Commonly Used Kernels

1. Inner products, $K(\mathbf{x},{\mathbf{x}}_i)=(\mathbf{x}\cdot {\mathbf{x}}_i)$
2. Polynomials, $K(\mathbf{x},{\mathbf{x}}_i)=[(\mathbf{x}\cdot {\mathbf{x}}_i)+1{]}^q$
3. Radial basis function

K(\mathbf{x}, \mathbf{x}{i}) = \exp\left{{\frac{-|\mathbf{x}-\mathbf{x}{i}|^2}{\sigma^2}}\right}

4. Sigmoid, $K(\mathbf{x}, \mathbf{x}_{i}) = \tanh(v(\mathbf{x} \cdot \mathbf{x}_{i}) + c)$