| In recent years,Extreme Learning Machine(ELM)has been widely used because of its simple structure,fast learning speed and strong generalization ability.It has been a popular learning strategy for single hidden layer feedforward neural networks(SLFNs).ELM has been extended from real domain to complex domain to establish the complex-valued extreme learning machine(CELM).CELM can get better accuracy than ELM when dealing with complex-valued signals.However,when dealing with complex-valued non-circular signals,CELM can only obtain the suboptimal solution because it cannot fully capture the second order statistics of complex-valued signals.To solve this problem,researchers proposed two augmented algorithms based on the CELM model.However,the introduced conjugate information of the complex-valued signal increases the computational complexity of the augmented algorithms,which means more training time is needed.To fix this drawback,this thesis proposes two methods to reduce the computational complexity of the augmented algorithms,in this way we arrive at several fast learning algorithms of the augmented CELM.The thesis is mainly developed according to the following five aspects:(1)Based on the original augmented CELMs and dual-channel estimation,a dual-channel CELM with augmented input layer and that with augmented hidden layer are proposed.The corresponding regularization models are also established based on Wirtinger calculus;(2)For the sake of the online signal processing,the corresponding dual-channel models for augmented CELM are also established;(3)Based on the special structure of the covariance matrix of the dual-channel CELM with augmented the hidden layer,the algorithm is further improved by computing the inverse of the covariance matrix based on the inverse of the sub-matrices;(4)The equivalence of the proposed dual-channel algorithms and the original augmented algorithms is proved,and their computational complexity is analyzed.It is theoretically proved that the proposed algorithm can effectively reduce the amount of calculations while maintaining the performance level of the original augmented algorithm;(5)Numerical experiments are performed to compare the proposed algorithms with the original ones,which verify the effectiveness of the proposed algorithms. |
