I don't know if this observation is that helpful, but to me it almost seems as if in this process you are trying to construct the smallest k n-dimensional "spheres" that encompass the data. (I say "spheres" loosely-a spheroid or ellipsoid might be more appropriate, upon thinking a little further about it.) When projected into one dimension, this would seem to appear as a range; in 2 dimensions, as a circle; and in 3+ dimensions, as a sphere. The "amorphous blob" effect you mentioned in the CB when I made this observation earlier could be a result of overlaps in the spheres, and choosing one to encompass a particular data point than another.

As I said, I don't know how helpful the observation may be, but hope it helps.