  Context: There have been many attempts to identify families of diffuse
interstellar bands (DIBs) with perfectly correlating band strengths. Although
major efforts have been made to classify broadly based DIB families and
important insights have been gained, no family has been identified with
sufficient accuracy or statistical significance to prove that a series of
selected DIBs originates from the same carrier. This can be attributed in part
to the exclusive use of equivalent widths to establish DIB families.
  Aims: In a change of strategy, we search for DIBs that are highly correlated
in both band strength and profile shape. This approach increases the chance of
correlating DIBs being members of one family and originating from the same
carrier molecule. We also search for correlations between DIB profile families
and atomic interstellar lines, with the goal of further chemically constraining
possible DIB carriers.
  Methods: We adapted the well-known method of time-series alignment to perform
a spectral alignment; that is, DIB alignment. In a second step, we analysed the
alignment results using a clustering analysis. This method required a
statistically significant data set of DIB sight lines. The ESO Diffuse
Interstellar Bands Large Exploration Survey (EDIBLES) data were perfectly
suited for this application.
  Results: We report eight DIB families with correlating strengths and
profiles, as well as four previously unreported DIBs in the visual range, found
using DIB alignment. All profile family members show Pearson correlation
coefficients in band strength higher than 0.9. In particular, we report the
6614 - 6521 AA DIB pair, in which both DIBs show the same triple-peak
substructure and an unprecedented band strength Pearson correlation coefficient
of 0.9935. The presented approach opens up new perspectives that can guide the
laboratory search for DIB carriers.
