I have a series of
n points in
d-dimensional continuous space. I want to find a series of hyperplanes such that
k points are below the hyperplane and that the set of
k points below each hyperplane is a unique set. It does not matter what the hyperplane is (e.g. if it connects
d points or if it is another hyperplane not intersecting any points). I can discretise the space if it helps. "below" is defined as the negative direction for the first dimension.
The way I have approached is to try all hyperplanes defined by all sets of
d points, project each point on to this hyperplane, and test if the projection is above the point. This results in
Is there a better way? What is it?