On 1/27/12 11:02 PM, H. S. Teoh wrote:
If you treat the attributes as components of an n-dimensional vector,
then you could recast the problem as the convex hull of k hypercuboids,
where each hypercuboid lies between (0,0,0,...) and (x1,x2,x3,...). The
points on the convex hull then are the high-ranking points (points
inside the hull are obviously suboptimal). Furthermore, the closest
points to the line spanned by the vector (1,1,1,...) are the points that
maximize the most number of attributes.
If you "peel away" the points on the convex hull, then the convex hull
generated by the remaining points gives you the "second class" points.
Peel away those, and the convex hull gives you the "third class" points,
etc..
Granted, this isn't exactly the original problem as stated, but it seems
to be closer to what you intend to achieve with your stocks example.
That's close. Closer is to use simplexes instead of hypercubes. And the
space is defined by rank, not the original features.
Andrei
