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

arXiv: https://arxiv.org/abs/2303.05683 · HTML: https://mlsanity.com/paper/2303.05683/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 10 Mar 2023.

## Builds on (most cited first, 3 of 3)

- [A framework for benchmarking clustering algorithms](https://mlsanity.com/paper/2209.09493/) (2022)
- [Genie: A new, fast, and outlier-resistant hierarchical clustering algorithm](https://mlsanity.com/paper/2209.05757/) (2022)
- [Data Fusion: Theory, Methods, and Applications](https://mlsanity.com/paper/2208.01644/) (2022)

## Abstract (arXiv)

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.