A new constructive neural network method for noise processing and its application on stock market prediction

•Some noise data are considered as singular values of a continuous function.•RBF neural networks are constructed to fit the singular value with every ɛ error.•A theorem about a function with m jumping discontinuity points has been proved.•The constructive part has no generalization influence to the learning system.•A real world problem has been presented to verify the correctness of the theory.

In this paper, in order to optimize neural network architecture and generalization, after analyzing the reasons of overfitting and poor generalization of the neural networks, we presented a class of constructive decay RBF neural networks to repair the singular value of a continuous function with finite number of jumping discontinuity points. We proved that a function with m   jumping discontinuity points can be approximated by a simplest neural network and a decay RBF neural network in L2(ℝ)L2(ℝ) by each ɛ error, and a function with m   jumping discontinuity point y=f(x), x∈E⊂ℝdy=f(x), x∈E⊂ℝd can be constructively approximated by a decay RBF neural network in L2(ℝd)L2(ℝd) by each ε>0ε>0 error. Then the whole networks will have less hidden neurons and well generalization in the same of the first part. A real world problem about stock closing price with jumping discontinuity have been presented and verified the correctness of the theory.