  I present a strategy for unsupervised manifold learning on local atomic
environments in molecular simulations based on simple rotation- and
permutation-invariant three-body features. These features are highly
descriptive, generalize to multiple chemical species, and are
human-interpretable. The low-dimensional embeddings of each atomic environment
can be used to understand and quantify messy crystal structures such as those
near interfaces and defects or well-ordered crystal lattices such as in bulk
materials without modification. The same method can also yield collective
variables describing collections of particles such as for an entire simulation
domain. I demonstrate the method on colloidal crystallization, ice crystals,
and binary mesophases to illustrate its broad applicability. In each case, the
learned latent space yields insights into the details of the observed
microstructures. For ices and mesophases, supervised classifiers are trained
based on the learned manifolds and directly compared against a recent
neural-network-based approach. Notably, while this method provides comparable
classification performance, it can also be deployed on even a handful of
observed environments without labels or \textit{a priori} knowledge. Thus, the
current approach provides an incredibly versatile strategy to characterize and
classify local atomic environments, and may unlock insights in a wide variety
of molecular simulation contexts.
