Data Classification
Find the minimum-degree polynomial that can separate two sets of points in the plane.
This example demonstrates how LinearOptimization may be used to test the feasibility (whether or not they can be satisfied) for a set of constraints. The constraints are generated symbolically from set data.
A polynomial 
is said to separate two sets 
and 
of points if 
for all 
and 
for all 
. Since there is no restriction on the size of the coefficients of 
, the problem can be rescaled to require 
and 
.
Define a polynomial power function that avoids issues with 
when 
or 
is 0.
Define a function of 
that is a polynomial of degree 
with coefficients 
.
The variables for a degree 
are the coefficients 
.
The constraints enforce separation between set 1 and set 2.
For example, here are the constraints for quadratics.
For separation, the only condition is that all the constraints must be satisfied. To find out if the constraints can be satisfied, the simplest thing is to set the objective vector to 0. Iteratively increase the polynomial degree till the constraints are satisfied.
Find the coefficients of the minimum-degree separating polynomial separating the two sets.
Visualize the separation of the sets using the polynomial.
