H. Akaike, Information theory and an extension of the maximum likelihood principle, Second International Symposium on Information Theory (Tsahkadsor, pp.267-281, 1971.

S. Arlot and P. Massart, Data-driven calibration of penalties for least-squares regression, J.Mach.Learn.Res, vol.10, pp.245-279, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00287631

M. Aupetit, Learning topology with the generative gaussian graph and the em algorithm, Advances in Neural Information Processing Systems, 2006.

A. Barron, L. Birgé, and P. Massart, Risk bounds for model selection via penalization. Probability Theory and Related Fields, pp.301-413, 1999.

L. Birgé and P. Massart, Gaussian model selection, Journal of the European Mathematical Society, vol.3, issue.3, pp.203-268, 2001.
DOI : 10.1007/s100970100031

L. Birgé and P. Massart, Minimal penalties for Gaussian model selection. Probab. Theory Related Fields, pp.33-73, 2007.

C. M. Bishop, Pattern recognition and machine learning. Information Science and Statistics, 2006.

J. D. Boissonnat, L. J. Guibas, and S. Oudot, Manifold reconstruction in arbitrary dimensions using witness complexes, Proc. 23rd ACM Sympos, pp.194-203, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00488434

K. P. Burnham and D. R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2002.
DOI : 10.1007/b97636

F. Chazal, D. Cohen-steiner, and A. Lieutier, A Sampling Theory for Compact Sets in Euclidean Space, Discrete & Computational Geometry, vol.18, issue.3, p.461, 2009.
DOI : 10.1007/s00454-009-9144-8

URL : https://hal.archives-ouvertes.fr/hal-00864493

F. Chazal and A. Lieutier, Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees, Computational Geometry, vol.40, issue.2, p.156, 2008.
DOI : 10.1016/j.comgeo.2007.07.001

URL : https://hal.archives-ouvertes.fr/hal-00864487

F. Chazal and S. Oudot, Towards persistence-based reconstruction in euclidean spaces, Proceedings of the twenty-fourth annual symposium on Computational geometry , SCG '08, pp.232-241, 2008.
DOI : 10.1145/1377676.1377719

URL : https://hal.archives-ouvertes.fr/inria-00197543

S. Cheng and M. Chiu, Dimension Detection via Slivers, SODA 09: ACM -SIAM Symposium on Discrete Algorithms, pp.1001-1010, 2009.
DOI : 10.1137/1.9781611973068.109

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.215.7639

S. Vin-de, A weak characterisation of the delaunay triangulation, Geometriae Dedicata, vol.135, 2008.

A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society. Series B, vol.39, pp.1-38, 1977.

H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological Persistence and Simplification, Discrete & Computational Geometry, vol.28, issue.4, pp.511-533, 2002.
DOI : 10.1007/s00454-002-2885-2

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.8802

H. Edelsbrunner and E. P. Mücke, Three-dimensional alpha shapes, ACM Transactions on Graphics, vol.13, issue.1, pp.43-72, 1994.
DOI : 10.1145/174462.156635

URL : http://arxiv.org/abs/math/9410208

E. R. Engdahl and A. Villaseñor, Global Seismicity: 1900?1999, Part A International Handbook of Earthquake and Engineering Seismology, chapter 41, pp.665-690, 2002.

P. Gaillard, M. Aupetit, and G. Govaert, Learning topology of a labeled data set with the supervised generative Gaussian graph, Neurocomputing, vol.71, issue.7-9, p.71, 2008.
DOI : 10.1016/j.neucom.2007.12.028

T. Hastie and W. Stuetzle, Principal Curves, Journal of the American Statistical Association, vol.26, issue.406, pp.502-516, 1989.
DOI : 10.1080/03610927508827223

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2001.

A. Hatcher, Algebraic Topology, 2001.

E. Lebarbier, Detecting multiple change-points in the mean of Gaussian process by model selection, Signal Processing, vol.85, issue.4, pp.717-736, 2005.
DOI : 10.1016/j.sigpro.2004.11.012

URL : https://hal.archives-ouvertes.fr/inria-00071847

J. B. Macqueen, Some methods of classification and analysis of multivariate observations, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp.281-297, 1967.

T. M. Martinetz, S. G. Berkovich, and K. J. Schulten, 'Neural-gas' network for vector quantization and its application to time-series prediction, IEEE Transactions on Neural Networks, vol.4, issue.4, pp.558-569, 1993.
DOI : 10.1109/72.238311

P. Massart, Concentration Inequalities and Model Selection, Lecture Notes in Mathematics, 2007.

C. Maugis and B. Michel, Slope heuristics for variable selection and clustering via Gaussian mixtures, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00284620

P. Niyogi, S. Smale, and S. Weinberger, A topological view of unsupervised learning and clustering

P. Niyogi, S. Smale, and S. Weinberger, Finding the Homology of Submanifolds with High Confidence from??Random??Samples, Discrete & Computational Geometry, vol.33, issue.11, pp.419-441, 2008.
DOI : 10.1007/s00454-008-9053-2

G. Pisier, The volume of convex bodies and Banach space geometry, 1999.
DOI : 10.1017/CBO9780511662454

G. Schwarz, Estimating the Dimension of a Model, The Annals of Statistics, vol.6, issue.2, pp.461-464, 1978.
DOI : 10.1214/aos/1176344136

T. Tibshirani, Principal curves revisited, Statistics and Computing, vol.11, issue.4, pp.183-190, 1992.
DOI : 10.1007/BF01889678

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.5261

M. E. Tipping and C. M. Bishop, Mixtures of Probabilistic Principal Component Analyzers, Neural Computation, vol.2, issue.1, pp.443-482, 1999.
DOI : 10.1007/BF00162527

V. Verzelen, Data-driven neighborhood selection of a Gaussian field, Computational Statistics & Data Analysis, vol.54, issue.5, 2009.
DOI : 10.1016/j.csda.2009.12.001

URL : https://hal.archives-ouvertes.fr/inria-00353260

F. Villers, Tests et sélection de modéles pour l'analyse de données protéomiques et transcriptomiques, 2007.

A. Zomorodian and G. Carlsson, Computing Persistent Homology, Discrete & Computational Geometry, vol.33, issue.2, pp.249-274, 2005.
DOI : 10.1007/s00454-004-1146-y

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.5064