Quote:
Originally Posted by MaciekLeks
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 ?

Here is my understanding:
For
any data set of size d + 2, we must have linear dependence, and the question is: With such inevitable linear dependence, can we find at least a specific data set that can be implemented 2^N dichotomies? The video lecture shows that for
any data set of size d + 2, there are
some dichotomies (specific to the data set) that the perceptron cannot implement, hence there's no such a data set of size d + 2 can be shattered by the perceptron hypothesis set.
The proof tries to consider
some dichotomies (specific to the data set) have two following properties:

with nonzero
get
.

gets
.
Hope this helps.