The $\xi_i$ are <slack variables of a support vector machine>. The solid line is the <support-vector-machine decision boundary>
$$
\widehat\alpha+x^\top\widehat\beta=0.
$$
The dashed lines are the two <support-vector-machine margin boundaries>
$$
\widehat\alpha+x^\top\widehat\beta=1,
\qquad
\widehat\alpha+x^\top\widehat\beta=-1.
$$
Each is at perpendicular distance $1/\lVert\widehat\beta\rVert_2$ from the decision boundary, so the full margin width is $2/\lVert\widehat\beta\rVert_2$.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 218 / 3 / a / Solution

The two margin boundaries of a linear support vector machine are the parallel hyperplanes $f(x)=1$ and $f(x)=-1$.


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 Incoming links: Support-vector-machine margin boundaries