  We propose a methodology to explore and measure the pairwise correlations
that exist between variables in a dataset. The methodology leverages copulas
for encoding dependence between two variables, state-of-the-art optimal
transport for providing a relevant geometry to the copulas, and clustering for
summarizing the main dependence patterns found between the variables. Some of
the clusters centers can be used to parameterize a novel dependence coefficient
which can target or forget specific dependence patterns. Finally, we illustrate
and benchmark the methodology on several datasets. Code and numerical
experiments are available online for reproducible research.
