structural:expansion, information:filtering
Kernel trick

Suppose now that we would like to learn a nonlinear classification rule which corresponds to a linear classification rule for the transformed data points φ (x i). {\displaystyle \varphi (\mathbf {x} _{i}).} Moreover, we are given a kernel function k {\displaystyle k} which satisfies k (x i, x j) = φ (x i) ⋅ φ (x j) {\displaystyle k(\mathbf {x} _{i},\mathbf {x} _{j})=\varphi (\mathbf {x} _{i})\cdot \varphi (\mathbf {x} _{j})}.