  We present AstroLink, an efficient and versatile clustering algorithm
designed to hierarchically classify astrophysically-relevant structures from
both synthetic and observational data sets. We build upon CluSTAR-ND, a
hierarchical galaxy/(sub)halo finder, so that AstroLink now generates a
two-dimensional representation of the implicit clustering structure as well as
ensuring that clusters are statistically distinct from the noisy density
fluctuations implicit within the $n$-dimensional input data. This redesign
replaces the three cluster extraction parameters from CluSTAR-ND with a single
parameter, $S$ -- the lower statistical significance threshold of clusters,
which can be automatically and reliably estimated via a dynamical model-fitting
process. We demonstrate the robustness of this approach compared to AstroLink's
predecessors by applying each algorithm to a suite of simulated galaxies
defined over various feature spaces. We find that AstroLink delivers a more
powerful clustering performance while being $\sim27\%$ faster and using less
memory than CluSTAR-ND. With these improvements, AstroLink is ideally suited to
extracting a meaningful set of hierarchical and arbitrarily-shaped
astrophysical clusters from both synthetic and observational data sets --
lending itself as a great tool for morphological decomposition within the
context of hierarchical structure formation.
