Gaussian kernel functionIt is a commonly used kernel function that can map finite-dimensional data to high-dimensional space. The Gaussian kernel function is defined as follows:

$latex {k{ \left( {x,x\text{'}} \right) }\text{ }=\text{ }e\mathop{{}}\nolimits^{{-\frac{{{ \left\Vert {xx\text{'}} \right\Vert }\mathop{{}}\nolimits^{{2}}}}{{2 \sigma \mathop{{}}\nolimits^{{2}}}}}}}$

The above formula involves the calculation of the Euclidean distance (2 norm) of two vectors, and the Gaussian kernel function is a monotonic function of the Euclidean distance of two vectors. σ is the bandwidth, which controls the radial range of action. In other words, σ controls the local range of action of the Gaussian kernel function. When the Euclidean distance between x and x′ is within a certain interval, assuming that x′ is fixed, k(x,x′) changes significantly with the change of x.

The core idea of the Gaussian kernel function is to map each sample point to an infinite-dimensional feature space, so that the originally linearly inseparable data can be linearly separable.