ON A KERNEL-BASED METHOD FOR PATTERN-RECOGNITION, REGRESSION, APPROXIMATION, AND OPERATOR INVERSION

We present a kernel-based framework for pattern recognition, regressio n estimation, function approximation, and multiple operator inversion. Adopting a regularization-theoretic framework, the above are formulat ed as constrained optimization problems. Previous approaches such as r idge regression, support vector methods, and regularization networks a re included as special cases. We show connections between the cost fun ction and some properties up to now believed to apply to support vecto r machines only. For appropriately chosen cost functions, the optimal solution of all the problems described above can be found by solving a simple quadratic programming problem.