Classifier

A classifier is a function that assigns an input to one of a discrete set of labels. A binary classifier has two possible labels.

An affine linear classifier assigns binary labels according to the sign of an affine function. Its boundary is an affine hyperplane, and its positive region is a closed half-space under the displayed convention. On ${\mathbb{R}}^d$ the full class has VC dimension $d+1$: arbitrary signs interpolate on $d+1$ affinely independent points, while the intersecting convex hull partition theorem prevents shattering any $d+2$ points. Requiring $b=0$ gives the homogeneous case and a different VC dimension.