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

Kernel principal component analysis can represent nonlinear low-dimensional structure by performing linear PCA in a nonlinear feature space. It can also work directly with structured objects such as strings through a kernel, without assigning them explicit finite-dimensional coordinates. Both capabilities are unavailable to ordinary linear PCA on the original variables.