Neural Networks

Abstract

In this chapter the first technology of CI-neural networks is considered. In the Sect. 1.2 neural network Back propagation (NN BP) is considered which is most widely used, its architecture and functions described. The important theorem on universal approximation for NN BP is considered which grounds its universal applications in forecasting, pattern recognition, approximation etc. gradient method of training neural network BP is described, its properties analyzed in Sect. 1.3. In Sect. 1.4 the extension of gradient algorithm for training NN BP with arbitrary number of layers is considered. In Sect. 1.5 some modifications of gradient algorithm improving its properties are described. In Sect. 1.6 method of conjugate gradient is considered for network training which has accelerated convergence as compared with conventional gradient method. In Sect. 1.7 genetic algorithm for training NNBP is considered, its properties are analyzed. In Sect. 1.8 is presented another class of widely used neural networks with radial basis functions . Its structure and properties are described and analyzed. Methods of training weights and parameters of radial functions are considered. The more general class of radial neural networks- so-called Hyper Radial Basis Function networks (HRBF) is considered, its properties are described and analyzed. In Sect. 1.9 efficient algorithm of RBF network training- hybrid algorithm is presented and its properties described. In the Sect. 1.10 some examples of application RBF neural network and methods of selection the number of radial basis functions are presented, comparison of back propagation neural networks and RBF NN is performed.