constructing a curve dividing two sets of points Lets assume I have two sets of points, each characterized as being  "A" or "B", respectively, that are in a Euclidean plane.  Theoretically these two sets are samplings from a space that has boundaries.  Now I want to construct a boundary.  So I want to construct the simplest curve that divides the two sets of points.  
A simple example would be a space where x< 0 is the A region,  x>0 is the B region.  Generate 100 random points in a unit box centered on the origin.   Now you want to find a line that divides the "A" points from the"B" points (forgetting that you know what the original answer was).   How would you do this?
How would you do this in general?
 A: Assuming the size of A and B are less than 10000 points, I would use a Support Vector Machine with a Gaussian Kernel.  
http://en.wikipedia.org/wiki/Support_vector_machine
A: This is not directly responsive to your question, but it might be relevant to what you're trying to accomplish.
Suppose you find a curve that correctly classifies all 100 of your points.  You'd like this curve to have a high probability of correctly classifying a large fraction of the points in the much larger sample from which your 100 points were drawn.  
In particular, suppose you'd like your curve to have probability at least $1-\delta$ of correctly classifying a fraction at least $1-\epsilon$ of that larger set of points (where $\delta$ and $\epsilon$ are some fixed --- and presumably small --- constants).
A sufficient condition for this is 
$$100 > {N\over\epsilon}Log(1/\delta)$$
where $N$ is the maximum number of points that can always be successfully separated by some member of your class of allowable curves.  E.g. if you restrict your curves to be lines, then $N=3$, because any 3 points, no matter how they are labeled $A$ and $B$, can be successfully separated by a line.
I wish I could remember where I learned this, so that I could point you to a source.  I have a reasonably powerful (but perhaps faulty) memory that Scott Aaronson had something to do with it.
