  Molecular dynamics is a versatile and powerful method to study diffusion in
solid-state ionic conductors, requiring minimal prior knowledge of equilibrium
or transition states of the system's free energy surface. However, the analysis
of trajectories for relevant but rare events, such as a jump of the diffusing
mobile ion, is still rather cumbersome, requiring prior knowledge of the
diffusive process in order to get meaningful results. In this work, we present
a novel approach to detect the relevant events in a diffusive system without
assuming prior information regarding the underlying process. We start from a
projection of the atomic coordinates into a landmark basis to identify the
dominant features in a mobile ion's environment. Subsequent clustering in
landmark space enables a discretization of any trajectory into a sequence of
distinct states. As a final step, the use of the smooth overlap of atomic
positions descriptor allows distinguishing between different environments in a
straightforward way. We apply this algorithm to ten Li-ionic systems and
conduct in-depth analyses of cubic Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$, tetragonal
Li$_{10}$GeP$_{2}$S$_{12}$, and the $\beta$-eucryptite LiAlSiO$_{4}$. We
compare our results to existing methods, underscoring strong points,
weaknesses, and insights into the diffusive behavior of the ionic conduction in
the materials investigated.
