Hierarchical clustering with OWA-based linkages, the Lance-Williams formula, and dendrogram inversions

Marek Gagolewski, Anna Cena, Simon James, Gleb Beliakov
3/10/2023
stat.MLcs.LG

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Abstract

Agglomerative hierarchical clustering based on Ordered Weighted Averaging (OWA) operators not only generalises the single, complete, and average linkages, but also includes intercluster distances based on a few nearest or farthest neighbours, trimmed and winsorised means of pairwise point similarities, amongst many others. We explore the relationships between the famous Lance-Williams update formula and the extended OWA-based linkages with weights generated via infinite coefficient sequences. Furthermore, we provide some conditions for the weight generators to guarantee the resulting dendrograms to be free from unaesthetic inversions.

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Cite this paper

@article{gagolewski2023hierarchical,
  title  = {Hierarchical clustering with OWA-based linkages, the Lance-Williams formula, and dendrogram inversions},
  author = {Marek Gagolewski and Anna Cena and Simon James and Gleb Beliakov},
  year   = {2023},
  eprint = {2303.05683},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2303.05683v2}
}

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