[Clustering] How and Where should you cut a dendrogram?

Hierarchical clustering methods produce dendrograms which contain more information than mere flat clustering, for instance cluster proximity. A particular hierarchical clustering method, namely Single-Linkage, enjoys several nice theoretical properties (Zadeh and Ben-David, 2009) and (Carlsson and Mémoli, 2010) despite being known to give poor results in practice. Nonetheless, in (Awasthi et al., 2012), authors show that if the center-based clustering instance verifies some perturbation resilient properties, finding the optimal center-based clustering is possible in polynomial time by cutting efficiently the Single-Linkage dendrogram while in the general case, finding the optimal clustering is NP-hard. The common practice to flatten dendrograms in $k$ clusters is to cut them off at constant height $k-1$. Yet it leads to poorer clusters than efficiently pruning the tree.