  We introduce a new algorithm, called CDER, for supervised machine learning
that merges the multi-scale geometric properties of Cover Trees with the
information-theoretic properties of entropy. CDER applies to a training set of
labeled pointclouds embedded in a common Euclidean space. If typical
pointclouds corresponding to distinct labels tend to differ at any scale in any
sub-region, CDER can identify these differences in (typically) linear time,
creating a set of distributional coordinates which act as a feature extraction
mechanism for supervised learning. We describe theoretical properties and
implementation details of CDER, and illustrate its benefits on several
synthetic examples.
