  Recently, Hierarchical Clustering (HC) has been considered through the lens
of optimization. In particular, two maximization objectives have been defined.
Moseley and Wang defined the \emph{Revenue} objective to handle similarity
information given by a weighted graph on the data points (w.l.o.g., $[0,1]$
weights), while Cohen-Addad et al. defined the \emph{Dissimilarity} objective
to handle dissimilarity information. In this paper, we prove structural lemmas
for both objectives allowing us to convert any HC tree to a tree with constant
number of internal nodes while incurring an arbitrarily small loss in each
objective. Although the best-known approximations are 0.585 and 0.667
respectively, using our lemmas we obtain approximations arbitrarily close to 1,
if not all weights are small (i.e., there exist constants $\epsilon, \delta$
such that the fraction of weights smaller than $\delta$, is at most $1 -
\epsilon$); such instances encompass many metric-based similarity instances,
thereby improving upon prior work. Finally, we introduce Hierarchical
Correlation Clustering (HCC) to handle instances that contain similarity and
dissimilarity information simultaneously. For HCC, we provide an approximation
of 0.4767 and for complementary similarity/dissimilarity weights (analogous to
$+/-$ correlation clustering), we again present nearly-optimal approximations.
