  Several enhanced sampling methods such as umbrella sampling or metadynamics
rely on the identification of an appropriate set of collective variables.
Recently two methods have been proposed to alleviate the task of determining
efficient collective variables. One is based on linear discriminant analysis,
the other on a variational approach to conformational dynamics, and uses
time-lagged independent component analysis. In this paper, we compare the
performance of these two approaches in the study of the homogeneous
crystallization of two simple metals. We focus on Na and Al and search for the
most efficient collective variables that can be expressed as a linear
combination of X-ray diffraction peak intensities. We find that the
performances of the two methods are very similar. However, the method based on
linear discriminant analysis, in its harmonic version, is to be preferred
because it is simpler and much less computationally demanding.
