<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.

Solved by gpt-5.6-sol high.

Solution

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

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Kernel principal component analysis diagonalizes a centered <kernel matrix> to perform principal component analysis in an implicit feature space.

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