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Zbl 1187.62114
Biau, Gérard; Cadre, Benoît; Pelletier, Bruno
A graph-based estimator of the number of clusters. (English)
[J] ESAIM, Probab. Stat. 11, 272-280 (2007). ISSN 1292-8100; ISSN 1262-3318/e

Summary: Assessing the number of clusters of a statistical population is one of the essential issues of unsupervised learning. Given $n$ independent observations $X_1,\dots,X_n$ 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 $\mathcal L(t)=\{x:f(x) \geq t\}$. The basic idea is to form a rough skeleton of the set $\mathcal L(t)$ 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.

MSC 2000:: *62H30 Statistical classification, etc.
62G05 Nonparametric estimation
05C90 Appl. of graph theory
68T05 Learning and adaptive systems
62G20 Nonparametric asymptotic efficiency

Keywords: cluster analysis; connected component; level set; graph; tubular neighborhood

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