= Affine linear classifier
{title2=$h(x)=\mathbf1_{\{w\cdot x+b\geq0\}}$}
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>.
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