Re: SVM and positive definiteness

> > Assume that you have training set and a similarity measure which is 
> > not positive definite. Does it make sense to compute the matrix (which 
> > is in fact not a gram matrix) of pairwise similarities and to apply svm?
>
>
> The kernel idea is that you can map the data into a feature space and 
> apply the linear SVM algorithm there without actually constructing the 
> feature space, because all you need is the inner product in the feature 
> space. This inner product is what is calculated by the kernel function.
> If your kernel matrix has negative eigenvalues, it cannot be an inner 
> product and the whole idea of SVMs does not work.


Ok, but assume you have patterns which are not from an Euclidean space. 
You do not have concepts like linearity but a similarity measure which 
does not yield a semi-positive definite kernel matrix, in general. All 
you want ist a classifier to separate your patterns. So one approach 
could be to abuse the idea of the svm for this problem. Is this approach 
ok or completely senseless?

With best wishes

bjj