Consistent procedures for cluster tree estimation and pruning

Kamalika Chaudhuri, Sanjoy Dasgupta, Samory Kpotufe, Ulrike Von Luxburg

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

For a density f on Rd, a high-density cluster is any connected component of {x: f(x) ≥ λ} , for some λ > 0. The set of all high-density clusters forms a hierarchy called the 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.

Original languageEnglish (US)
Article number6915900
Pages (from-to)7900-7912
Number of pages13
JournalIEEE Transactions on Information Theory
Volume60
Issue number12
DOIs
StatePublished - Dec 1 2014

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Clustering algorithms
  • convergence

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