The Research On Neural Network With Walsh Weight Function And Its Application

In recent years, Artificial Neural Networks have been widely used in many fields. The feedforward neural networks were often trained by gradient algorithm. Many techniques have been introduced to improve the performance of the gradient algorithm. But the drawbacks of gradient algorithm still exist such as the local minima, the slow convergence speed and the limited scale of problems.In order to avoid the aforementioned problems, this dissertation researches the Walsh weight function neural network and its algorithm based on the spline weight function neural network theory and approximation theory of Walsh function. The algorithm in this dissertation can determine the specific form of Walsh weight function through the solution of linear equations or the fast Walsh transform. This dissertation analyzes the attributes of this new neural network such as the convergence, the convergence speed and network error. It's proved that the error of Walsh weight function neural network is related to the first-order derivative of theoretical weight function and decreases as the number of samples increases. To make use of Walsh function, the number of the coefficients of the Walsh weight function will decrease without causing unacceptable network error through the data compression technology. Some simulation examples are presented to show that the Walsh weight function neural network not only overcomes the drawbacks of conventional gradient algorithm such as backpropagation and radial basis function, but also has the good performance in the network topology, the training time, the convergence, the generalization and so on.The Walsh weight function neural network in this dissertation applies to the signal modulation recognition based on the signal modulation recognition theory and its parameters are signal higher-order cumulants. Some simulation examples results indicate that the classifier of Walsh weight function neural network has the advantages of the conventional neural networks classifier and also has the good performance such as stability, recognition rate and so on.