Proximity matrix reorganization and hierarchical clustering

Connections between hierarchical clustering and the seriation of objects along a continuum that depend on the patterning of entries in a proximity matrix are pointed out. Based on the similarity between the central notion of an ultrametric in hierarchical clustering and what is called an anti-Robinson property in seriation, it is suggested that the two data-analysis procedures are compatible. Indeed, preliminary seriation of a proximity matrix may help verify the adequacy of the results obtained from a hierarchical clustering or suggest alternatives that may be better. A numerical example using data from the area of criminal justice completes the paper.