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Complex-valued neural network is a kind of learning model which can deal with problems in complex domain. Fully complex extreme learning machine (CELM) is a much faster training algorithm than the complex backpropagation (CBP) scheme. However, it is at the cost of using more hidden nodes to obtain the comparable performance. An upper-layer-solution-aware algorithm has been proposed for training single-hidden layer feedforward neural networks, which performs much better than its counterparts, pseudo-inverse learning (PIL)/extreme learning machine and gradient decent-based backpropagation neural networks. Consequently, there exist two challenges that need to be dealt with: 1) How to combine the advantages of CBP and CELM to develop a novel complex learning algorithm? and 2) What is the convergent behavior of the presented algorithm? In this article, an input weights dependent complex-valued (IWDCV) learning algorithm based on Wirtinger calculus has been proposed, which effectively solves the nonanalytic problem of the common activation functions during training neural networks. In addition, the monotonicity of the error function and the deterministic convergence of the proposed model have been strictly proved, which theoretically guarantee the efficiency and effectiveness of the given model, IWDCV. Finally, for real and complex-valued problems, a variety of simulations have been done to demonstrate the comparable performance of the proposed algorithm which support the theoretical observations as well. [ABSTRACT FROM AUTHOR]

This brief proposes an enhanced fractional derivative that can prevent the tap weight coefficients from destroying the gradient information, solve the problem caused by the fractional extreme point, and improve the convergence speed with the help of error estimation information and Sign function. Based on this fractional derivative, an enhanced fractional least mean square (EFLMS) filter algorithm is proposed. We analyze the influence of unknown system vector on the convergence performance of the EFLMS algorithm. The computational complexity of the proposed algorithm is also analyzed. Simulation experiments show that the EFLMS algorithm achieves better performance in system identification than the classic least mean square (LMS) algorithm and the existing algorithms based on fractional calculus. [ABSTRACT FROM AUTHOR]