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Consistent Procedures for Cluster Tree Estimation and Pruning

机译:群集树估计和修剪的一致过程

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For a density on , a high-density cluster is any connected component of , for some . The set of all high-density clusters forms a hierarchy called the cluster tree of . We present two procedures for estimating the cluster tree given samples from . The first is a robust variant of the single linkage algorithm for hierarchical clustering. The second is based on the -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.
机译:对于某个密度,对于某些密度,高密度簇是任何连接的组件。所有高密度群集的集合形成一个称为的群集树的层次结构。我们提供了两种程序来估计聚类树。第一个是用于层次聚类的单链接算法的鲁棒变体。第二个基于样本的-最近邻图。我们为这些算法提供了有限的样本收敛速度,这也暗示了一致性,并且得出了聚类树估计的样本复杂度的下界。最后,我们研究了一种树木修剪程序,该程序可在比平常更温和的条件下保证除去虚假的群集,同时恢复明显的群集。

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