  Recent work on dissimilarity-based hierarchical clustering has led to the
introduction of global objective functions for this classical problem. Several
standard approaches, such as average linkage, as well as some new heuristics
have been shown to provide approximation guarantees. Here we introduce a broad
new class of objective functions which satisfy desirable properties studied in
prior work. Many common agglomerative and divisive clustering methods are shown
to be greedy algorithms for these objectives, which are inspired by related
concepts in phylogenetics.
