  We have re-analysed the rich plethora of ground state configurations of the
asymmetric Wigner bilayer system that we had recently published in a related
diagram of states [M. Antlanger \textit{et al.}, Phys. Rev. Lett. \textbf{117},
118002 (2016)], comprising roughly 60~000 state points in the phase space
spanned by the distance between the plates and the charge asymmetry parameter
of the system. In contrast to this preceding contribution where the
classification of the emerging structures was carried out ``by hand'', we have
used this time machine learning concepts, notably based on a principal
component analysis and a $k$-means clustering approach: using a 30-dimensional
feature vector for each emerging structure (containing relevant information,
such as the composition of the configuration as well as the most relevant order
parameters) we were able to re-analyse these ground state configurations in a
considerably more systematic and comprehensive manner than we could possibly do
in the previously published classification scheme. Indeed we were now able to
identify new structures in previously unclassified regions of the parameter
space and could considerably refine the previous classification scheme,
identifying thereby a rich wealth of new emerging ground state configurations.
Thorough consistency checks confirm the validity of the newly defined diagram
of states.
