| Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
|---|---|---|
| Page(s) | 272 - 280 | |
| DOI | https://doi.org/10.1051/ps:2007019 | |
| Published online | 19 June 2007 | |
A graph-based estimator of the number of clusters
Institut de Mathématiques et de Modélisation de Montpellier, UMR CNRS 5149, Équipe de Probabilités et Statistique, Université Montpellier II, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France; biau@math.univ-montp2.fr; cadre@math.univ-montp2.fr; pelletier@math.univ-montp2.fr
Received:
20
June
2006
Revised:
23
October
2006
Assessing the number of clusters of a statistical population is one of the essential issues of unsupervised learning. Given n independent observations X1,...,Xn drawn from an unknown multivariate probability density f, we propose a new approach to estimate the number of connected components, or clusters, of the t-level set 
. The basic idea is to form a rough skeleton of the set 
using any preliminary estimator of f, and to count the number of connected components of the resulting graph. Under mild analytic conditions on f, and using tools from differential geometry, we establish the consistency of our method.
Mathematics Subject Classification: 62G05 / 62G20
Key words: Cluster analysis / connected component / level set / graph / tubular neighborhood.
© EDP Sciences, SMAI, 2007
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