  We introduce an atomistic classifier based on a combination of spectral graph
theory and a Voronoi tessellation method. This classifier allows for the
discrimination between structures from different minima of a potential energy
surface, making it a useful tool for sorting through large datasets of atomic
systems. We incorporate the classifier as a filtering method in the Global
Optimization with First-principles Energy Expressions (GOFEE) algorithm. Here
it is used to filter out structures from exploited regions of the potential
energy landscape, whereby the risk of stagnation during the searches is
lowered. We demonstrate the usefulness of the classifier by solving the global
optimization problem of 2-dimensional pyroxene, 3-dimensional olivine, Au12,
and Lennard-Jones LJ55 and LJ75 nanoparticles.
