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.

翻译：基于有序加权平均（OWA）算子的凝聚型分层聚类不仅概括了单连接、全连接和平均连接方法，还涵盖了基于最近或最远若干邻居的簇间距离、成对点相似度的修剪均值与温索化均值等多种距离度量。我们探讨了著名的Lance-Williams更新公式与通过无限系数序列生成权重的扩展OWA连接之间的关系。此外，我们为权重生成器提供了保证所得树状图不出现不合美学逆序的条件。