Quote:
Originally Posted by ntvy95
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.

I agree. I tried to write it in
Context part of my post.
Quote:
Originally Posted by ntvy95
The proof tries to consider some dichotomies (specific to the data set) have two following properties:
 with nonzero get .
 gets .
Hope this helps.

Unfortunately it does not help. I understand the assumption, but I do not understand the source of confidence that we can correlate
with perceptron outputs.