  A general scheme for divisive hierarchical clustering algorithms is proposed.
It is made of three main steps : first a splitting procedure for the
subdivision of clusters into two subclusters, second a local evaluation of the
bipartitions resulting from the tentative splits and, third, a formula for
determining the nodes levels of the resulting dendrogram. A number of such
algorithms is given. These algorithms are compared using the Goodman-Kruskal
correlation coefficient. As a global criterion it is an internal
goodness-of-fit measure based on the set order induced by the hierarchy
compared to the order associated to the given dissimilarities. Applied to a
hundred of random data tables, these comparisons are in favor of two methods
based on unusual ratio-type formulas for the splitting procedures, namely the
Silhouette criterion and Dunn's criterion. These two criteria take into account
both the within cluster and the between cluster mean dissimilarity. In general
the results of these two algorithms are better than the classical Agglomerative
Average Link method.
