Re: SVM and positive definiteness

Stefan Rueping wrote:

> BJ Jain wrote:
>
> > 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 
>
>
> The SVM is based on the concept of linear separability (because that 
> lets you define the large-margin-property which connects the SVM to the 
> structural risk minimization principle from statistical learning 
> theory). If you do not have the concept of linearity, obviously you 
> cannot apply the SVM idea to your problem.
> Of course you can still run the same algorithm on your similarity matrix 
> to get some classification function, but you'll have no theoretical 
> foundation that will give generalization properties of this classifier.


Thanks. I know that almost nothing is left, but I obtain a classifier 
and can estimate its generalization performance in the same way like for 
other machines. Meanwhile I've found an approach by Mangasarian about 
generalized svm. Let me know, if you are interested.

With best wishes

j