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-   -   meaning of gamma in polynomial kernel (http://book.caltech.edu/bookforum/showthread.php?t=1272)

Andrs 09-02-2012 01:01 AM

meaning of gamma in polynomial kernel
 
In libsvm the polynomial kernel is defined in the following way:
(gamma*u'*v + coef0)^degree).
What is the meaning of gamma in the poly kernel? In our exercise the polynomial kernel only contains the parameters coef0 and degree (and C). There is no reference to a gamma parameter.
I have guessed the value 1 to gamma (no effect when multiplying the inner product) but I am not sure because its purpose is not clear for me in the poly case.
If we do not assign any values, the default value given by libsvm is 1/# features. In our case,it will be 1/2.
Any clarifications about this gamma in poly is appreciated:clueless:

tzs29970 09-02-2012 01:23 AM

Re: meaning of gamma in polynomial kernel
 
See slide 6 of lecture 15, and the discussion starting about 21 minutes into the lecture.

yaser 09-02-2012 01:27 AM

Re: meaning of gamma in polynomial kernel
 
Quote:

Originally Posted by Andrs (Post 4767)
In libsvm the polynomial kernel is defined in the following way:
(gamma*u'*v + coef0)^degree).
What is the meaning of gamma in the poly kernel? In our exercise the polynomial kernel only contains the parameters coef0 and degree (and C). There is no reference to a gamma parameter.
I have guessed the value 1 to gamma (no effect when multiplying the inner product) but I am not sure because its purpose is not clear for me in the poly case.
If we do not assign any values, the default value given by libsvm is 1/# features. In our case,it will be 1/2.
Any clarifications about this gamma in poly is appreciated:clueless:

As mentioned on slide 6 of Lecture 15, sometimes the polynomial kernel is defined with constants inside the expression that balance the relative value of the coefficients in the equivalent transformation. The slide uses different notation from that of libsvm. For our purposes, these constants are set to 1 (both gamma and coeff0 in the notation you mention).

Edit: I wrote this before I saw the above reply. :)

Andrs 09-02-2012 01:34 AM

Re: meaning of gamma in polynomial kernel
 
Thanks for the quick reply!..may be i should have been more alert

htlin 09-02-2012 06:24 AM

Re: meaning of gamma in polynomial kernel
 
A simple way to view \gamma is that it is as if you have scaled all your \mathbf{x} down by \sqrt{\gamma} before applying the no-\gamma polynomial kernel. Hope this helps.

Andrs 09-03-2012 03:04 AM

Re: meaning of gamma in polynomial kernel
 
Quote:

Originally Posted by htlin (Post 4774)
A simple way to view \gamma is that it is as if you have scaled all your \mathbf{x} down by \sqrt{\gamma} before applying the no-\gamma polynomial kernel. Hope this helps.

Thanks for the explanation!


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