Frames, Reproducing Kernels, Regularization and Learning

Alain Rakotomamonjy, St├ęphane Canu.

Year: 2005, Volume: 6, Issue: 51, Pages: 1485−1515


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.