Abstract

We present a Kernel--based framework for Pattern Recognition, Regression Estimation, Function Approximation and multiple Operator Inversion. Previous approaches such as ridge-regression, Support Vector methods and regression by Smoothing Kernels are included as special cases. We will show connections between the cost-function and some properties up to now believed to apply to Support Vector Machines only. The optimal solution of all the problems described above can be found by solving a simple quadratic programming problem. The paper closes with a proof of the equivalence between Support Vector kernels and Greene's functions of regularization operators.

Citations