LFD Book Forum - View Single Post - Help in understanding proof for VC-dimension of perceptron.

MaciekLeks · #10 05-09-2016, 08:18 AM

Quote:

Originally Posted by ntvy95

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

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

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.