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#4
05-05-2016, 06:55 AM
 MaciekLeks Member Join Date: Jan 2016 Location: Katowice, Upper Silesia, Poland Posts: 17
Re: Help in understanding proof for VC-dimension of perceptron.

Context:
To show that we need to prove we cannot shatter any set od points. In this case we have vectors of , where , hence we have vector than the total number of dimensions (our space is -dimensional). According to the theory of vector spaces when we have more vectors than dimensions of the space then they are linearly dependent (one of the vectors is a linear combination of the others). Which means that for instance our extra point , can be computed by the equation (in -dimensional space): , (where not all coefficients are zeros).
We need to show that we can't get ( ) dichotomies, where is of size.

Problem:

And now let me define my problem I have with understanding the video proof. Why do we correlate coefficient with the while they don't correlate? On what basis we can draw that , and that's why , hence we can't generate ?