Expanding the class of global objective functions for dissimilarity-based hierarchical clustering

Background In hierarchical clustering, one seeks a recursive partitioning of the data that captures clustering information at different levels of granularity. Classical work on the subject mostly takes an algorithmic perspective. In particular, various iterative clustering methods have been developed, including the well-known bottom-up dissimilarity-based approaches single linkage, average linkage, etc. (see, e.g., [Mur12, Chapter 25]). Recent work on dissimilarity-based hierarchical clustering has emphasized a different, optimization-based, perspective. This has led to the introduction of global objective functions for this classical problem [Das16].