## On a Kernel-based Method for Pattern Recognition, Regression, Approximation, and Operator Inversion (1997)

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Citations: | 77 - 25 self |

### BibTeX

@MISC{Smola97ona,

author = {Alex J. Smola and Bernhard Schölkopf},

title = {On a Kernel-based Method for Pattern Recognition, Regression, Approximation, and Operator Inversion},

year = {1997}

}

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### 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.