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-   -   Lecture 7: Shattering for d+2 points (http://book.caltech.edu/bookforum/showthread.php?t=4642)

sandeeps 11-01-2015 08:02 PM

Lecture 7: Shattering for d+2 points
 
In the argument,
d_{VC} <= d + 1
After we arrive at the result that
w^T x_j > 0
but also state that
y_j = -1
it is concluded that H does not shatter the given d+2 points. (I understood this).

However you then stated:
"You cannot shatter your set for any set you choose. Therefore you cannot shatter any set of d+2 points"

How did we go from not shattering a given set of d+2 points to not being to shatter any set of d+2 points? :clueless:

yaser 11-02-2015 12:33 AM

Re: Lecture 7: Shattering for d+2 points
 
Quote:

Originally Posted by sandeeps (Post 12191)
In the argument,
d_{VC} <= d + 1
After we arrive at the result that
w^T x_j > 0
but also state that
y_j = -1
it is concluded that H does not shatter the given d+2 points. (I understood this).

However you then stated:
"You cannot shatter your set for any set you choose. Therefore you cannot shatter any set of d+2 points"

How did we go from not shattering a given set of d+2 points to not being to shatter any set of d+2 points? :clueless:

There were no restrictions on the choice of the d+2 points. The argument started by taking any d+2 points then proving that you cannot shatter them by going through the linear-algebra argument.


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