Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Multi-Valued and Universal Binary Neurons: Theory, Learning and Applications
Multi-Valued and Universal Binary Neurons: Theory, Learning and Applications
Complex-Valued Neural Networks (Studies in Computational Intelligence)
Complex-Valued Neural Networks (Studies in Computational Intelligence)
Duality between widely linear and dual channel adaptive filtering
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models
Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models
Nonlinear adaptive prediction of complex-valued signals by complex-valued PRNN
IEEE Transactions on Signal Processing
Second-order analysis of improper complex random vectors and processes
IEEE Transactions on Signal Processing
Widely linear estimation with complex data
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Complex random vectors and ICA models: identifiability, uniqueness, and separability
IEEE Transactions on Information Theory
The multivariate complex normal distribution-a generalization
IEEE Transactions on Information Theory
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This paper uses new developments in the statistics of complex variable and recent results on the duality between the bivariate and complex calculus to provide a unified design of complex valued temporal neural networks. For generality, the case of recurrent neural networks is addressed in detail, as they simplify into feedforward networks upon cancellation of the feedback. The use of CIR. calculus provides a convenient framework for the calculation of gradients of real functions of complex variables (cost functions) which do not obey the Cauchy-Riemann conditions. Further, the analysis is based on so called augmented complex statistics, to provide a rigorous treatment of complex noncircularity and nonlinearity, thus avoiding the deficiencies inherent in several mathematical shortcuts typically used in the treatment of complex random signals. The complex models addressed in this work, are based on widely linear nonlinear autoregressive moving average (NARMA) models and are shown to be suitable for processing the generality of complex signals, both second order circular (proper) and noncircular (improper).