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Download Complex-Valued Neural Networks: Advances and Applications by Akira Hirose PDF

By Akira Hirose

Presents the most recent advances in complex-valued neural networks by means of demonstrating the idea in a variety of applications

Complex-valued neural networks is a quickly constructing neural community framework that makes use of advanced mathematics, displaying particular features in its studying, self-organizing, and processing dynamics. they're hugely compatible for processing advanced amplitude, composed of amplitude and section, that's one of many center thoughts in actual structures to house electromagnetic, gentle, sonic/ultrasonic waves in addition to quantum waves, particularly, electron and superconducting waves. This truth is a serious virtue in functional functions in diversified fields of engineering, the place signs are many times analyzed and processed in time/space, frequency, and section domains.

Complex-Valued Neural Networks: Advances and Applications covers state-of-the-art issues and purposes surrounding this well timed topic. Demonstrating complicated theories with a variety of purposes, together with conversation platforms, picture processing platforms, and brain-computer interfaces, this article deals complete assurance of:

  • Conventional complex-valued neural networks
  • Quaternionic neural networks
  • Clifford-algebraic neural networks

Presented by means of foreign specialists within the box, Complex-Valued Neural Networks: Advances and Applications is perfect for advanced-level computational intelligence theorists, electromagnetic theorists, and mathematicians attracted to computational intelligence, man made intelligence, computing device studying theories, and algorithms.

Content:
Chapter 1 program Fields and basic benefits of Complex?Valued Neural Networks (pages 1–31): Akira Hirose
Chapter 2 Neural method studying on Complex?Valued Manifolds (pages 33–57): Simone Fiori
Chapter three N?Dimensional Vector Neuron and Its software to the N?Bit Parity challenge (pages 59–74): Tohru Nitta
Chapter four studying Algorithms in Complex?Valued Neural Networks utilizing Wirtinger Calculus (pages 75–102): Md. Faijul Amin and Kazuyuki Murase
Chapter five Quaternionic Neural Networks for Associative stories (pages 103–131): Teijiro Isokawa, Haruhiko Nishimura and Nobuyuki Matsui
Chapter 6 types of Recurrent Clifford Neural Networks and Their Dynamics (pages 133–151): Yasuaki Kuroe
Chapter 7 Meta?Cognitive Complex?Valued leisure community and Its Sequential studying set of rules (pages 153–183): Ramasamy Savitha, Sundaram Suresh and Narasimhan Sundarara
Chapter eight Multilayer Feedforward Neural community with Multi?Valued Neurons for Brain–Computer Interfacing (pages 185–208): Nikolay V. Manyakov, Igor Aizenberg, Nikolay Chumerin and Marc M. Van Hulle
Chapter nine Complex?Valued B?Spline Neural Networks for Modeling and Inverse of Wiener structures (pages 209–234): Xia Hong, Sheng Chen and Chris J. Harris
Chapter 10 Quaternionic Fuzzy Neural community for View?Invariant colour Face picture acceptance (pages 235–278): Wai equipment Wong, Gin Chong Lee, Chu Kiong bathroom lavatory, method Soong Lim and Raymond Lock

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Additional info for Complex-Valued Neural Networks: Advances and Applications

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Special session on Clifford algebraic neural networks. In International Conference on Neural Information Processing (ICONIP) 2011 Shanghai. Springer, 2011. 55. Dong-Chul Park and Tae-Kyun Jung Jeong. Complex-bilinear recurrent neural networks for equilization of a digital satellite channel. IEEE Transactions on Neural Networks, 13(3):711-725, March 2002. 56. Bernard Picinbono and Pascal Chevalier. Widely linear estimation with complex data. IEEE Transactions on Signal Processing, 43(8):2030-2033, August 1995.

Geodesic stepping is based on the calculation of geodesic arcs in closed form and provides a geometrically sound way of moving from a point along a given direction on a Riemannian manifold proportionally to a learning stepsize. A method to compute a numerically optimal learning stepsize schedule is discussed as well, which resembles the line-search method on Euclidean spaces, termed geodesic-search method. An advantage of the devised geodesic-search method is that, in the space §£ (C), the geodesic curve is periodic of finite period, hence the learning stepsize belongs to a closed interval.

A matrix has a logarithm if and only if it is invertible. The logarithm is not unique, but if a matrix has no negative real eigenvalues, then it has a unique logarithm known as the principal logarithm, which is denoted by log(^). Furthermore, if, for any given matrix norm || · || it holds \\g — Ip11 < 1, where Ip denotes the identity element in Gl(p), then it holds that k=l In general, given matrices gi,g2 G G7(p, C), it holds that log(pi^2) Φ log(#i) + log(<72)· In practice, matrix exponential and logarithm may be computed efficiently by making use of the spectral decomposition of matrices or by various approximate methods [9, 31].

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