  To reach a deeper understanding of fluid interfaces it is necessary to
identify a meaningful coarse-graining length that separates intrinsic
fluctuations from capillary ones, given the lack of a proper statistical
mechanical definition of the latter. Here, with the help of unsupervised
learning techniques, we introduce a new length scale based on the local density
of the fluid. This length scale follows a scaling law that diverges more mildly
than the bulk correlation length upon approaching the critical point. This
allows to distinguish regimes of correlated and uncorrelated capillary waves
from that of intrinsic fluctuations.
