  In this paper, we build an organization of high-dimensional datasets that
cannot be cleanly embedded into a low-dimensional representation due to missing
entries and a subset of the features being irrelevant to modeling functions of
interest. Our algorithm begins by defining coarse neighborhoods of the points
and defining an expected empirical function value on these neighborhoods. We
then generate new non-linear features with deep net representations tuned to
model the approximate function, and re-organize the geometry of the points with
respect to the new representation. Finally, the points are locally z-scored to
create an intrinsic geometric organization which is independent of the
parameters of the deep net, a geometry designed to assure smoothness with
respect to the empirical function. We examine this approach on data from the
Center for Medicare and Medicaid Services Hospital Quality Initiative, and
generate an intrinsic low-dimensional organization of the hospitals that is
smooth with respect to an expert driven function of quality.
