×

Frames, reproducing kernels, regularization and learning. (English) Zbl 1222.68284

Summary: 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.

MSC:

68T05 Learning and adaptive systems in artificial intelligence

Software:

TDSL
PDFBibTeX XMLCite
Full Text: Link