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Computational Intelligence and Neuroscience
Volume 2017, Article ID 4894278, 6 pages
Research Article

Fast Recall for Complex-Valued Hopfield Neural Networks with Projection Rules

Mathematical Science Center, University of Yamanashi, Takeda 4-3-11, Kofu, Yamanashi 400-8511, Japan

Correspondence should be addressed to Masaki Kobayashi;

Received 12 April 2016; Accepted 6 March 2017; Published 3 May 2017

Academic Editor: Silvia Conforto

Copyright © 2017 Masaki Kobayashi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Many models of neural networks have been extended to complex-valued neural networks. A complex-valued Hopfield neural network (CHNN) is a complex-valued version of a Hopfield neural network. Complex-valued neurons can represent multistates, and CHNNs are available for the storage of multilevel data, such as gray-scale images. The CHNNs are often trapped into the local minima, and their noise tolerance is low. Lee improved the noise tolerance of the CHNNs by detecting and exiting the local minima. In the present work, we propose a new recall algorithm that eliminates the local minima. We show that our proposed recall algorithm not only accelerated the recall but also improved the noise tolerance through computer simulations.