Thread: Break points?
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Old 07-26-2012, 05:53 AM
dvs79 dvs79 is offline
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Join Date: Jul 2012
Location: Moscow, Russia
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Default Re: Break points?

Quote:
Originally Posted by costas View Post
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 N-1 were "shatterable", then N is a break point.
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