Inversion Problems In Pyramidal Classification
Rainer Lasch · 1994
Pyramidal classification of multidimensional data allows the construction of overlapping clusters. The pyramidal representation is a natural extension of the hierarchical classification. The graphical representaion of indexed hierarchies by dendrograms is well-known. For the graphical representation of indexed pyramids a similar procedure can be used. Milligan (1979) has shown that the most used agglomerative hierarchical techniques single and complete linkage generate hierarchical structures with monotonically increasing distance values so the resulting dendrogram is free of inversions. Transferring this agglomerative techniques to the pyramidal classification it can be shown that only the complete linkage technique generates pyramidal structures with monotonically increasing distance values. Using the single linkage technique inversions are possible in the graphical representation. For the existence of an inversion a necessary and sufficient condition is formulated.