Approximation of functions by a wavelet neural network built using a hybrid approach based on the genetic algorithm and the Gram-Schmidt Selection method

The performance and power of Wavelet Neural Networks (WNNs) rely on the proper structure of the WNN. In this study, a hybrid approach is suggested to build a Wavelet Neural Network. We design a network based on the genetic algorithm (GA), the Gram-Schmidt Selection (GSS) method, and the multilibrary wavelet function (MLWF). The initialization of the WNN is performed by the GSS method, which aims to select the candidate library wavelet functions (MLWF) to develop the WNN. The GA is used to solve the structure and the learning of the WNN and the GSS algorithm is applied to select the important wavelets. The GA was used to calculate the suitable values of the Network parameters, to solve the structure and learning of the WNN. In this research, the GSS method is used to determine a set of best wavelets whose centres and dilation parameters are used as initial values for subsequent training. Experimental tests proved that the proposed approach is very efficient and accurate.