Kernel trick

Mathematics: the kernel trick

The kernel trick avoids the explicit mapping that is needed to get linear learning algorithms to learn a nonlinear function or decision boundary. For all ${\displaystyle \mathbf {x} }$ and ${\displaystyle \mathbf {x'} }$ in the input space ${\displaystyle {\mathcal {X}}}$, certain functions ${\displaystyle k(\mathbf {x} ,\mathbf {x'} )}$ can be expressed as an inner product in another space ${\displaystyle {\mathcal {V}}}$. The function ${\displaystyle k\colon {\mathcal {X}}\times {\mathcal {X}}\to \mathbb {R} }$ is often referred to as a kernel or a kernel function. The word "kernel" is used in mathematics to denote a weighting function for a weighted sum or integral.