Ward minimum-variance clustering ($\Delta (A,B)=\frac{|A||B|}{|A|+|B|}\Vert {\bar{x}}_A-{\bar{x}}_B{\Vert }^2$)

Ward clustering merges the pair causing the smallest increase in within-cluster sum of squares. Expanding each cluster's squared deviations about the merged mean gives the displayed increase. Its Euclidean sum-of-squares interpretation must not be asserted for arbitrary non-Euclidean dissimilarities.