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Neural Networks

A Systematic Introduction

Erschienen am 01.07.1996
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ISBN/EAN: 9783540605058
Sprache: Englisch
Auflage: 1. Auflage

Beschreibung

Inhaltsangabe1. The Biological Paradigm.- 1.1 Neural computation.- 1.1.1 Natural and artificial neural networks.- 1.1.2 Models of computation.- 1.1.3 Elements of a computing model.- 1.2 Networks of neurons.- 1.2.1 Structure of the neurons.- 1.2.2 Transmission of information.- 1.2.3 Information processing at the neurons and synapses.- 1.2.4 Storage of information - learning.- 1.2.5 The neuron - a self-organizing system.- 1.3 Artificial neural networks.- 1.3.1 Networks of primitive functions.- 1.3.2 Approximation of functions.- 1.3.3 Caveat.- 1.4 Historical and bibliographical remarks.- 2. Threshold Logic.- 2.1 Networks of functions.- 2.1.1 Feed-forward and recurrent networks.- 2.1.2 The computing units.- 2.2 Synthesis of Boolean functions.- 2.2.1 Conjunction, disjunction, negation.- 2.2.2 Geometric interpretation.- 2.2.3 Constructive synthesis.- 2.3 Equivalent networks.- 2.3.1 Weighted and unweighted networks.- 2.3.2 Absolute and relative inhibition.- 2.3.3 Binary signals and pulse coding.- 2.4 Recurrent networks.- 2.4.1 Stored state networks.- 2.4.2 Finite automata.- 2.4.3 Finite automata and recurrent networks.- 2.4.4 A first classification of neural networks.- 2.5 Harmonic analysis of logical functions.- 2.5.1 General expression.- 2.5.2 The Hadamard-Walsh transform.- 2.5.3 Applications of threshold logic.- 2.6 Historical and bibliographical remarks.- 3.Weighted Networks - The Perceptron.- 3.1 Perceptrons and parallel processing.- 3.1.1 Perceptrons as weighted threshold elements.- 3.1.2 Computational limits of the perceptron model.- 3.2 Implementation of logical functions.- 3.2.1 Geometric interpretation.- 3.2.2 The XOR problem.- 3.3 Linearly separable functions.- 3.3.1 Linear separability.- 3.3.2 Duality of input space and weight space.- 3.3.3 The error function in weight space.- 3.3.4 General decision curves.- 3.4 Applications and biological analogy.- 3.4.1 Edge detection with perceptrons.- 3.4.2 The structure of the retina.- 3.4.3 Pyramidal networks and the neocognitron.- 3.4.4 The silicon retina.- 3.5 Historical and bibliographical remarks.- 4. Perceptron Learning.- 4.1 Learning algorithms for neural networks.- 4.1.1 Classes of learning algorithms.- 4.1.2 Vector notation.- 4.1.3 Absolute linear separability.- 4.1.4 The error surface and the search method.- 4.2 Algorithmic learning.- 4.2.1 Geometric visualization.- 4.2.2 Convergence of the algorithm.- 4.2.3 Accelerating convergence.- 4.2.4 The pocket algorithm.- 4.2.5 Complexity of perceptron learning.- 4.3 Linear programming.- 4.3.1 Inner points of polytopes.- 4.3.2 Linear separability as linear optimization.- 4.3.3 Karmarkar's algorithm.- 4.4 Historical and bibliographical remarks.- 5. Unsupervised Learning and Clustering Algorithms.- 5.1 Competitive learning.- 5.1.1 Generalization of the perceptron problem.- 5.1.2 Unsupervised learning through competition.- 5.2 Convergence analysis.- 5.2.1 The one-dimensional case - energy function.- 5.2.2 Multidimensional case - the classical methods.- 5.2.3 Unsupervised learning as minimization problem.- 5.2.4 Stability of the solutions.- 5.3 Principal component analysis.- 5.3.1 Unsupervised reinforcement learning.- 5.3.2 Convergence of the learning algorithm.- 5.3.3 Multiple principal components.- 5.4 Some applications.- 5.4.1 Pattern recognition.- 5.4.2 Image compression.- 5.5 Historical and bibliographical remarks.- 6. One and Two Layered Networks.- 6.1 Structure and geometric visualization.- 6.1.1 Network architecture.- 6.1.2 The XOR problem revisited.- 6.1.3 Geometric visualization.- 6.2 Counting regions in input and weight space.- 6.2.1 Weight space regions for the XOR problem.- 6.2.2 Bipolar vectors.- 6.2.3 Projection of the solution regions.- 6.2.4 Geometric interpretation.- 6.3 Regions for two layered networks.- 6.3.1 Regions in weight space for the XOR problem.- 6.3.2 Number of regions in general.- 6.3.3 Consequences.- 6.3.4 The Vapnik-Chervonenkis dimension.- 6.3.5 The problem of local minima.- 6.4 Historical and bibliographical remarks