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 linear time, creating a set of distributional coordinates which act as a feature extraction mechanism for supervised learning. We describe the use of CDER both directly on point clouds and on persistence diagrams.