You cannot build a sparse version of a kernel by "cutting" its tails off.
If I remember correctly, there is a good discussion about this issue in
Marc G. Genton,
"Classes of Kernels for Machine Learning: A Statistics Perspective"
JMLR, 2(12):299--312, 2001.
The new book from Shawe-Taylor and Cristianini should also have some info.
We have a paper on the use of sparse kernels but has not been published yet.
Hope it helps,
-- Davide.
www.smartlab.dibe.unige.it
----- Original Message -----
From: "Koby Crammer" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Friday, September 03, 2004 9:30 PM
Subject: sparse kernels
> Hi,
>
> I am looking for 'sparse kernels' : kernels which are *exactly* zero for
most of
> the elements of the kernel matrix. Assume k(a,b) is a kernel function,
then
> two ways to build such kernels are :
>
> (a) k'(a,b) = max { k(a,b)-q, 0} for some q>=0
>
> { k(a,b) if k(a,b)>q
> (b) k'(a,b) = {
> { 0 otherwise
>
>
> for some q>=0 (the second method is not continuous)
>
> Does anyone know if any of these methods yield a valid kernel function for
> any k(.,.)? for the RBF kernel function? Is there a sparse kernel function
(not
> built this way)?
>
>
> Thanks, Koby
>
> ============================================
> Koby Crammer [log in to unmask]
>
> http://www.cs.huji.ac.il/~kobics
> ============================================
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