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arXiv · 2303.05683

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

Marek Gagolewski·Anna Cena·Simon James·Gleb Beliakov
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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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Marek Gagolewski, Anna Cena, Simon James, Gleb Beliakov. 2023-03-10. Hierarchical clustering with OWA-based linkages, the Lance-Williams formula, and dendrogram inversions. https://doi.org/10.1016/j.fss.2023.108740

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