On ziggurats and dendrograms

The indeterminacy in the horizontal ordering of the objects in the usual tree diagram representation of a dendrogram, and the associated dangers of misinterpretation, are well-known. A systematic choice of ordering is presented and seen to have a variety of attractive features. In particular, it induces a strengthened form of the Robinson property of the associated ultrametric matrix, permitting an exact one dimensional visual display of maximal subsets of objects. These systematic orderings are based upon the ziggurat decomposition of an arbitrary binary dendrogram. Worked examples motivate and illustrate the development. Connections with 'chaining' in single-link hierarchical cluster analysis are noted.