Study Of Training Algorithms Of Several Classes Of Complex-valued Neural Networks With Applications

This thesis mainly focuses on three kinds of training algorithms for complex-valued neural networks, including multi-layer feedforward neural networks, radial basis function neural networks and recurrent neural networks. Based on extensive research, we have proposed effective training algorithms for the three kinds of complex-valued neural networks, which have been applied to solve some partical problems in the field of pattern recognition.The complex-valued Backpropagation algorithm(BP) is a popular training algorithm for complex-valued feedforward neural networks. However, when the activation function is the split-sigmoid function, there exists saturation areas. The existence of saturation areas could reduce the training speed of the backpropagation algorithm, even lead to the failure of training process. In order to solve this issue, we proposed a complex-valued BP algorithm based on adaptive gain parameters. In the process of training, the gain parameters were adjusted according to the ouput error such that the activation function can adjust the saturation areas adaptively. Therefore, the affect of the saturation area on training speed can be overcome.One of the important steps in training a complex-valued radial basis function neural network is to effectively determine the centers and widths of neurons in hidden layer. The recently-proposed max-spread algorithm selects the centers based on the distance between samples from different classes. However, this algorithm ignores the distance relationship between samples in the same class. This disadvantage degrades the performance of the algorithm. To eliminate this disadvantage, we proposed a new algorithm in which the choice of centers not only depends on the distances between samples from different classes, but also is affected by the distances between the samples in the same class. The relationship between the external and inner distances is taken into account when determining the centers.This thesis has also investigated the training algorithm of complex-valued recurrent neural network. To our knowledge, the complex-valued Levenberg-Marquardt(LM) algorithm has not been applied to train a complex-valued recurrent neural network. Therefore, the complex-valued LM algorithm has been proposed to train a compelx-valued recurrent neural network with Jordan structure. The Jordan-type recurrent neural network is composed of feedforward network and feedback connections. One of the advantages is that the convergence of the algorithm is very fast via an adaptive adjustment of damping factor.In order to verify the effectiveness of the proposed training algorithms for complex-valued neural networks, we applied these algorithms to solve the hand gestures recognition and some classification problems of public dataset from UCI. As the experimental results shown, the training algorithms of complex-valued neural networks proposed in this thesis have higher recognition accuracy.