  A rank-invariant clustering of variables is introduced that is based on the
predictive strength between groups of variables, i.e., two groups are assigned
a high similarity if the variables in the first group contain high predictive
information about the behaviour of the variables in the other group and/or vice
versa. The method presented here is model-free, dependence-based and does not
require any distributional assumptions. Various general invariance and
continuity properties are investigated, with special attention to those that
are beneficial for the agglomerative hierarchical clustering procedure. A fully
non-parametric estimator is considered whose excellent performance is
demonstrated in several simulation studies and by means of real-data examples.
