  Intrinsic dimension and differential entropy estimators are studied in this
paper, including their systematic bias. A pragmatic approach for joint
estimation and bias correction of these two fundamental measures is proposed.
Shared steps on both estimators are highlighted, along with their useful
consequences to data analysis. It is shown that both estimators can be
complementary parts of a single approach, and that the simultaneous estimation
of differential entropy and intrinsic dimension give meaning to each other,
where estimates at different observation scales convey different perspectives
of underlying manifolds. Experiments with synthetic and real datasets are
presented to illustrate how to extract meaning from visual inspections, and how
to compensate for biases.
