  The nature of an atom in a bonded structure -- such as in molecules, in
nanoparticles or solids, at surfaces or interfaces -- depends on its local
atomic environment. In atomic-scale modeling and simulation, identifying groups
of atoms with equivalent environments is a frequent task, to gain an
understanding of the material function, to interpret experimental results or to
simply restrict demanding first-principles calculations. While routine, this
task can often be challenging for complex molecules or non-ideal materials with
breaks of symmetries or long-range order. To automatize this task, we here
present a general machine-learning framework to identify groups of (nearly)
equivalent atoms. The initial classification rests on the representation of the
local atomic environment through a high-dimensional smooth overlap of atomic
positions (SOAP) vector. Recognizing that not least thermal vibrations may lead
to deviations from ideal positions, we then achieve a fuzzy classification by
mean-shift clustering within a low-dimensional embedded representation of the
SOAP points as obtained through multidimensional scaling. The performance of
this classification framework is demonstrated for simple aromatic molecules and
crystalline Pd surface examples.
