  Fully automated classification methods that yield direct physical insights
into phase diagrams are of current interest. Here, we demonstrate an
unsupervised machine learning method for phase classification which is rendered
interpretable via an analytical derivation of its optimal predictions and
allows for an automated construction scheme for order parameters. Based on
these findings, we propose and apply an alternative, physically-motivated,
data-driven scheme which relies on the difference between mean input features.
This mean-based method is computationally cheap and directly interpretable. As
an example, we consider the physically rich ground-state phase diagram of the
spinless Falicov-Kimball model.
