Research On Learning Algorithms For Complex-valued Neural Networks With Non-analytic Activation Functions

In recent years,neural networks have received extensive attention and been widely used in many research fields such as pattern recognition,automatic control and signal processing.The neural network is divided into real value neural network and complex value neural network,ince a single real valued neuron can only deal with linear separable problems,a single complex valued neuron can deal with nonlinear separable problems,so complex neural network has received more attention.But because liouville’s theorem puts forward that any bounded analytic function is a constant value function,the complex analytic extraordinary value function is usually unbounded on the complex plane.However,the bounded activation function is very necessary for the practical application of CVNNs,so we introduce CVNNs network with non-analytic activation function,which can guarantee that it is bounded in any bounded closed region.The main work of this paper is the third chapter and the fourth chapter.Third chapter on the premise of limited training samples,the analysis for a class of non-parse complex neural network activation function of CR after convergence of gradient algorithm,proves that the enhancement of analytic CVNNs after CR value function after weak convergence and strong convergence of gradient method,the objective function of the CR after gradient converges to zero sequence and weight tend to a fixed value,and on the classification and regression problems demonstrate the theoretical results of the algorithm.The fourth chapter use CVNNs can effectively deal with the complex signal,on the basis of the relationship between the complex and diverse real,for the real learning algorithm in complex domain proposed a simpler method,called low complexity algorithm,in the same way the objective function converges to zero,the low complexity of CR after gradient and through common UCI data sets such as the convergence of the proposed algorithm is demonstrated.Finally,the accuracy,convergence performance and convergence time of CR gradient algorithms with different non-analytic activation functions are compared.