# Bounded and unbounded support vectors for nu-SVMs

How do we find out which of the support vectors for a nu-svm are its bounded or unbounded support vectors? For c-SVMs the test is easy: a support vector with $\alpha_i = C$ denotes a bounded support vector, while the others are unbounded. Whats an analogous test for nu-SVMs?

Also it would be of great help if you could direct me to how to do this test for libSVM output.

Thanks!

The same approach applies - depending on your scaling you will have $0 \leq \alpha_i \leq \frac{1}{n}$ or $0 \leq \alpha_i \leq 1$ usually for $\nu$-SVM. libSVM in particular scales the output so as to be equivalent to $C$-SVM. Thus, you should check the maximum absolute values for your $\alpha_i$ (since they are multiplied through by $y_i$ before being output). Note that in general, it is still possible in $C$-SVM to have a point on the margin which has $\alpha_i = C$ (but all points which have some error will have $\alpha_i = C$).