A Generalized Sorting Strategy for Computer Classifications

AGGLOMERATIVE hierarchical methods of computer classification all begin by calculating distance-measures between elements. The hierarchy is then generated by subjecting these measures to a sorting-strategy, which depends essentially on the definition of a distance-measure between groups of elements. In nearest-neighbour sorting, this is defined as the distance between the closest pair of elements, one in each group. Macnaughton-Smith has pointed out that much more intense clustering can be produced by taking the most remote pair of elements ( furthest-neighbour sorting). In group-average sorting 1 the distance is defined as the mean of all between-group inter-element distances; in centroid sorting it is the distance between group centroids, defined by a conventional Euclidean model. In median 2 sorting the distance of a third group from two which have just fused depends on the previous three inter-group distances in the manner of Apollonius's theorem. Although the earlier of these strategies have received some comparative assessment 1,3–5 no attempt seems to have been made to generalize them into a single system. As a result, quite different computer strategies have commonly been used, necessitating a separate computer program for each.