A new hybrid constructive neural network method for impacting and its application on tungsten price prediction

To accurately predict the price of tungsten with an optimal architecture of neural networks (NNs) and better generalization performance, based on poor generalization and overfitting of a predictor such as a NNs, this paper presents a new hybrid constructive neural network method (HCNNM) to repair the impacting value in the original data in the same manner as the jumping points of a function. A series of theorems was proven that show a function with m jumping discontinuity points (or impacting points) can be approximated with the simplest NNs and a constructive decay Radial basis function (RBF) NNs, and a function with m jumping discontinuity points can be constructively approximated by hybrid constructive NNs. The hybrid networks have an optimal architecture and generalize well. Additionally, a practical problem regarding Tungsten prices from 1900 to 2014 is presented with some impacting points to more accurately approximate the sample data set and forecast future prices with the HCNNM, and some performance measures, such as the training time, testing RMSE and neurons, are compared with traditional algorithms (BP, SVM, ELM and Deep Learning) through many numerical experiments that fully verify the superiority, correctness and validity of the theory.