Издательство IEEE/John Wiley, 2013, -303 pp.Complex-valued neural networks (CVNNs) have continued to open doors to various new applications. The CVNNs are the neural networks that deal with complex amplitude, i.e. signal having phase and amplitude, which is one of the most core concepts in science and technology, in particular in electrical and electronic engineering. A CVNN is not equivalent to a double-dimensional real-valued neural network. It has different dynamics and characteristics such as generalization, which is significantly useful in treatment of complex-amplitude information and wave-related phenomena. This is a critical point in applications in engineering fields. It is also crucial for developing new devices in the future. That is, the CVNN framework will play an important role in introduction of learning and self-organization into future quantum devices dealing with electron waves and photonic waves.
We can further expect that broad-sense CVNNs such as quatemion neural networks break ground in unique directions respectively. Quatemion has been essential in computer graphics to render three-dimensional moving objects. When we introduce learning and self-organization in virtual realities and computer-aided amenities, quatemion neural networks will surely bring an important fundamental basis. CVNNs may be useful even in physiological analysis and modeling where the researchers suggest, for example, that the phase information of neuron firing timing against the theta wave in electroencephalography possesses a close relationship to short-term position memory in the brain.Application Fields and Fundamental Merits
Neural System Learning on Complex-Valued Manifolds
N -Dimensional Vector Neuron and Parity Problem Its Application to the N -Bit
Learning Algorithms in Complex-Valued Neural Networks using Wirtinger Calculus
Quaternionic Neural Networks for Associative Memories
Models of Recurrent Clifford Neural Networks and Their Dynamics
Meta-cognitive Complex-valued Relaxation Network and its Sequential Learning Algorithm
Multilayer Feedforward Neural Network with Multi-Valued Neurons for Brain-Computer Interfacing
Complex-Valued B-Spline Neural Networks for Modeling and Inverse of Wiener Systems

Quaternionic Fuzzy Neural Network for View-invariant Color Face Image Recognition

Издательство IEEE/John Wiley, 2013, -303 pp.复值神经网络（CVNNs）不断为各种新的应用打开大门。复杂值神经网络是处理复杂振幅的神经网络，即具有相位和振幅的信号，这是科学技术，特别是电气和电子工程中最核心的概念之一。一个CVNN并不等同于一个双维实值神经网络。它具有不同的动态和特性，如泛化，这在处理复杂振幅信息和波浪相关现象方面有很大作用。这是工程领域应用中的一个关键点。它对于未来开发新设备也是至关重要的。也就是说，CVNN框架将在未来处理电子波和光子波的量子设备中引入学习和自组织方面发挥重要作用。

我们可以进一步期待广义的CVNN，如quatemion神经网络分别在独特的方向上有所突破。Quatemion在计算机图形学中对渲染三维移动物体至关重要。当我们在虚拟现实和计算机辅助设施中引入学习和自组织时，quatemion神经网络肯定会带来重要的基础。CVNN甚至在生理分析和建模中也可能是有用的，例如，研究人员提出，神经元发射时间与脑电图中θ波的相位信息与大脑中的短期位置记忆有密切关系。

复杂值流形上的神经系统学习

N-维向量神经元和奇偶性问题及其在N-位上的应用

使用韦尔廷格微积分的复值神经网络的学习算法

关联记忆的四元神经网络

循环克利福德神经网络的模型及其动态变化

元认知复值松弛网络及其顺序学习算法

用于脑机接口的多层前馈神经网络与多值神经元的关系

用于维纳系统建模和逆向的复值B-Spline神经网络

四元模糊神经网络用于视变彩色人脸图像识别