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Mathematics of Neural Networks : Models, Algorithms, and Applications :  Models, Algorithms, and Applications - Stephen W. Ellacott

Mathematics of Neural Networks : Models, Algorithms, and Applications

Models, Algorithms, and Applications

By: Stephen W. Ellacott (Editor), John C. Mason (Editor), Iain J. Anderson (Editor)

Hardcover Published: 1st April 2002
ISBN: 9780792399339
Number Of Pages: 403

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This book examines the mathematics, probability, statistics, and computational theory underlying neural networks and their applications. In addition to the theoretical work, the book covers a considerable range of neural network topics such as learning and training, neural network classifiers, memory-based networks, self-organizing maps and unsupervised learning, Hopfeld networks, radial basis function networks, and general network modelling and theory. Added to the book's mathematical and neural network topics are applications in chemistry, speech recognition, automatic control, nonlinear programming, medicine, image processing, finance, time series, and dynamics. As a result, the book surveys a wide range of recent research on the theoretical foundations of creating neural network models in a variety of application areas.

Preface
N-Tuple Neural Networksp. 3
Information Geometry of Neural Networks - An Overviewp. 15
Q-Learning: A Tutorial and Extensionsp. 24
Are There Universal Principles of Brain Computation?p. 34
On-line Training of Memory-Driven Attractor Networksp. 41
Mathematical Problems Arising from Constructing an Artificial Brainp. 47
The Successful Use of Probability Data in Connectionist Modelsp. 61
Weighted Mixture of Models for On-Line Learningp. 67
Local Modifications to Radial Basis Networksp. 73
A Statistical Analysis of the Modified NLMS Rulesp. 78
Finite Size Effects in On-Line Learning of Multi-Layer Neural Networksp. 84
Constant Fan-In Digital Neural Networks are VLSI-Optimalp. 89
The Application of Binary Encoded 2nd Differential Spectrometry in Preprocessing of UV-VIS Absorption Spectral Datap. 95
A Non-Equidistant Elastic Net Algorithmp. 101
Unimodal Loading Problemsp. 107
On the Use of Simple Classifiers for the Initialisation of One-Hidden-Layer Neural Netsp. 113
Modelling Conditional Probability Distributions for Periodic Variablesp. 118
Integro-Differential Equations in Compartmental Model Neurodynamicsp. 123
Nonlinear Models for Neural Networksp. 129
A Neural Network for the Travelling Salesman Problem with a Well Behaved Energy Functionp. 134
Semiparametric Artificial Neural Networksp. 140
An Event-Space Feedforward Network Using Maximum Entropy Partitioning with Application to Low Level Speech Datap. 146
Approximating the Bayesian Decision Boundary for Channel Equalisation Using Subset Radial Basis Function Networkp. 151
Applications of Graph Theory to the Design of Neural Networks for Automated Fingerprint Identificationp. 156
Zero Dynamics and Relative Degree of Dynamic Recurrent Neural Networksp. 161
Irregular Sampling Approach to Neurocontrol: The Band- and Space-Limited Functions Questionsp. 166
Unsupervised Learning of Temporal Constancies by Pyramidal-Type Neuronsp. 171
Numerical Aspects of Machine Learning in Artificial Neural Networksp. 176
Learning Algorithms for Ram-Based Neural Networksp. 181
Analysis of Correlation Matrix Memory and Partial Match-Implications for Cognitive Psychologyp. 186
Regularization and Realizability in Radial Basis Function Networksp. 192
A Universal Approximator Network for Learning Conditional Probability Densitiesp. 198
Convergence of a Class of Neural Networksp. 204
Applications of the Compartmental Model Neuron to Time Series Analysisp. 209
Information Theoretic Neural Networks for Contextually Guided Unsupervised Learningp. 215
Convergence in Noisy Trainingp. 220
Non-Linear Learning Dynamics with a Diffusing Messengerp. 225
A Variational Approach to Associative Memoryp. 230
Transformation of Nonlinear Programming Problems into Separable Ones Using Multilayer Neural Networksp. 235
A Theory of Self-Organising Neural Networksp. 240
Neural Network Supervised Training Based on a Dimension Reducing Methodp. 245
A Training Method for Discrete Multilayer Neural Networksp. 250
Local Minimal Realisations of Trained Hopfield Networksp. 255
Data Dependent Hyperparameter Assignmentp. 259
Training Radial Basis Function Networks by Using Separable and Orthogonalized Gaussiansp. 265
Error Bounds for Density Estimation by Mixturesp. 270
On Smooth Activation Functionsp. 275
Generalisation and Regularisation by Gaussian Filter Convolution of Radial Basis Function Networksp. 280
Dynamical System Prediction: A Lie Algebraic Approach for a Novel Neural Architecturep. 285
Stochastic Neurodynamics and the System Size Expansionp. 290
An Upper Bound on the Bayesian Error Bars for Generalized Linear Regressionp. 295
Capacity Bounds for Structured Neural Network Architecturesp. 300
On-Line Learning in Multilayer Neural Networksp. 306
Spontaneous Dynamics and Associative Learning in an Assymetric Recurrent Random Neural Networkp. 312
A Statistical Mechanics Analysis of Genetic Algorithms for Search and Learningp. 318
Volumes of Attraction Basins in Randomly Connected Boolean Networksp. 323
Evidential Rejection Strategy for Neural Network Classifiersp. 328
Dynamics Approximation and Change Point Retrieval from a Neural Network Modelp. 333
Query Learning for Maximum Information Gain in a Multi-Layer Neural Networkp. 339
Shift, Rotation and Scale Invariant Signatures for Two-Dimensional Contours, in a Neural Network Architecturep. 344
Function Approximation by Three-Layer Artificial Neural Networksp. 349
Neural Network Versus Statistical Clustering Techniques: A Pilot Study in a Phoneme Recognition Taskp. 355
Multispectral Image Analysis Using Pulsed Coupled Neural Networksp. 361
Reasoning Neural Networksp. 366
Capacity of the Upstart Algorithmp. 372
Regression with Gaussian Processesp. 378
Stochastic Forward-Perturbation, Error Surface and Progressive Learning in Neural Networksp. 383
Dynamical Stability of a High-Dimensional Self-Organizing Mapp. 389
Measurements of Generalisation Based on Information Geometryp. 394
Towards an Algebraic Theory of Neural Networks: Sequential Compositionp. 399
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792399339
ISBN-10: 0792399331
Series: Operations Research/Computer Science Interfaces Series
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 403
Published: 1st April 2002
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 2.3
Weight (kg): 0.78