  Agglomerative hierarchical clustering can be implemented with several
strategies that differ in the way elements of a collection are grouped together
to build a hierarchy of clusters. Here we introduce versatile linkage, a new
infinite system of agglomerative hierarchical clustering strategies based on
generalized means, which go from single linkage to complete linkage, passing
through arithmetic average linkage and other clustering methods yet unexplored
such as geometric linkage and harmonic linkage. We compare the different
clustering strategies in terms of cophenetic correlation, mean absolute error,
and also tree balance and space distortion, two new measures proposed to
describe hierarchical trees. Unlike the $\beta$-flexible clustering system, we
show that the versatile linkage family is space-conserving.
