  Developing effective descriptions of the microscopic dynamics of many
physical phenomena can both dramatically enhance their computational
exploration and lead to a more fundamental understanding of the underlying
physics. Previously, an effective description of a driven interface in the
presence of mobile impurities, based on an Ising variant model and a single
empirical coarse variable, was partially successful; yet it underlined the
necessity of selecting additional coarse variables in certain parameter
regimes. In this paper we use a data mining approach to help identify the
coarse variables required. We discuss the implementation of this diffusion map
approach, the selection of a similarity measure between system snapshots
required in the approach, and the correspondence between empirically selected
and automatically detected coarse variables. We conclude by illustrating the
use of the diffusion map variables in assisting the atomistic simulations, and
we discuss the translation of information between fine and coarse descriptions
using lifting and restriction operators.
