Linear support vector machines

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: ...

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