A graph-based estimator of the number of clusters
Gérard Biau; Benoît Cadre; Bruno Pelletier
ESAIM: Probability and Statistics (2007)
- Volume: 11, page 272-280
- ISSN: 1292-8100
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top- G.E. Bredon, Topology and Geometry, Springer-Verlag, New York, Graduate Texts in Mathematics 139 (1993).
- M.R. Brito, E.L. Chavez, A.J. Quiroz and J.E. Yukich, Connectivity of the mutual k-nearest neighbor graph in clustering and outlier detection. Statist. Probab. Lett.35 (1997) 33–42.
- B. Cadre, Kernel estimation of density level sets. J. Multivariate Anal.97 (2006) 999–1023.
- I. Chavel, Riemannian Geometry: A Modern Introduction. Cambridge University Press, Cambridge (1993).
- T.H. Cormen, C.E. Leiserson and R.L. Rivest, Introduction to Algorithms. The MIT Press, Cambridge (1990).
- A. Cuevas, M. Febrero and R. Fraiman, Estimating the number of clusters. Canad. J. Statist.28 (2000) 367–382.
- A. Cuevas, M. Febrero and R. Fraiman, Cluster analysis: a further approach based on density estimation. Comput. Statist. Data Anal.36 (2001) 441–459.
- L. Devroye and G. Wise, Detection of abnormal behavior via nonparametric estimation of the support. SIAM J. Appl. Math.38 (1980) 480–488.
- R.O. Duda, P.E. Hart and D.G. Stork, Pattern Classification, 2nd edition. Wiley-Interscience, New York (2000).
- L. Györfi, M. Kohler, A. Krzyżak and H. Walk, A Distribution-Free Theory of Nonparametric Regression. Springer-Verlag, New York (2002).
- J.A. Hartigan, Clustering Algorithms. John Wiley, New York (1975).
- T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York (2001).
- S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I & II, 2nd edition. Wiley, New York (1996).
- U. von Luxburg and S. Ben-David, Towards a statistical theory of clustering. PASCAL Workshop on Statistics and Optimization of Clustering (2005).
- M.D. Penrose, A strong law for the longest edge of the minimal spanning tree. Ann. Probab.27 (1999) 246–260.
- A. Polonik, Measuring mass concentrations and estimating density contour clusters–an excess mass approach. Ann. Statist.23 (1995) 855–881.
- B.L.S. Prakasa Rao, Nonparametric Functional Estimation. Academic Press, Orlando (1983).
- A.B. Tsybakov, On nonparametric estimation of density level sets. Ann. Statist.25 (1997) 948–969.
Citations in EuDML Documents
top- Markus Maier, Ulrike von Luxburg, Matthias Hein, How the result of graph clustering methods depends on the construction of the graph
- Elena Di Bernardino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur, Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory