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On the complex backpropagation algorithm
IEEE Transactions on Signal Processing
The complex backpropagation algorithm
IEEE Transactions on Signal Processing
Channel equalization using adaptive complex radial basis function networks
IEEE Journal on Selected Areas in Communications
Nonlinear blind equalization schemes using complex-valued multilayer feedforward neural networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Fast learning fully complex-valued classifiers for real-valued classification problems
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Single layer complex valued neural network with entropic cost function
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
Information Sciences: an International Journal
Complex-Valued neuro-fuzzy inference system based classifier
SEMCCO'12 Proceedings of the Third international conference on Swarm, Evolutionary, and Memetic Computing
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In a fully complex-valued feed-forward network, the convergence of the Complex-valued Back Propagation (CBP) learning algorithm depends on the choice of the activation function, learning sample distribution, minimization criterion, initial weights and the learning rate. The minimization criteria used in the existing versions of CBP learning algorithm in the literature do not approximate the phase of complex-valued output well in function approximation problems. The phase of a complex-valued output is critical in telecommunication and reconstruction and source localization problems in medical imaging applications. In this paper, the issues related to the convergence of complex-valued neural networks are clearly enumerated using a systematic sensitivity study on existing complex-valued neural networks. In addition, we also compare the performance of different types of split complex-valued neural networks. From the observations in the sensitivity analysis, we propose a new CBP learning algorithm with logarithmic performance index for a complex-valued neural network with exponential activation function. The proposed CBP learning algorithm directly minimizes both the magnitude and phase errors and also provides better convergence characteristics. Performance of the proposed scheme is evaluated using two synthetic complex-valued function approximation problems, the complex XOR problem, and a non-minimum phase equalization problem. Also, a comparative analysis on the convergence of the existing fully complex and split complex networks is presented.