Kernel trick
Also: kernel methods, kernel function, RBF kernel
Algorithms that only use dot products between examples, such as SVMs, can swap xᵢ·xⱼ for a kernel K(xᵢ, xⱼ) = φ(xᵢ)·φ(xⱼ). This acts like a linear model on the mapped features φ(x) at the cost of evaluating K.
K(x, z) = φ(x)·φ(z), e.g. RBF: K(x, z) = exp(−γ ‖x − z‖²)
Example
On a number line, class A sits at |x| < 1 and class B outside it; no single threshold separates them, but mapping x → (x, x²) makes them separable by the line x² = 1.