[monkeyjoe]

I think there is hidden gold in the linked research paper. In the second to last paragraph, it says if you are willing to discard the trivial partition (each point on its own) from Richness, then you *can* have Scale-Invariance and Refinement-Consistency as well. To me this suggests an optimal (in some sense) class of algorithms, perhaps to be chosen from based on computational complexity, cross-validation, etc.