  Hierarchical structure is ubiquitous in data across many domains. There are
many hierarchical clustering methods, frequently used by domain experts, which
strive to discover this structure. However, most of these methods limit
discoverable hierarchies to those with binary branching structure. This
limitation, while computationally convenient, is often undesirable. In this
paper we explore a Bayesian hierarchical clustering algorithm that can produce
trees with arbitrary branching structure at each node, known as rose trees. We
interpret these trees as mixtures over partitions of a data set, and use a
computationally efficient, greedy agglomerative algorithm to find the rose
trees which have high marginal likelihood given the data. Lastly, we perform
experiments which demonstrate that rose trees are better models of data than
the typical binary trees returned by other hierarchical clustering algorithms.
