. Oudot, and D. Sheehy, Efficient and Robust Persistent Homology for Measures, Proceedings of the 26th Symposium on Discrete Algorithms, pp.168-180, 2015.
DOI : 10.1137/1.9781611973730.13
URL : https://hal.archives-ouvertes.fr/hal-01342385

D. Burago, Y. Burago, and S. Ivanov, A Course in Metric Geometry, 2001.
DOI : 10.1090/gsm/033

F. Cagliari and C. Landi, Finiteness of rank invariants of multidimensional persistent homology groups, Applied Mathematics Letters, vol.24, issue.4, pp.516-518, 2011.
DOI : 10.1016/j.aml.2010.11.004

P. Camara, A. Levine, and R. Rabadan, Inference of Ancestral Recombination Graphs through Topological Data Analysis, PLoS Computational Biology, vol.12, issue.8, pp.1-25, 2016.

Z. Cang and G. Wei, TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions, PLOS Computational Biology, vol.13, issue.2, p.2017
DOI : 10.1371/journal.pcbi.1005690.s004

G. Carlsson, V. De, and S. , Zigzag Persistence, Foundations of Computational Mathematics, vol.33, issue.2, pp.367-405, 2010.
DOI : 10.1007/s00454-002-2885-2
URL : https://link.springer.com/content/pdf/10.1007%2Fs10208-010-9066-0.pdf

G. Carlsson, D. Vin-de-silva, and . Morozov, Zigzag persistent homology and real-valued functions, Proceedings of the 25th annual symposium on Computational geometry, SCG '09, pp.247-256, 2009.
DOI : 10.1145/1542362.1542408
URL : http://math.stanford.edu/comptop/preprints/zigzags-socg-final.pdf

G. Carlsson and A. Zomorodian, The Theory of Multidimensional Persistence, Discrete & Computational Geometry, vol.33, issue.2, pp.71-93, 2009.
DOI : 10.1017/CBO9781139644136

. Mathieucarrì-ere, Cover complexes, GUDHI User and Reference Manual. GUDHI Editorial Board, 2017.

. Mathieucarrì-ere, Kernels for persistence diagrams, GUDHI User and Reference Manual. GUDHI Editorial Board, 2017.

M. Mathieucarrì-ere, S. Cuturi, and . Oudot, Sliced Wasserstein Kernel for Persistence Diagrams, Proceedings of the 34th International Conference on Machine Learning, 2017.

B. Mathieucarrì-ere, S. Michel, and . Oudot, Statistical Analysis and Parameter Selection for Mapper. CoRR, abs, 1706.

S. Mathieucarrì-ere and . Oudot, Structure and Stability of the 1-Dimensional Mapper. CoRR, abs, 1511.

S. Mathieucarrì-ere and . Oudot, Structure and Stability of the 1-Dimensional Mapper, Proceedings of the 32nd Symposium on Computational Geometry, pp.1-2516, 2016.

S. Mathieucarrì-ere and . Oudot, Local Equivalence and Induced Metrics for Reeb Graphs, Proceedings of the 33rd Symposium on Computational Geometry, 2017.

S. Mathieucarrì-ere, M. Oudot, and . Ovsjanikov, Local Signatures using Persistence Diagrams, 2015.

S. Mathieucarrì-ere, M. Oudot, and . Ovsjanikov, Stable Topological Signatures for Points on 3D Shapes, Computer Graphics Forum, vol.34, 2015.

J. Chan, G. Carlsson, and R. Rabadan, Topology of viral evolution, Proceedings of the National Academy of Science, pp.18556-18571, 2013.
DOI : 10.1099/vir.0.19277-0

C. Chang and C. Lin, LIBSVM, ACM Transactions on Intelligent Systems and Technology, vol.2, issue.3, pp.1-27, 2011.
DOI : 10.1145/1961189.1961199

F. Chazal, D. Cohen-steiner, M. Glisse, L. Guibas, and S. Oudot, Proximity of persistence modules and their diagrams, Proceedings of the 25th annual symposium on Computational geometry, SCG '09, pp.237-246, 2009.
DOI : 10.1145/1542362.1542407
URL : https://hal.archives-ouvertes.fr/inria-00292566

F. Chazal, D. Cohen-steiner, L. Guibas, F. Mémoli, and S. Oudot, Gromov-Hausdorff Stable Signatures for Shapes using Persistence, Computer Graphics Forum, vol.33, issue.5, pp.1393-1403, 2009.
DOI : 10.1109/TPAMI.2006.208
URL : https://hal.archives-ouvertes.fr/hal-00772413

F. Chazal, D. Cohen-steiner, and Q. Mérigot, Geometric Inference for Probability Measures, Foundations of Computational Mathematics, vol.40, issue.2, pp.733-751, 2011.
DOI : 10.1090/gsm/058
URL : https://hal.archives-ouvertes.fr/hal-00772444

F. Chazal, M. Vin-de-silva, S. Glisse, and . Oudot, The Structure and Stability of Persistence Modules, 2016.
DOI : 10.1007/978-3-319-42545-0
URL : https://hal.archives-ouvertes.fr/hal-01107617

F. Chazal, B. Fasy, F. Lecci, B. Michel, A. Rinaldo et al., Robust topological inference: distance to a measure and kernel distance. CoRR, abs/1412, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01232217

F. Chazal, B. Fasy, F. Lecci, B. Michel, A. Rinaldo et al., Subsampling Methods for Persistent Homology, Proceedings of the 32nd International Conference on Machine Learning, pp.2143-2151, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01073073

F. Chazal, M. Glisse, C. , and B. Michel, Optimal rates of convergence for persistence diagrams in Topological Data Analysis, 1305.
URL : https://hal.archives-ouvertes.fr/hal-00827162

F. Chazal, M. Glisse, C. , and B. Michel, Convergence rates for persistence diagram estimation in topological data analysis, Journal of Machine Learning Research, vol.16, pp.3603-3635, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01284275

F. Chazal, L. Guibas, S. Oudot, and P. Skraba, Analysis of scalar fields over point cloud data, Proceedings of the 20th Symposium on Discrete Algorithm, pp.1021-1030, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00294591

F. Chazal, P. Massart, and B. Michel, Rates of convergence for robust geometric inference, Electronic Journal of Statistics, vol.10, issue.2, pp.2243-2286, 2016.
DOI : 10.1214/16-EJS1161
URL : https://hal.archives-ouvertes.fr/hal-01157551

X. Chen, A. Golovinskiy, and T. Funkhouser, A Benchmark for 3D Mesh Segmentation, ACM Transactions on Graphics, vol.28, issue.3, pp.1-12, 2009.

J. Cochoy and S. Oudot, Decomposition of exact pfd persistence bimodules . CoRR, abs, 1605.

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/s00454-002-2885-2

E. Colin-deverdì-ere, G. Ginot, and X. Goaoc, Multinerves and helly numbers of acyclic families, Proceedings of the 2012 symposuim on Computational Geometry, SoCG '12, pp.209-218, 2012.
DOI : 10.1145/2261250.2261282

E. Corman, M. Ovsjanikov, and A. Chambolle, Supervised Descriptor Learning for Non-Rigid Shape Matching, Proceedings of the 6th Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment, 2014.
DOI : 10.1007/978-3-319-16220-1_20
URL : http://www.lix.polytechnique.fr/%7Emaks/papers/learning.pdf

A. Cuevas, Set Estimation, pp.71-85, 2009.
DOI : 10.1093/acprof:oso/9780199232574.003.0011

A. Cuevas and A. Rodríguez, On boundary estimation, Advances in Applied Probability, pp.340-354, 2004.

N. Dalal and B. Triggs, Histograms of Oriented Gradients for Human Detection, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), pp.886-893, 2005.
DOI : 10.1109/CVPR.2005.177
URL : https://hal.archives-ouvertes.fr/inria-00548512

E. Vin-de-silva, A. Munch, and . Patel, Categorified Reeb Graphs, Discrete & Computational Geometry, vol.130, issue.14, pp.854-906, 2016.
DOI : 10.1063/1.3103496

R. Devore and G. Lorentz, Constructive approximation, 1993.

T. Dey, F. Fan, and Y. Wang, Graph Induced Complex on Point Data, Proceedings of the 29th Symposium on Computational Geometry, pp.107-116, 2013.
DOI : 10.1145/2462356.2462387

T. Dey and Y. Wang, Reeb graphs, Proceedings of the 27th annual ACM symposium on Computational geometry, SoCG '11, pp.46-73, 2013.
DOI : 10.1145/1998196.1998230

B. Di, F. , and M. Ferri, Comparing persistence diagrams through complex vectors, 2015.

B. Di, F. , and C. Landi, The Edit Distance for Reeb Graphs of Surfaces, Discrete and Computational Geometry, vol.55, issue.2, pp.423-461, 2016.

P. Dlotko, Cubical complex, GUDHI User and Reference Manual. GUDHI Editorial Board, 2015.

H. Edelsbrunner and J. Harer, Jacobi sets of multiple Morse functions, Foundations of Computational Mathematics, pp.37-57, 2002.

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

H. Edelsbrunner, J. Harer, and A. Patel, Reeb spaces of piecewise linear mappings, Proceedings of the twenty-fourth annual symposium on Computational geometry , SCG '08, pp.242-250, 2008.
DOI : 10.1145/1377676.1377720

B. Fasy, F. Lecci, A. Rinaldo, L. Wasserman, S. Balakrishnan et al., Confidence Sets for Persistence Diagrams. The Annals of Statistics, pp.2301-2339, 2014.
DOI : 10.1214/14-aos1252
URL : http://arxiv.org/pdf/1303.7117

J. Friedman, T. Hastie, and R. Tibshirani, The Elements of Statistical Learning, 2001.

M. Gameiro, Y. Hiraoka, and I. Obayashi, Continuation of point clouds via persistence diagrams, Physica D: Nonlinear Phenomena, vol.334, pp.118-132, 2016.
DOI : 10.1016/j.physd.2015.11.011

X. Ge, I. Safa, M. Belkin, and Y. Wang, Data Skeletonization via Reeb Graphs, Advances in Neural Information Processing Systems 24, pp.837-845, 2011.

C. Genovese, M. Perone-pacifico, I. Verdinelli, and L. Wasserman, Manifold estimation and singular deconvolution under Hausdorff loss. The Annals of Statistics, pp.941-963, 2012.
DOI : 10.1214/12-aos994
URL : http://doi.org/10.1214/12-aos994

C. Genovese, M. Perone-pacifico, I. Verdinelli, and L. Wasserman, Minimax Manifold Estimation, Journal of Machine Learning Research, vol.13, pp.1263-1291, 2012.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning, 2016.

S. Goodwin, J. Mcpherson, and R. Mccombie, Coming of age: ten years of next-generation sequencing technologies, Nature Reviews Genetics, vol.4, issue.6, pp.333-351, 2016.
DOI : 10.1111/j.1755-0998.2011.03024.x

Z. Guo, L. Zhang, and D. Zhang, A completed modeling of local binary pattern operator for texture classification, IEEE Transaction on Image Processing, pp.1657-1663, 2010.

H. Harrington, N. Otter, H. Schenck, and U. Tillmann, Stratifying multiparameter persistent homology. CoRR, abs, 1708.

W. Harvey, Y. Wang, and R. Wenger, A randomized O(m log m) time algorithm for computing Reeb graphs of arbitrary simplicial complexes, Proceedings of the 26th Symposium on Computational Geometry, pp.267-276, 2010.

J. Hertzsch, R. Sturman, and S. Wiggins, DNA Microarrays: Design Principles for Maximizing Ergodic, Chaotic Mixing, Small, vol.4, issue.2, pp.202-218, 2007.
DOI : 10.1007/978-1-4757-3896-4

T. Hinks, X. Zhou, K. Staples, B. Dimitrov, A. Manta et al., Innate and adaptive T cells in asthmatic patients: Relationship to severity and disease mechanisms, Journal of Allergy and Clinical Immunology, vol.136, issue.2, pp.323-333, 2015.
DOI : 10.1016/j.jaci.2015.01.014

Y. Hiraoka, T. Nakamura, A. Hirata, E. Escolar, K. Matsue et al., Hierarchical structures of amorphous solids characterized by persistent homology, Proceedings of the National Academy of Science, 2016.
DOI : 10.1006/jcph.1995.1039

C. Hofer, R. Kwitt, M. Niethammer, and A. Uhl, Deep Learning with Topological Signatures, Accepted to Advances in Neural Information Processing Systems 30, 2017.

A. Johnson and M. Hebert, Using spin images for efficient object recognition in cluttered 3D scenes, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.21, issue.5, pp.433-449, 1999.
DOI : 10.1109/34.765655

E. Kalogerakis, A. Hertzmann, and K. Singh, Learning 3D Mesh Segmentation and Labeling, ACM Transactions on Graphics, vol.29, issue.4, p.102, 2010.
DOI : 10.1145/1833351.1778839
URL : http://www.cs.jhu.edu/%7Emisha/ReadingSeminar/Papers/Kalogerakis10.pdf

M. Kim, B. Hur, and S. Kim, RDDpred: a condition-specific RNA-editing prediction model from RNA-seq data, BMC Genomics, vol.39, issue.suppl 1, p.2016
DOI : 10.1093/nar/gkq1019

A. Krizhevsky, Learning multiple layers of features from tiny images, 2009.

G. Kusano, K. Fukumizu, and Y. Hiraoka, Persistence Weighted Gaussian Kernel for Topological Data Analysis, Proceedings of the 33rd International Conference on Machine Learning, pp.2004-2013, 2016.

G. Kusano, K. Fukumizu, and Y. Hiraoka, Kernel method for persistence diagrams via kernel embedding and weight factor, 1706.

R. Kwitt, S. Huber, M. Niethammer, W. Lin, and U. Bauer, Statistical Topological Data Analysis -A Kernel Perspective, Advances in Neural Information Processing Systems 28, pp.3070-3078, 2015.

Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, Gradient-based learning applied to document recognition, Proceedings of the IEEE, pp.2278-2324, 1998.
DOI : 10.1109/5.726791
URL : http://www.cs.berkeley.edu/~daf/appsem/Handwriting/papers/00726791.pdf

C. Li, M. Ovsjanikov, and F. Chazal, Persistence-Based Structural Recognition, 2014 IEEE Conference on Computer Vision and Pattern Recognition, 2003.
DOI : 10.1109/CVPR.2014.257
URL : https://hal.archives-ouvertes.fr/hal-01073075

J. Liu, S. Jeng, and Y. Yang, Applying Topological Persistence in Convolutional Neural Network for Music Audio Signals, 1608.

D. Lowe, Distinctive Image Features from Scale-Invariant Keypoints, International Journal of Computer Vision, vol.60, issue.2, pp.91-110, 2004.
DOI : 10.1023/B:VISI.0000029664.99615.94
URL : http://www.cs.ubc.ca/~lowe/papers/ijcv03.ps

P. Lum, G. Singh, A. Lehman, T. Ishkanov, M. Vejdemo-johansson et al., Extracting insights from the shape of complex data using topology, Scientific Reports, vol.2, issue.1, 2013.
DOI : 10.1002/wics.101

S. Mallat, A Wavelet Tour of Signal Processing, 2008.

C. Maria, Persistent cohomology, GUDHI User and Reference Manual. GUDHI Editorial Board, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00761468

M. Metzker, Sequencing technologies ??? the next generation, Nature Reviews Genetics, vol.37, issue.1, pp.31-46, 2010.
DOI : 10.1016/j.tig.2007.12.006

W. Mohamed and A. B. Hamza, Reeb graph path dissimilarity for 3d object matching and retrieval. The Visual Computer, pp.305-318, 2012.
DOI : 10.1007/s00371-011-0640-5

V. Morariu, B. Srinivasan, V. Raykar, R. Duraiswami, and L. Davis, Automatic online tuning for fast Gaussian summation, Advances in Neural Information Processing Systems 21, pp.1113-1120, 2009.

D. Morozov, Homological Illusions of Persistence and Stability, 2008.

T. Mukasa, S. Nobuhara, A. Maki, and T. Matsuyama, Finding Articulated Body in Time-Series Volume Data, Proceedings of the 4th International Conference on Articulated Motion and Deformable Objects, pp.395-404, 2006.
DOI : 10.1007/11789239_41

E. Munch and B. Wang, Convergence between Categorical Representations of Reeb Space and Mapper, Proceedings of the 32nd Symposium on Computational Geometry, pp.1-5316, 2016.

J. Munkres, Elements of Algebraic Topology, 1993.

S. Nene, S. Nayar, and H. Murase, Columbia Object Image Library (COIL-100), 1996.

M. Nicolau, A. Levine, and G. Carlsson, Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival, Proceedings of the National Academy of Sciences, vol.30, issue.16, pp.7265-7270, 2011.
DOI : 10.1128/MCB.01284-09

J. Nielson, J. Paquette, A. Liu, C. Guandique, A. Tovar et al., Topological data analysis for discovery in preclinical spinal cord injury and traumatic brain injury, Nature Communications, vol.21, issue.1, 2015.
DOI : 10.1089/neu.2004.21.1601

S. Ohta, Gradient flows on Wasserstein spaces over compact Alexandrov spaces, American Journal of Mathematics, vol.131, issue.2, pp.475-516, 2009.
DOI : 10.1353/ajm.0.0048

S. Ohta, Barycenters in Alexandrov spaces of curvature bounded below Advances in Geometry, pp.571-587, 2012.

T. Ojala, T. Mäenpää, M. Pietikäinen, J. Viertola, J. Kyllönen et al., Outex - new framework for empirical evaluation of texture analysis algorithms, Object recognition supported by user interaction for service robots, pp.701-706, 2002.
DOI : 10.1109/ICPR.2002.1044854

S. Oudot, Persistence Theory: From Quiver Representations to Data Analysis. Number 209 in Mathematical Surveys and Monographs, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01247501

M. Ovsjanikov, M. Ben-chen, J. Solomon, A. Butscher, and L. Guibas, Functional maps, ACM Transactions on Graphics, vol.31, issue.4, p.30, 2012.
DOI : 10.1145/2185520.2185526
URL : https://hal.archives-ouvertes.fr/hal-01664767

G. Valerio-pascucci and . Scorzelli, Peer-Timo Bremer, and Ajith Mascarenhas. Robust On-line Computation of Reeb Graphs: Simplicity and Speed, Proceedings of ACM SIGGRAPH, 2007.

J. Rabin, G. Peyré, J. Delon, and M. Bernot, Wasserstein Barycenter and Its Application to Texture Mixing, International Conference on Scale Space and Variational Methods in Computer Vision, pp.435-446, 2011.
DOI : 10.1109/18.119725
URL : https://hal.archives-ouvertes.fr/hal-00476064/document

A. Rahimi and B. Recht, Random Features for Large-Scale Kernel Machines, Advances in Neural Information Processing Systems, pp.1177-1184, 2008.

G. Reaven and R. Miller, An attempt to define the nature of chemical diabetes using a multidimensional analysis, Diabetologia, vol.13, issue.1, pp.17-24, 1979.
DOI : 10.1007/BF00423145

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), 1412.
DOI : 10.1109/CVPR.2015.7299106

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), 2015.
DOI : 10.1109/CVPR.2015.7299106

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, pp.1-186, 2016.
DOI : 10.1016/j.physd.2016.03.007

M. Rucco, E. Merelli, D. Herman, D. Ramanan, T. Petrossian et al., Using topological data analysis for diagnosis pulmonary embolism, Journal of Theoretical and Applied Computer Science, vol.9, issue.1, pp.41-55, 2015.

B. Russell, A. Torralba, K. Murphy, and W. Freeman, LabelMe: A Database and Web-Based Tool for Image Annotation, International Journal of Computer Vision, vol.3, issue.1, pp.157-173, 2008.
DOI : 10.1007/s11263-007-0090-8
URL : http://staff.science.uva.nl/%7Ecgmsnoek/pub/readinggroup/LabelMe.pdf

F. Santambrogio, Optimal transport for applied mathematicians, 2015.
DOI : 10.1007/978-3-319-20828-2
URL : https://link.springer.com/content/pdf/bfm%3A978-3-319-20828-2%2F1.pdf

G. Sarikonda, J. Pettus, S. Phatak, S. Sachithanantham, J. Miller et al., CD8 T-cell reactivity to islet antigens is unique to type 1 while CD4 T-cell reactivity exists in both type 1 and type 2 diabetes, Journal of Autoimmunity, vol.50, pp.77-82, 2014.
DOI : 10.1016/j.jaut.2013.12.003

B. Schölkopf, R. Herbrich, and A. Smola, A Generalized Representer Theorem, Proceedings of the 14th Annual Conference on Computational Learning Theory, pp.416-426, 2001.
DOI : 10.1007/3-540-44581-1_27

J. Shawe-taylor and N. Cristianini, Kernel Methods for Pattern Analysis, 2004.
DOI : 10.1017/CBO9780511809682

J. Shawe-taylor, C. Williams, N. Cristianini, and J. Kandola, On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel-PCA, IEEE Transactions on Information Theory, vol.51, issue.7, pp.2510-2522, 2005.
DOI : 10.1109/TIT.2005.850052

G. Singh, F. Mémoli, and G. Carlsson, Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition, Symposium on Point Based Graphics, pp.91-100, 2007.

G. Soumya and J. Shibily, Text Classification by Augmenting Bag of Words (BOW) Representation with Co-occurrence Feature, IOSR Journal of Computer Engineering, vol.16, pp.34-38, 2014.

W. Sutherland, Introduction to Metric and Topological Spaces, 2009.

J. Tenenbaum, J. Vin-de-silva, and . Langford, A Global Geometric Framework for Nonlinear Dimensionality Reduction, Science, vol.290, issue.5500, p.290, 2000.
DOI : 10.1126/science.290.5500.2319

J. Tierny and H. Carr, Jacobi Fiber Surfaces for Bivariate Reeb Space Computation, IEEE Transactions on Visualization and Computer Graphics, vol.23, issue.1, pp.960-969, 2017.
DOI : 10.1109/TVCG.2016.2599017
URL : https://hal.archives-ouvertes.fr/hal-01349907

J. Tierny, D. Guenther, and V. Pascucci, Optimal General Simplification of Scalar Fields on Surfaces, Topological and Statistical Methods for Complex Data, 2015.
DOI : 10.1007/978-3-662-44900-4_4
URL : https://hal.archives-ouvertes.fr/hal-01206848

J. Tierny, J. Vandeborre, and M. Daoudi, Invariant High Level Reeb Graphs of 3D Polygonal Meshes, Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06), pp.105-112, 2006.
DOI : 10.1109/3DPVT.2006.84
URL : https://hal.archives-ouvertes.fr/hal-00725581

K. Turner, Y. Mileyko, S. Mukherjee, and J. Harer, Fr??chet Means for Distributions of Persistence Diagrams, Discrete & Computational Geometry, vol.11, issue.4, pp.44-70, 2014.
DOI : 10.4310/SDG.2006.v11.n1.a6

C. Villani, Optimal transport : old and new, 2009.
DOI : 10.1007/978-3-540-71050-9

Y. Yao, J. Sun, X. Huang, G. Bowman, G. Singh et al., Topological methods for exploring low-density states in biomolecular folding pathways, The Journal of Chemical Physics, vol.222, issue.14, p.130, 2009.
DOI : 10.1021/bi992297n