### Asymptotic normality in density support estimation.

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Assessing the number of clusters of a statistical population is one of the essential issues of unsupervised learning. Given independent observations drawn from an unknown multivariate probability density , we propose a new approach to estimate the number of connected components, or clusters, of the -level set $\mathcal{L}\left(t\right)=\{x:f(x)\ge t\}$. The basic idea is to form a rough skeleton of the set $\mathcal{L}\left(t\right)$ using any preliminary estimator of , and to count the number of connected components of the resulting graph. Under mild analytic...

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