# What is the loss function for C - Support Vector Classification?

In article LIBSVM: A Library for Support Vector Machines there is written, than C-SVC uses loss function:

$$\frac{1}{2}w^Tw+C\sum\limits_{i=1}^l\xi_i$$

OK, I know, what is $w^Tw$.

But what is $\xi_i$? I know, that it is somehow connected with misclassifications, but is it calculated exactly?

P.S. I don't use any non-linear kernels.

$\xi_i$ are the slack variables. They are typically nonzero when the 2-class data is non-separable. We are trying the minimize the slack as much as possible (by minimizing their sum, since they are non-negative) along with maximizing the margin ($w^Tw$) term.
• Yes, it is the hinge loss. The hinge loss has been removed from the objective and made into a bunch of constraints (their number equalt to the number of examples, $l$ in your notation). In particular, $\max[0,1-y_iw^Tx_i]$ is the loss on example $i$. Oct 14 '13 at 21:14