G. Biau and L. Bleakley, Statistical Inference on Graphs. Statistics & Decisions, vol.24, pp.209-232, 2006.

S. Boucheron, O. Bousquet, and G. Lugosi, Theory of Classification: A Survey of Some Recent Advances, ESAIM: Probability and Statistics, vol.9, pp.323-375, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00017923

S. Ben-david, A framework for statistical clustering with a constant time approximation algorithms for k-median clustering, Proceedings of COLT'04, vol.3120, pp.415-426, 2004.

G. Biau, L. Devroye, and G. Lugosi, On the Performance of Clustering in Hilbert Space, IEEE Trans. Inform. Theory, vol.54, issue.2, pp.781-790, 2008.

S. Bubeck and U. Luxburg, Nearest neighbor clustering: A baseline method for consistent clustering with arbitrary objective functions, Journal of Machine Learning Research, vol.10, pp.657-698, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00185780

B. Clarke, E. Fokoué, and H. ,

. Zhang, Principles and Theory for Data-Mining and MachineLearning, 2009.

S. Clémençon, G. Lugosi, and N. Vayatis, Ranking and empirical risk minimization of U-statistics, The Annals of Statistics, vol.36, issue.2, pp.844-874, 2008.

L. Devroye, L. Györfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition, 1996.

V. De-la-pena and E. Giné, Decoupling: from Dependence to Independence, 1999.

R. M. Dudley, Uniform Central Limit Theorems, 1999.

J. A. Hartigan, Asymptotic distributions for clustering criteria, The Annals of Statistics, vol.6, pp.117-131, 1978.

W. Hoeffding, A class of statistics with asymptotically normal distribution, Ann. Math. Stat, vol.19, pp.293-325, 1948.

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning, pp.520-528, 2009.

S. Kutin and P. Niyogi, Almost-everywhere algorithmic stability and generalization error, Proceedings of the of the 18th Conference in Uncertainty in Artificial Intelligence, 2002.

V. Koltchinskii, Local Rademacher complexities and oracle inequalities in risk minimization (with discussion), The Annals of Statistics, vol.34, pp.2593-2706, 2006.

R. Peck, L. Fisher, and J. Van-ness, Bootstrap confidence intervals for the number of clusters in cluster analysis, J. Am. Stat. Assoc, vol.84, pp.184-191, 1989.

D. Pollard, Strong consistency of k-means clustering, The Annals of Statistics, vol.9, pp.135-140, 1981.

D. Pollard, A central limit theorem for k-means clustering, The Annals of Probability, vol.10, pp.919-926, 1982.
DOI : 10.1214/aop/1176993713

URL : https://doi.org/10.1214/aop/1176993713

R. J. Serfling, Approximation theorems of mathematical statistics, 1980.

O. Shamir and N. Tishby, Model selection and stability in k-means clustering, Proceedings of the 21rst Annual Conference on Learning Theory, 2008.
DOI : 10.1007/s10994-010-5177-8

URL : https://link.springer.com/content/pdf/10.1007%2Fs10994-010-5177-8.pdf

O. Shamir and N. Tishby, On the reliability of clustering stability in the large sample regime, Advances in Neural Information Processing Systems, vol.21, 2009.

R. Tibshirani, G. Walther, and T. Hastie, Estimating the number of clusters in a data set via the gap statistic, J. Royal Stat. Soc, vol.63, issue.2, pp.411-423, 2001.

A. Van-der and . Vaart, Asymptotic Statistics, 1998.

U. Luxburg, Clustering stability: An overview. Foundations and Trends in Machine Learning, vol.2, pp.235-274, 2009.

U. Luxburg and S. Ben-david, Towards a statistical theory of clustering, Pascal workshop on Statistics and Optimization of Clustering, 2005.

U. Luxburg and S. Ben-david, A sober look at clustering stability, Proceedings of the 19th Conference on Learning Theory, 2006.

U. Luxburg and S. Ben-david, Relating clustering stability to properties of cluster boundaries, Proceedings of the 21th Conference on Learning Theory, 2008.

D. M. Witten and R. Tibshirani, A framework for feature selection in clustering, J. Amer. Stat. Assoc, vol.105, issue.490, pp.713-726, 2010.