Feature Functions and Kernels

The idea of transforming the input space into a feature space of a higher dimension by using feature functions (j)(x) and then performing a linear 

Under certain conditions, an inner product in feature space has an equivalent kernel in input space  

If the kernel fC is a symmetric positive definite function, which satisfies the Mercer s conditions 

Consider the two-dimensional pattern x=(xi,xz) and the feature function defined for a two-dimensional pattern x  

From the expression of this feature function, it is easy to obtain the corresponding kernel function 

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