Given a point described by \(D\) numbers, decide which class it belongs to.
$$ f : \mathbb{R}^D \to \{ 0, 1 \} $$
$$ f : \mathbb{R}^D \to \{ +1, -1 \} $$
A function from \(D\) real numbers (the features) to one of two labels. The two codings mean the same thing; different algorithms prefer one or the other.
update 0
misclassified 0
Each update nudges the line toward a point it got wrong (a perceptron). It stops when every point is on its own side.
\(f(\mathbf{x}) = 1\) on one side of the line, \(0\) on the other: the line is the decision boundary.
$$ f : \mathbb{R}^D \to \{ 1, 2, \dots, K \} $$
The same idea with \(K > 2\) labels: digits 0 to 9, or cat / dog / bird.