Complex-Valued Neural Networks have higher functionality, learn faster and generalize better than their real-valued counterparts. This book is devoted to the Multi-Valued Neuron (MVN) and MVN-based neural networks. It contains a comprehensive observation of MVN theory, its learning, and applications. MVN is a complex-valued neuron whose inputs and output are located on the unit circle. Its activation function is a function only of argument (phase) of the weighted sum. MVN derivative-free learning is based on the error-correction rule. A single MVN can learn those input/output mappings that are non-linearly separable in the real domain. Such classical non-linearly separable problems as XOR and Parity n are the simplest that can be learned by a single MVN. Another important advantage of MVN is a proper treatment of the phase information. These properties of MVN become even more remarkable when this neuron is used as a basic one in neural networks. The Multilayer Neural Network based on Multi-Valued Neurons (MLMVN) is an MVN-based feedforward neural network. Its backpropagation learning algorithm is derivative-free and based on the error-correction rule. It does not suffer from the local minima phenomenon. MLMVN outperforms many other machine learning techniques in terms of learning speed, network complexity and generalization capability when solving both benchmark and real-world classification and prediction problems. Another interesting application of MVN is its use as a basic neuron in multi-state associative memories. The book is addressed to those readers who develop theoretical fundamentals of neural networks and use neural networks for solving various real-world problems. It should also be very suitable for Ph.D. and graduate students pursuing their degrees in computational intelligence.

Complex-Valued Neural Networks have higher functionality, learn faster and generalize better than their real-valued counterparts. This book is devoted to the Multi-Valued Neuron (MVN) and MVN-based neural networks. It contains a comprehensive observation of MVN theory, its learning, and applications. MVN is a complex-valued neuron whose inputs and output are located on the unit circle. Its activation function is a function only of argument (phase) of the weighted sum. MVN derivative-free learning is based on the error-correction rule. A single MVN can learn those input/output mappings that are non-linearly separable in the real domain. Such classical non-linearly separable problems as XOR and Parity n are the simplest that can be learned by a single MVN. Another important advantage of MVN is a proper treatment of the phase information. These properties of MVN become even more remarkable when this neuron is used as a basic one in neural networks. The Multilayer Neural Network based on Multi-Valued Neurons (MLMVN) is an MVN-based feedforward neural network. Its backpropagation learning algorithm is derivative-free and based on the error-correction rule. It does not suffer from the local minima phenomenon. MLMVN outperforms many other machine learning techniques in terms of learning speed, network complexity and generalization capability when solving both benchmark and real-world classification and prediction problems. Another interesting application of MVN is its use as a basic neuron in multi-state associative memories. The book is addressed to those readers who develop theoretical fundamentals of neural networks and use neural networks for solving various real-world problems. It should also be very suitable for Ph.D. and graduate students pursuing their degrees in computational intelligence.

Multi-Valued and Universal Binary Neurons deals with two new types of neurons: multi-valued neurons and universal binary neurons. These neurons are based on complex number arithmetic and are hence much more powerful than the typical neurons used in artificial neural networks. Therefore, networks with such neurons exhibit a broad functionality. They can not only realise threshold input/output maps but can also implement any arbitrary Boolean function. Two learning methods are presented whereby these networks can be trained easily. The broad applicability of these networks is proven by several case studies in different fields of application: image processing, edge detection, image enhancement, super resolution, pattern recognition, face recognition, and prediction. The book is hence partitioned into three almost equally sized parts: a mathematical study of the unique features of these new neurons, learning of networks of such neurons, and application of such neural networks. Most of this work was developed by the first two authors over a period of more than 10 years and was only available in the Russian literature. With this book we present the first comprehensive treatment of this important class of neural networks in the open Western literature. Multi-Valued and Universal Binary Neurons is intended for anyone with a scholarly interest in neural network theory, applications and learning. It will also be of interest to researchers and practitioners in the fields of image processing, pattern recognition, control and robotics.

Multi-Valued and Universal Binary Neurons deals with two new types of neurons: multi-valued neurons and universal binary neurons. These neurons are based on complex number arithmetic and are hence much more powerful than the typical neurons used in artificial neural networks. Therefore, networks with such neurons exhibit a broad functionality. They can not only realise threshold input/output maps but can also implement any arbitrary Boolean function. Two learning methods are presented whereby these networks can be trained easily. The broad applicability of these networks is proven by several case studies in different fields of application: image processing, edge detection, image enhancement, super resolution, pattern recognition, face recognition, and prediction. The book is hence partitioned into three almost equally sized parts: a mathematical study of the unique features of these new neurons, learning of networks of such neurons, and application of such neural networks. Most of this work was developed by the first two authors over a period of more than 10 years and was only available in the Russian literature. With this book we present the first comprehensive treatment of this important class of neural networks in the open Western literature. Multi-Valued and Universal Binary Neurons is intended for anyone with a scholarly interest in neural network theory, applications and learning. It will also be of interest to researchers and practitioners in the fields of image processing, pattern recognition, control and robotics.