Hierarchical Clustering with OWA-based Linkages, the Lance-Williams Formula, and Dendrogram Inversions

A paper by Anna Cena, Simon James, Gleb Beliakov, and I entitled Hierarchical Clustering with OWA-based Linkages, the Lance-Williams Formula, and Dendrogram Inversions has been accepted for publication in Fuzzy Sets and Systems (DOI:10.1016/j.fss.2023.108740). A preprint is available on arXiv.

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.