Functional data learning by Hilbert feedforward neural networks
Jianwei Zhao · Mathematical Methods in the Applied Sciences · 2012
This paper focuses on learning algorithms for approximating functional data that are chosen from some Hilbert spaces. An effective algorithm, called Hilbert parallel overrelaxation backpropagation (HPORBP) algorithm, is proposed for training the Hilbert feedforward neural networks that are extensions of feedforward neural networks from Euclidean space to some Hilbert spaces. Furthermore, the convergence of the iterative HPORBP algorithm is analyzed, and a deterministic convergence theorem is proposed for the HPORBP algorithm on the basis of the perturbation results of Mangasarian and Solodov. Some experimental results of learning functional data on some Hilbert spaces illustrate the convergence theorem and show that the proposed HPORBP algorithm has a better accuracy than the Hilbert backpropagation algorithm. Copyright © 2012 John Wiley & Sons, Ltd.