Idea for improved hyperplane splits

[MrChrisJohnson]

Instead of sampling just 2 points, sample k points for some reasonable k as well as a uniformly random hyperplane h. Then, project all k points down to h. In 2d this would amount to points on a line. It's now trivial to find a second hyperplane h' perpendicular to h that splits the projected points and will in turn split the points in the original space. See the diagram below for a visual representation. This method should improve splits by making the splits more evenly distributed while still maintaining the nondeterminism to avoid trees replicating the same splits.