Re: SVM and positive definiteness

Uwe Schmitt wrote:

> BJ Jain <[EMAIL PROTECTED]> wrote:
>
> > Hello,
>
> > is there some work about svm using "kernels" which are not positive 
> > definite?
>
> > Does ist make sense to use "kernels" which are not positive definite?
>
> That depends. AFAIK there are cases where "invalid" kernels work, 
> the theory says "kernel positive ==> SVM can be trained", but there
> is no general proof negating the other direction.
>
> I think you should try it. I think it depends on how "not positive"
> your kernel is: build the Kernel-Matrix and look at the negative
> eigenvalues...


We already tried and it works better than all other approaches on that 
dataset. But what is left from a svm? Almost nothing? I mean, we even do 
not know the primal form of the optimization problem we are solving. So 
what are we exactly doing?

Do you have any references of work about invalid kernels?

Best wishes

bjj