Quote:
Originally Posted by costas
How can I find the smallest break point for a given problem?

Hi costas,
actually, the break point can be only one for each set of hypothesis (and it's the smallest by definition).
I found the break point for 3D perceptron just by imagining points in 3D space and trying to separate them by a plane in all possible ways.
But then decided to do it more "strictly" and used Octave in a following fashion:
1. generate N random points
2. create all possible 2^N dichotomies
3. for each dichotomy find ideally separating plane, using PLA, if possible.
4a. if for all dichotomies PLA "converged"  then your N points can be shattered and it's not a break point, program stop.
4b. if not for all  repeat experiment, generating new random set of N points (just in case your previous set happened to be "special"  3 points in line, e.g.)
If after some number of experiments (I used 1000, but suppose it's too much, 10 will do) for N points your dichotomies are still not all converged, you can state, that N points can't be shattered, and if N1 were "shatterable", then N is a break point.