Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 218 / 4 / f / Solution

The feature space may be extremely high-dimensional or infinite-dimensional, and $\varphi$ may be known only implicitly. Instead, compute the leading eigenvector $\alpha$ of the kernel matrix $K$, normalize it by ${\alpha }^{\top }K\alpha =1$, and use the kernel trick:This requires only kernel evaluations.