A Brief Introduction of Neural Networks
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Contents
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Language
English
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A small preface
I From biology to formalization – motivation, philosophy, history and realization of neural models
1 Introduction, motivation and history
1.1 Why neural networks?
1.1.1 The 100-step rule
1.1.2 Simple application examples
1.2 History of neural networks
1.2.1 The beginning
1.2.2 Golden age
1.2.3 Long silence and slow reconstruction
1.2.4 Renaissance
Exercises
2 Biological neural networks
2.1 The vertebrate nervous system
2.1.1 Peripheral and central nervous system
2.1.2 Cerebrum
2.1.3 Cerebellum
2.1.4 Diencephalon
2.1.5 Brainstem
2.2 The neuron
2.2.1 Components
2.2.2 Electrochemical processes in the neuron
2.3 Receptor cells
2.3.1 Various types
2.3.2 Information processing within the nervous system
2.3.3 Light sensing organs
2.4 The amount of neurons in living organisms
2.5 Technical neurons as caricature of biology
Exercises
3 Components of artificial neural networks (fundamental)
3.1 The concept of time in neural networks
3.2 Components of neural networks
3.2.1 Connections
3.2.2 Propagation function and network input
3.2.3 Activation
3.2.4 Threshold value
3.2.5 Activation function
3.2.6 Common activation functions
3.2.7 Output function
3.2.8 Learning strategy
3.3 Network topologies
3.3.1 Feedforward
3.3.2 Recurrent networks
3.3.3 Completely linked networks
3.4 The bias neuron
3.5 Representing neurons
3.6 Orders of activation
3.6.1 Synchronous activation
3.6.2 Asynchronous activation
3.7 Input and output of data
Exercises
4 Fundamentals on learning and training samples (fundamental)
4.1 Paradigms of learning
4.1.1 Unsupervised learning
4.1.2 Reinforcement learning
4.1.3 Supervised learning
4.1.4 Offline or online learning?
4.1.5 Questions in advance
4.2 Training patterns and teaching input
4.3 Using training samples
4.3.1 Division of the training set
4.3.2 Order of pattern representation
4.4 Learning curve and error measurement
4.4.1 When do we stop learning?
4.5 Gradient optimization procedures
4.5.1 Problems of gradient procedures
4.6 Exemplary problems
4.6.1 Boolean functions
4.6.2 The parity function
4.6.3 The 2-spiral problem
4.6.4 The checkerboard problem
4.6.5 The identity function
4.6.6 Other exemplary problems
4.7 Hebbian rule
4.7.1 Original rule
4.7.2 Generalized form
Exercises
II Supervised learning network paradigms
5 The perceptron, backpropagation and its variants
5.1 The singlelayer perceptron
5.1.1 Perceptron learning algorithm and convergence theorem
5.1.2 Delta rule
5.2 Linear separability
5.3 The multilayer perceptron
5.4 Backpropagation of error
5.4.1 Derivation
5.4.2 Boiling backpropagation down to the delta rule
5.4.3 Selecting a learning rate
5.5 Resilient backpropagation
5.5.1 Adaption of weights
5.5.2 Dynamic learning rate adjustment
5.5.3 Rprop in practice
5.6 Further variations and extensions to backpropagation
5.6.1 Momentum term
5.6.2 Flat spot elimination
5.6.3 Second order backpropagation
5.6.4 Weight decay
5.6.5 Pruning and Optimal Brain Damage
5.7 Initial configuration of a multilayer perceptron
5.7.1 Number of layers
5.7.2 The number of neurons
5.7.3 Selecting an activation function
5.7.4 Initializing weights
5.8 The 8-3-8 encoding problem and related problems
Exercises
6 Radial basis functions
6.1 Components and structure
6.2 Information processing of an RBF network
6.2.1 Information processing in RBF neurons
6.2.2 Analytical thoughts prior to the training
6.3 Training of RBF networks
6.3.1 Centers and widths of RBF neurons
6.4 Growing RBF networks
6.4.1 Adding neurons
6.4.2 Limiting the number of neurons
6.4.3 Deleting neurons
6.5 Comparing RBF networks and multilayer perceptrons
Exercises
7 Recurrent perceptron-like networks (depends on chapter 5)
7.1 Jordan networks
7.2 Elman networks
7.3 Training recurrent networks
7.3.1 Unfolding in time
7.3.2 Teacher forcing
7.3.3 Recurrent backpropagation
7.3.4 Training with evolution
8 Hopfield networks
8.1 Inspired by magnetism
8.2 Structure and functionality
8.2.1 Input and output of a Hopfield network
8.2.2 Significance of weights
8.2.3 Change in the state of neurons
8.3 Generating the weight matrix
8.4 Autoassociation and traditional application
8.5 Heteroassociation and analogies to neural data storage
8.5.1 Generating the heteroassociative matrix
8.5.2 Stabilizing the heteroassociations
8.5.3 Biological motivation of heterassociation
8.6 Continuous Hopfield networks
Exercises
9 Learning vector quantization
9.1 About quantization
9.2 Purpose of LVQ
9.3 Using codebook vectors
9.4 Adjusting codebook vectors
9.4.1 The procedure of learning
9.5 Connection to neural networks
Exercises
III Unsupervised learning network paradigms
10 Self-organizing feature maps
10.1 Structure
10.2 Functionality and output interpretation
10.3 Training
10.3.1 The topology function
10.3.2 Monotonically decreasing learning rate and neighborhood
10.4 Examples
10.4.1 Topological defects
10.5 Adjustment of resolution and position-dependent learning rate
10.6 Application
10.6.1 Interaction with RBF networks
10.7 Variations
10.7.1 Neural gas
10.7.2 Multi-SOMs
10.7.3 Multi-neural gas
10.7.4 Growing neural gas
Exercises
11 Adaptive resonance theory
11.1 Task and structure of an ART network
11.1.1 Resonance
11.2 Learning process
11.2.1 Pattern input and top-down learning
11.2.2 Resonance and bottom-up learning
11.2.3 Adding an output neuron
11.3 Extensions
IV Excursi, appendices and registers
A Excursus: Cluster analysis and regional and online learnable fields
A.1 k-means clustering
A.2 k-nearest neighboring
A.3 -nearest neighboring
A.4 The silhouette coefficient
A.5 Regional and online learnable fields
A.5.1 Structure of a ROLF
A.5.2 Training a ROLF
A.5.3 Evaluating a ROLF
A.5.4 Comparison with popular clustering methods
A.5.5 Initializing radii, learning rates and multiplier
A.5.6 Application examples
Exercises
B Excursus: neural networks used for prediction
B.1 About time series
B.2 One-step-ahead prediction
B.3 Two-step-ahead prediction
B.3.1 Recursive two-step-ahead prediction
B.3.2 Direct two-step-ahead prediction
B.4 Additional optimization approaches for prediction
B.4.1 Changing temporal parameters
B.4.2 Heterogeneous prediction
B.5 Remarks on the prediction of share prices
C Excursus: reinforcement learning
C.1 System structure
C.1.1 The gridworld
C.1.2 Agent und environment
C.1.3 States, situations and actions
C.1.4 Reward and return
C.1.5 The policy
C.2 Learning process
C.2.1 Rewarding strategies
C.2.2 The state-value function
C.2.3 Monte Carlo method
C.2.4 Temporal difference learning
C.2.5 The action-value function
C.2.6 Q learning
C.3 Example applications
C.3.1 TD gammon
C.3.2 The car in the pit
C.3.3 The pole balancer
C.4 Reinforcement learning in connection with neural networks
Exercises
Bibliography
List of Figures
Index
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