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H.-G. Zimmermann, A. Minin and V. Kusherbaeva, “Comparison of the Complex Valued and Real Valued Neural Networks Trained with Gradient Descent and Random Search Algorithms,” 19th European Symposium on Artificial Neural Networks, Bruges, 27-29 April 2011, pp. 216-222.

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.