Combining Artificial Neural Nets : Ensemble and Modular Multi-Net Systems

By: Amanda J.C. Sharkey (Editor)

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The past decade could be seen as the heyday of neurocomputing: in which the capabilities of monolithic nets have been well explored and exploited. The question then is where do we go from here? A logical next step is to examine the potential offered by combinations of artificial neural nets, and it is that step that the chapters in this volume represent. Intuitively, it makes sense to look at combining ANNs. Clearly complex biological systems and brains rely on modularity. Similarly the principles of modularity, and of reliability through redundancy, can be found in many disparate areas, from the idea of decision by jury, through to hardware re- dundancy in aeroplanes, and the advantages of modular design and reuse advocated by object-oriented programmers. And it is not surprising to find that the same principles can be usefully applied in the field of neurocomput- ing as well, although finding the best way of adapting them is a subject of on-going research.

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Non-Fiction Computing & I.T.Computer Science Artificial Intelligence Neural Networks & Fuzzy Systems Science Physics Mathematical Physics

Multi-Net Systems	p. 1
Different Forms of Multi-Net System	p. 2
Ensembles	p. 5
Why Create Ensembles?	p. 5
Methods for Creating Ensemble Members	p. 8
Methods for Combining Nets in Ensembles	p. 10
Choosing a Method for Ensemble Creation and Combination	p. 11
Modular Approaches	p. 15
Why Create Modular Systems?	p. 15
Methods for Creating Modular Components	p. 16
Methods for Combining Modular Components	p. 18
The Chapters in this Book	p. 21
References	p. 27
Combining Predictors	p. 31
Combine and Conquer	p. 31
Regression	p. 32
Bias and Variance	p. 32
Bagging - The Pseudo-Fairy Godmother	p. 33
Results of Bagging	p. 34
Classification	p. 35
Bias and Spread	p. 35
Examples	p. 37
Bagging Classifiers	p. 39
Remarks	p. 41
Pruning	p. 41
Randomising the Construction	p. 41
Randomising the Outputs	p. 41
Adaboost and Arcing	p. 42
The Adaboost Algorithm	p. 43
What Makes Adaboost Work?	p. 44
Recent Research	p. 45
Margins	p. 45
Using Simple Classifiers	p. 46
Instability is Needed	p. 47
Coda	p. 47
Heisenberg's Principle for Statistical Prediction	p. 47
References	p. 49
Boosting Using Neural Networks	p. 51
Introduction	p. 51
Bagging	p. 54
Classification	p. 55
Regression	p. 55
Remarks	p. 55
Boosting	p. 56
Introduction	p. 56
A First Implementation: Boost1	p. 56
Adaboost.M1	p. 57
AdaBoost.M2	p. 59
AdaBoost.R2	p. 59
Other Ensemble Techniques	p. 59
Neural Networks	p. 60
Classification	p. 60
Early Stopping	p. 64
Regression	p. 65
Trees	p. 66
Training Classification Trees	p. 66
Pruning Classification Trees	p. 67
Training Regression Trees	p. 68
Pruning Regression Trees	p. 69
Trees vs. Neural Nets	p. 69
Experiments	p. 70
Experiments Using Boost1	p. 70
Experiments Using AdaBoost	p. 72
Experiments Using AdaBoost.R2	p. 74
Conclusions	p. 76
References	p. 77
A Genetic Algorithm Approach for Creating Neural Network Ensembles	p. 79
Introduction	p. 79
Neural Network Ensembles	p. 81
The ADDEMUP Algorithm	p. 82
ADDEMUP's Top-Level Design	p. 82
Creating and Crossing-Over KNNs	p. 84
Experimental Study	p. 87
Generalisation Ability of ADDEMUP	p. 88
Lesion Study of ADDEMUP	p. 91
Discussion and Future Work	p. 92
Additional Related Work	p. 94
Conclusions	p. 95
References	p. 97
Treating Harmful Collinearity in Neural Network Ensembles	p. 101
Introduction	p. 101
Overview of Optimal Linear Combinations (OLC) of Neural Networks	p. 102
Effects of Collinearity on Combining Neural Networks	p. 104
Collinearity in the Literature on Combining Estimators	p. 105
Testing the Robustness of NN Ensembles	p. 106
Collinearity, Correlation, and Ensemble Ambiguity	p. 106
The Harmful Effects of Collinearity	p. 108
Improving the Generalisation of NN Ensembles by Treating Harmful Collinearity	p. 110
Two Algorithms for Selecting the Component NNs in the Ensemble	p. 111
Modification to the Algorithms	p. 112
Experimental Results	p. 112
Problem I	p. 113
Problem II	p. 114
Discussion of the Experimental Results	p. 116
Concluding Remarks	p. 117
References	p. 123
Linear and Order Statistics Combiners for Pattern Classification	p. 127
Introduction	p. 127
Class Boundary Analysis and Error Regions	p. 130
Linear Combining	p. 134
Linear Combining of Unbiased Classifiers	p. 134
Linear Combining of Biased Classifiers	p. 135
Order Statistics	p. 136
Introduction	p. 136
Background	p. 137
Combining Unbiased Classifiers Through OS	p. 138
Combining Biased Classifiers Through OS	p. 139
Correlated Classifier Combining	p. 141
Introduction	p. 141
Combining Unbiased Correlated Classifiers	p. 142
Combining Biased Correlated Classifiers	p. 145
Discussion	p. 146
Experimental Combining Results	p. 147
Oceanic Data Set	p. 147
Proben 1 Benchmarks	p. 149
Discussion	p. 153
References	p. 157
Variance Reduction via Noise and Bias Constraints	p. 163
Introduction	p. 163
Theoretical Considerations	p. 164
The BootstrapEnsemble with Noise Algorithm	p. 166
Results on the Two-Spirals Problem	p. 169
Problem Description	p. 169
Feed-Forward Network Architecture	p. 170
Discussion	p. 172
References	p. 177
A Comparison of Visual Cue Combination Models	p. 179
Introduction	p. 179
Stimulus	p. 184
Tasks	p. 188
Models of Cue Combination	p. 190
Simulation Results	p. 193
Summary	p. 199
References	p. 203
Model Selection of Combined Neural Nets for Speech Recognition	p. 205
Introduction	p. 205
The Acoustic Mapping	p. 208
Network Architectures	p. 209
Combining Networks for Acoustic Mapping	p. 209
Linear Mappings	p. 210
RBFLinear Networks	p. 211
Multilayer Perceptron Networks	p. 211
Experimental Environment	p. 212
System Architecture	p. 212
Acoustic Analysis	p. 212
The Speech Recogniser	p. 213
Generation of the Training Set	p. 213
Application 1: Datasets and Recognition Task	p. 213
WER and MSE	p. 216
Booststrap Estimates and Model Selection	p. 217
Bootstrap Error Estimates	p. 217
The Bootstrap and Model Selection	p. 218
The Number of Bootstrap Replicates	p. 220
Bootstrap Estimates: Evaluation	p. 221
Normalisation Results	p. 222
Continuous Digit Recognition Over the Telephone Network	p. 225
Conclusions	p. 228
References	p. 251
Self-Organised Modular Neural Networks for Encoding Data	p. 235
Introduction	p. 235
An Image Processing Problem	p. 235
Vector Quantisers	p. 236
Curved Manifolds	p. 237
Structure of this Chapter	p. 239
Basic Theoretical Framework	p. 240
Objective Function	p. 241
Stationarity Conditions	p. 244
Joint Encoding	p. 245
Factorial Encoding	p. 247
Circular Manifold	p. 248
2 Overlapping Posterior Probabilities	p. 249
3 Overlapping Posterior Probabilities	p. 251
Toroidal Manifold: Factorial Encoding	p. 253
2 Overlapping Posterior Probabilities	p. 254
3 Overlapping Posterior Probabilities	p. 255
Asymptotic Results	p. 256
Approximate the Posterior Probability	p. 258
Joint Versus Factorial Encoding	p. 260
Conclusions	p. 262
References	p. 265
Mixtures of X	p. 267
Introduction	p. 267
Mixtures of X	p. 269
Mixtures of Distributions from the Exponential Family	p. 270
Hidden Markov Models	p. 271
Mixtures of Experts	p. 273
Mixtures of Marginal Models	p. 279
Mixtures of Cox Models	p. 283
Mixtures of Factor Models	p. 287
Mixtures of Trees	p. 290
Summary	p. 292
References	p. 293
Index	p. 297
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Combining Artificial Neural Nets : Ensemble and Modular Multi-Net Systems

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