Abstract--A clustering termination procedure which is locally adaptive (with respect to the hierarchical tree of sets representative of the agglomerative merging) is proposed, for agglomerative hierarchical clustering on a set equipped with a distance function. It represents a multi-scale alternative to conventional scale dependent threshold based termination criteria. We trim the tree at specific locations by studying cumulative extreme values of rates of change of parameters along paths of the agglomeration hierarchy, each path representing the "history" of successive merges with respect to an initial set. Thus the method considers the smallest localities. We refer to this qualitative phenomenon as geometric "paradigm shift".