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Ability of the 1-n-1 Complex-Valued Neural Network to Learn Transformations

Ability of the 1-n-1 Complex-Valued Neural Network to Learn Transformations

Tohru Nitta (National Institute of Advanced Industrial Science and Technology (AIST), Japan)
Copyright: © 2011 |Pages: 31
ISBN13: 9781609605513|ISBN10: 1609605519|EISBN13: 9781609605520
DOI: 10.4018/978-1-60960-551-3.ch022
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MLA

Nitta, Tohru. "Ability of the 1-n-1 Complex-Valued Neural Network to Learn Transformations." Computational Modeling and Simulation of Intellect: Current State and Future Perspectives, edited by Boris Igelnik, IGI Global, 2011, pp. 566-596. https://doi.org/10.4018/978-1-60960-551-3.ch022

APA

Nitta, T. (2011). Ability of the 1-n-1 Complex-Valued Neural Network to Learn Transformations. In B. Igelnik (Eds.), Computational Modeling and Simulation of Intellect: Current State and Future Perspectives (pp. 566-596). IGI Global. https://doi.org/10.4018/978-1-60960-551-3.ch022

Chicago

Nitta, Tohru. "Ability of the 1-n-1 Complex-Valued Neural Network to Learn Transformations." In Computational Modeling and Simulation of Intellect: Current State and Future Perspectives. edited by Igelnik, Boris, 566-596. Hershey, PA: IGI Global, 2011. https://doi.org/10.4018/978-1-60960-551-3.ch022

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Abstract

The ability of the 1-n-1 complex-valued neural network to learn 2D affine transformations has been applied to the estimation of optical flows and the generation of fractal images. The complex-valued neural network has the adaptability and the generalization ability as inherent nature. This is the most different point between the ability of the 1-n-1 complex-valued neural network to learn 2D affine transformations and the standard techniques for 2D affine transformations such as the Fourier descriptor. It is important to clarify the properties of complex-valued neural networks in order to accelerate their practical applications more and more. In this chapter, the behavior of the 1-n-1 complex-valued neural network that has learned a transformation on the Steiner circles is demonstrated, and the relationship the values of the complex-valued weights after training and a linear transformation related to the Steiner circles is clarified via computer simulations. Furthermore, the relationship the weight values of the 1-n-1 complex-valued neural network learned 2D affine transformations and the learning patterns used is elucidated. These research results make it possible to solve complicated problems more simply and efficiently with 1-n-1 complex-valued neural networks. As a matter of fact, an application of the 1-n-1 type complex-valued neural network to an associative memory is presented.

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