JMLR

An Axiomatic Definition of Hierarchical Clustering

Authors
Ery Arias-Castro Elizabeth Coda
Paper Information
  • Journal:
    Journal of Machine Learning Research
  • Added to Tracker:
    Jul 15, 2025
Abstract

In this paper, we take an axiomatic approach to defining a population hierarchical clustering for piecewise constant densities, and in a similar manner to Lebesgue integration, extend this definition to more general densities. When the density satisfies some mild conditions, e.g., when it has connected support, is continuous, and vanishes only at infinity, or when the connected components of the density satisfy these conditions, our axiomatic definition results in Hartigan's definition of cluster tree.

Author Details
Ery Arias-Castro
Author
Elizabeth Coda
Author
Citation Information
APA Format
Ery Arias-Castro & Elizabeth Coda . An Axiomatic Definition of Hierarchical Clustering. Journal of Machine Learning Research .
BibTeX Format
@article{JMLR:v26:24-1052,
  author  = {Ery Arias-Castro and Elizabeth Coda},
  title   = {An Axiomatic Definition of Hierarchical Clustering},
  journal = {Journal of Machine Learning Research},
  year    = {2025},
  volume  = {26},
  number  = {10},
  pages   = {1--26},
  url     = {http://jmlr.org/papers/v26/24-1052.html}
}
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