  The convex hull of a set of points, $C$, serves to expose extremal properties
of $C$ and can help identify elements in $C$ of high interest. For many
problems, particularly in the presence of noise, the true vertex set (and
facets) may be difficult to determine. One solution is to expand the list of
high interest candidates to points lying near the boundary of the convex hull.
We propose a quadratic program for the purpose of stratifying points in a data
cloud based on proximity to the boundary of the convex hull. For each data
point, a quadratic program is solved to determine an associated weight vector.
We show that the weight vector encodes geometric information concerning the
point's relationship to the boundary of the convex hull. The computation of the
weight vectors can be carried out in parallel, and for a fixed number of points
and fixed neighborhood size, the overall computational complexity of the
algorithm grows linearly with dimension. As a consequence, meaningful
computations can be completed on reasonably large, high dimensional data sets.
