Question

I have three arrays (it’s written in C but that is not important, it could be any language):

  float x[] = {
        0.72, 0.91, 0.46, 0.03, 0.12, 0.96, 0.79, 0.46, 0.66, 0.72, 0.35, -0.16,
        -0.04, -0.11, 0.31, 0.00, -0.43, 0.57, -0.47, -0.72, -0.57, -0.25,
        0.47, -0.12, -0.58, -0.48, -0.79, -0.42, -0.76, -0.77
  };

  float y[] = {
        0.82, -0.69, 0.80, 0.93, 0.25, 0.47, -0.75, 0.98, 0.24, -0.15, 0.01,
        0.84, 0.68, 0.10, -0.96, -0.26, -0.65, -0.97, -0.03, -0.64, 0.15, -0.43,
        -0.88, -0.90, 0.62, 0.05, -0.92, -0.09, 0.65, -0.76      
  };

  int outputs[] = {
      -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
      1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
  };

First two arrays are X and Y coordinates of a points on two dimensional plane.

Third array decides if the point is from set 1 or set -1.

I need an algorithm that will linearry separate these two sets of points. I.e. it should return a and b coeficients from this equation:

y = a*x + b

Which is a general line equation.

Look at the first image here:

http://dynamicnotions.blogspot.com/2008/09/single-layer-perceptron.html

To better understanbd what I need.

Answer 1

Support Vector Machines will do what you want (albeit somewhat difficult to implement)