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D. H. Brandwood, “A Complex Gradient Operator and Its Application in Adaptive Array Theory,” IEEE Proceedings, F: Communications, Radar and Signal Processing, Vol. 130, No. 1, 1983, p. 1116.

has been cited by the following article:

• TITLE: Complex Valued Recurrent Neural Network: From Architecture to Training

  AUTHORS: Alexey Minin, Alois Knoll, Hans-Georg Zimmermann

  KEYWORDS: Complex Valued Neural Networks; Complex Valued System Identification; Recurrent Neural Networks; Complex Valued Recurrent Neural Networks

  JOURNAL NAME: Journal of Signal and Information Processing, Vol.3 No.2, May 30, 2012

  ABSTRACT: Recurrent Neural Networks were invented a long time ago, and dozens of different architectures have been published. In this paper we generalize recurrent architectures to a state space model, and we also generalize the numbers the network can process to the complex domain. We show how to train the recurrent network in the complex valued case, and we present the theorems and procedures to make the training stable. We also show that the complex valued recurrent neural network is a generalization of the real valued counterpart and that it has specific advantages over the latter. We conclude the paper with a discussion of possible applications and scenarios for using these networks.