Hierarchical clustering with OWA-based linkages, the Lance-Williams formula, and dendrogram inversions
Machine Learning
2023-10-27 v2 Machine Learning
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.
Cite
@article{arxiv.2303.05683,
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},
journal= {arXiv preprint arXiv:2303.05683},
year = {2023}
}