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arXiv · 1406.1546

Consistent procedures for cluster tree estimation and pruning

Kamalika Chaudhuri·Sanjoy Dasgupta·Samory Kpotufe·Ulrike von Luxburg
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Abstract

For a density $f$ on ${\mathbb R}^d$, a {\it high-density cluster} is any connected component of $\{x: f(x) \geq \lambda\}$, for some $\lambda > 0$. The set of all high-density clusters forms a hierarchy called the {\it cluster tree} of $f$. We present two procedures for estimating the cluster tree given samples from $f$. The first is a robust variant of the single linkage algorithm for hierarchical clustering. The second is based on the $k$-nearest neighbor graph of the samples. We give finite-sample convergence rates for these algorithms which also imply consistency, and we derive lower bounds on the sample complexity of cluster tree estimation. Finally, we study a tree pruning procedure that guarantees, under milder conditions than usual, to remove clusters that are spurious while recovering those that are salient.

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Kamalika Chaudhuri, Sanjoy Dasgupta, Samory Kpotufe, Ulrike von Luxburg. 2014-06-05. Consistent procedures for cluster tree estimation and pruning. https://arxiv.org/abs/1406.1546

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