Let's consider a dataset of feature vectors we want to classify:
For simplicity, we assume it as a binary classification (in all the other cases, it's possible to use automatically the one-versus-all strategy) and we set our class labels as -1 and 1:
Our goal is to find the best separating hyperplane, for which the equation is:
In the following figure, there's a bidimensional representation of such a hyperplane: ...