Weights and structure determination of feed-forward two-input neural network activated by chebyshev polynomials of class 2

Abstract

Based on the theory of polynomial interpolation and approximation, a new feed-forward two-input neural network activated by a group of Chebyshev polynomials of Class 2 (i.e., TINN-CP2) is constructed and investigated in this paper. To overcome the weaknesses of conventional back-propagation (BP) neural networks, a weights-direct-determination (WDD) method is exploited to obtain the optimal linking weights of the proposed neural network directly. Furthermore, a new structure-automatic-determination (SAD) algorithm is developed to determine the optimal number of hidden-layer neurons of the TINN-CP2, and thus the weights-and-structure-determination (WASD) algorithm is built up. Numerical studies further substantiate the efficacy and superior abilities of the proposed TINN-CP2 in approximation, denoising and prediction, with the aid of the WASD algorithm which obtains the optimal number of hidden-layer neurons of the TINN-CP2.