Study Of Learning Algorithms For Complex-Valued Radial Basis Function Neural Networks With Applications

Complex-valued neural networks have become a new branch of artificial neural networks due to their powerful computation capacity, strong generalization ability and relatively-small structure. Especially, radial basis function neural network s(RBFNN), with simple structure, easy training process and fast convergence, have been widely used in function fitting, image process and pattern recognition. Centers and weights are the parameters which are needed to be determined in a RBFNN. It is known that the determination of the number and locations of centers and their corresponding widths play an essential role in training a RBFNN. Then the weights between the neurons of the output and hidden layers can be ob tained by solving linear equations after centers are selected. That is to say, the determination of centers is an improtant issue such that a well-trained RBFNN can have successful applications in many fields. In this thesis, three kinds of learning algorithms are proposed to select the centers of RBFNN.The first one is an improved tunable kernel based orthogonal least squares algorithm for complex-valued RBF neural networks. Random traversal process(RTP) and filtering center(FC) are adopted to choose suitable centers. The RTP is employed to guarantee that new center is better than samples and the FC is used to e nsure that selected centers obey the orthogonal least squares decline law.The second one is the density weighted means(DWM) to select initial centers. It is known that centers are generated randomly from sample set in gradient descent method. Hence, this will lead to unreasonable structure of RBFNN for an unknow sample set and affect the convergence in algorithm. The density weighted means is used to solve the deficiency above.The last one is an improved clustering estimation based repeat weighted boosting search strategy to choose the centers. It searches the best center in the feasible solution space. A better way of determining the parameters in clustering estimation is presented.The first algorithm is applied in function approximation and pattern recognition. The results show that the optimization algorithm is better than the original one in approximation and generalization ability. The latter two algorithms are applied in channel equalization problems. S imulation experiments are complished and numerical results show that better performance can be achieved by our algorithm than by some existing ones.