Suppose two datasets A(N) and B(N), each representing N measurements of some property — a(p) and b(p), respectively — amongst a population p of items, and A'(n) and B'(n) being the hierarchies obtained after n steps of divisive hierarchical clustering. Then, the proximity q(A',B') between these two hierarchies can probably be taken as a measure s(a,b) of statistical correlation between the properties a and b within the population p.
Is there a known relationship between q(A',B') and s(a,b) for some specific proximity measures (which ones?) used for clustering?
Any hints would be appreciated.