Frames, Reproducing Kernels, Regularization and Learning

Alain Rakotomamonjy, Stéphane Canu; 6(Sep):1485--1515, 2005.

Abstract

This work deals with a method for building a reproducing kernel Hilbert space (RKHS) from a Hilbert space with frame elements having special properties. Conditions on existence and a method of construction are given. Then, these RKHS are used within the framework of regularization theory for function approximation. Implications on semiparametric estimation are discussed and a multiscale scheme of regularization is also proposed. Results on toy and real-world approximation problems illustrate the effectiveness of such methods.

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