Hierarchical clustering algorithms can be characterized as greedy. A sequence of irreversible algorithm steps is used to construct the desired data structure. Assume that a pair of clusters, including possibly singletons, is merged or agglomerated at each step of the algorithm. Then the following are equivalent views of the same output structure constructed on n objects: a set of n − 1 partitions, starting with the fine partition consisting of n classes and ending with the trivial partition consisting of just one class, the entire object set; a binary tree (one or two child nodes at each non-terminal node) commonly referred to as a dendrogram; a partially ordered set (poset) which is a subset of the power set of the n objects; and an ultrametric topology on the n objects.