• Corpus ID: 88523087

DBSCAN: Optimal Rates For Density Based Clustering

  title={DBSCAN: Optimal Rates For Density Based Clustering},
  author={Daren Wang and Xin Yang Lu and Alessandro Rinaldo},
  journal={arXiv: Statistics Theory},
We study the problem of optimal estimation of the density cluster tree under various assumptions on the underlying density. Building up from the seminal work of Chaudhuri et al. [2014], we formulate a new notion of clustering consistency which is better suited to smooth densities, and derive minimax rates of consistency for cluster tree estimation for Holder smooth densities of arbitrary degree \alpha. We present a computationally efficient, rate optimal cluster tree estimator based on a… 
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