Banach Space Valued Neural Network PDF Download
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Author: George A. Anastassiou
Publisher: Springer Nature
ISBN: 3031164008
Category : Technology & Engineering
Languages : en
Pages : 429
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Book Description
This book is about the generalization and modernization of approximation by neural network operators. Functions under approximation and the neural networks are Banach space valued. These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. Ordinary, fractional, fuzzy, and stochastic approximations are exhibited at the univariate, fractional, and multivariate levels. Iterated-sequential approximations are also covered. The book’s results are expected to find applications in the many areas of applied mathematics, computer science and engineering, especially in artificial intelligence and machine learning. Other possible applications can be in applied sciences like statistics, economics, etc. Therefore, this book is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.
Author: George A. Anastassiou
Publisher: Springer Nature
ISBN: 3031164008
Category : Technology & Engineering
Languages : en
Pages : 429
Get Book
Book Description
This book is about the generalization and modernization of approximation by neural network operators. Functions under approximation and the neural networks are Banach space valued. These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. Ordinary, fractional, fuzzy, and stochastic approximations are exhibited at the univariate, fractional, and multivariate levels. Iterated-sequential approximations are also covered. The book’s results are expected to find applications in the many areas of applied mathematics, computer science and engineering, especially in artificial intelligence and machine learning. Other possible applications can be in applied sciences like statistics, economics, etc. Therefore, this book is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.
Author: George A. Anastassiou
Publisher: Springer Nature
ISBN: 3031430212
Category : Technology & Engineering
Languages : en
Pages : 854
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Book Description
In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.
Author: George A. Anastassiou
Publisher: Springer
ISBN: 3319669362
Category : Technology & Engineering
Languages : en
Pages : 319
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Book Description
This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book’s results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read independently. This concise book is suitable for use in related graduate classes and many research projects. An extensive list of references is provided for each chapter. The book’s results are relevant for many areas of pure and applied mathematics. As such, it offers a unique resource for researchers, and a valuable addition to all science and engineering libraries.
Author: Monica Bianchini
Publisher: Springer Science & Business Media
ISBN: 3642366570
Category : Technology & Engineering
Languages : en
Pages : 547
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Book Description
This handbook presents some of the most recent topics in neural information processing, covering both theoretical concepts and practical applications. The contributions include: Deep architectures Recurrent, recursive, and graph neural networks Cellular neural networks Bayesian networks Approximation capabilities of neural networks Semi-supervised learning Statistical relational learning Kernel methods for structured data Multiple classifier systems Self organisation and modal learning Applications to content-based image retrieval, text mining in large document collections, and bioinformatics This book is thought particularly for graduate students, researchers and practitioners, willing to deepen their knowledge on more advanced connectionist models and related learning paradigms.
Author: Jean-Pierre Aubin
Publisher: Cambridge University Press
ISBN: 9780521445320
Category : Computers
Languages : en
Pages : 306
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Book Description
This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a "learning algorithm" of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints.
Author: Jagdev Singh
Publisher: Springer Nature
ISBN: 3031563042
Category :
Languages : en
Pages : 365
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Book Description
Author: Akira Hirose
Publisher: World Scientific
ISBN: 9814485373
Category : Computers
Languages : en
Pages : 388
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Book Description
In recent years, complex-valued neural networks have widened the scope of application in optoelectronics, imaging, remote sensing, quantum neural devices and systems, spatiotemporal analysis of physiological neural systems, and artificial neural information processing. In this first-ever book on complex-valued neural networks, the most active scientists at the forefront of the field describe theories and applications from various points of view to provide academic and industrial researchers with a comprehensive understanding of the fundamentals, features and prospects of the powerful complex-valued networks. Contents:Complex-Valued Neural Networks: An Introduction (A Hirose)Orthogonal Decision Boundaries and Generalization of Complex-Valued Neural Networks (T Nitta)Clifford Networks (J Pearson)Applications of Complex-Valued Neural Networks for Image Processing (H Aoki)Phasor Model with Application to Multiuser Communication (T Miyajima & K Yamanaka)Adaptive Interferometric Radar Image Processing by Using Complex-Valued Neural Network (A B Suksmono & A Hirose)Coherent Lightwave Neural Network Systems: Use of Frequency Domain (S Kawata & A Hirose)and other articles Readership: Graduate students, academics, researchers, and industrialists in neural networks. Keywords:Neural Networks;Associative Memories;Image Processing;Signal Processing
Author: Nitta, Tohru
Publisher: IGI Global
ISBN: 1605662151
Category : Computers
Languages : en
Pages : 504
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Book Description
"This book covers the current state-of-the-art theories and applications of neural networks with high-dimensional parameters"--Provided by publisher.
Author: Akira Hirose
Publisher: John Wiley & Sons
ISBN: 1118590066
Category : Computers
Languages : en
Pages : 238
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Book Description
Presents the latest advances in complex-valued neural networks by demonstrating the theory in a wide range of applications Complex-valued neural networks is a rapidly developing neural network framework that utilizes complex arithmetic, exhibiting specific characteristics in its learning, self-organizing, and processing dynamics. They are highly suitable for processing complex amplitude, composed of amplitude and phase, which is one of the core concepts in physical systems to deal with electromagnetic, light, sonic/ultrasonic waves as well as quantum waves, namely, electron and superconducting waves. This fact is a critical advantage in practical applications in diverse fields of engineering, where signals are routinely analyzed and processed in time/space, frequency, and phase domains. Complex-Valued Neural Networks: Advances and Applications covers cutting-edge topics and applications surrounding this timely subject. Demonstrating advanced theories with a wide range of applications, including communication systems, image processing systems, and brain-computer interfaces, this text offers comprehensive coverage of: Conventional complex-valued neural networks Quaternionic neural networks Clifford-algebraic neural networks Presented by international experts in the field, Complex-Valued Neural Networks: Advances and Applications is ideal for advanced-level computational intelligence theorists, electromagnetic theorists, and mathematicians interested in computational intelligence, artificial intelligence, machine learning theories, and algorithms.
Author: Igor Aizenberg
Publisher: Springer Science & Business Media
ISBN: 3642203523
Category : Computers
Languages : en
Pages : 273
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Book Description
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.
