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Article Dans Une Revue ESAIM: Probability and Statistics Année : 2007

A graph-based estimator of the number of clusters

Résumé

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 L(t) = {x : f(x) ! t}. The basic idea is to form a rough skeleton of the set L(t) 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.
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Dates et versions

hal-00455749 , version 1 (11-02-2010)

Identifiants

  • HAL Id : hal-00455749 , version 1

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Gérard Biau, Benoît Cadre, Bruno Pelletier. A graph-based estimator of the number of clusters. ESAIM: Probability and Statistics, 2007, pp.272-280. ⟨hal-00455749⟩
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