English

Moving Up the Cluster Tree with the Gradient Flow

Statistics Theory 2021-12-13 v2 Machine Learning Statistics Theory

Abstract

The paper establishes a strong correspondence between two important clustering approaches that emerged in the 1970's: clustering by level sets or cluster tree as proposed by Hartigan and clustering by gradient lines or gradient flow as proposed by Fukunaga and Hostetler. We do so by showing that we can move up the cluster tree by following the gradient ascent flow.

Cite

@article{arxiv.2109.08362,
  title  = {Moving Up the Cluster Tree with the Gradient Flow},
  author = {Ery Arias-Castro and Wanli Qiao},
  journal= {arXiv preprint arXiv:2109.08362},
  year   = {2021}
}

Comments

This is an expanded version. We changed the title to better reflect the contribution made in the paper

R2 v1 2026-06-24T06:03:48.180Z