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Old 05-09-2016, 08:18 AM
MaciekLeks MaciekLeks is offline
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Join Date: Jan 2016
Location: Katowice, Upper Silesia, Poland
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Default Re: Help in understanding proof for VC-dimension of perceptron.

Quote:
Originally Posted by ntvy95 View Post
I'm not sure if this is the point you are talking about: Here is my understanding:

If the perceptron hypothesis set can shatter the data set then: If y_{i} = sign(a_{i}) for every x_{i} that a_{i} \neq 0 then there exists such a w that satisfies sign(w^{T}x_{i}) = sign(a_{i}) for every x_{i} that a_{i} \neq 0. In other words, we first have y_{i} = sign(a_{i}) for every x_{i} that a_{i} \neq 0, then we must be able to find a w that satisfies the equation y_{i} = sign(a_{i}) = sign(w^{T}x_{i}) if the perceptron hypothesis set can shatter the data set.
You've built up the intuition for the proof. I knew this, but when I read what you wrote, I started to have less doubt. Thanks for that. I still have some doubt, but it's even hard to describe. It's high time to move on.
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