Neural Networks for Applied Sciences and Engineering

From Fundamentals to Complex Pattern Recognition

By: Sandhya Samarasinghe

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Hardcover | 1 September 2006 | Edition Number 1

At a Glance

Hardcover
594 Pages

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23.4 x 15.6 x 3.68

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In response to the exponentially increasing need to analyze vast amounts of data, Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition provides scientists with a simple but systematic introduction to neural networks.

Beginning with an introductory discussion on the role of neural networks in scientific data analysis, this book provides a solid foundation of basic neural network concepts. It contains an overview of neural network architectures for practical data analysis followed by extensive step-by-step coverage on linear networks, as well as, multi-layer perceptron for nonlinear prediction and classification explaining all stages of processing and model development illustrated through practical examples and case studies. Later chapters present an extensive coverage on Self Organizing Maps for nonlinear data clustering, recurrent networks for linear nonlinear time series forecasting, and other network types suitable for scientific data analysis.

With an easy to understand format using extensive graphical illustrations and multidisciplinary scientific context, this book fills the gap in the market for neural networks for multi-dimensional scientific data, and relates neural networks to statistics.

Features
Explains neural networks in a multi-disciplinary context
Uses extensive graphical illustrations to explain complex mathematical concepts for quick and easy understanding
? Examines in-depth neural networks for linear and nonlinear prediction, classification, clustering and forecasting
Illustrates all stages of model development and interpretation of results, including data preprocessing, data dimensionality reduction, input selection, model development and validation, model uncertainty assessment, sensitivity analyses on inputs, errors and model parameters

Sandhya Samarasinghe obtained her MSc in Mechanical Engineering from Lumumba University in Russia and an MS and PhD in Engineering from Virginia Tech, USA. Her neural networks research focuses on theoretical understanding and advancements as well as practical implementations.

Industry Reviews

"Beginning with the basics, she [Samarasinghe] explains a variety of neural networks' internal workings, and how to apply them to solve real problems."
-SciTech Book News, December 2006

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Non-Fiction Computing & I.T.Computer Science Artificial Intelligence Neural Networks & Fuzzy Systems Engineering & Technology Electronics & Communications Engineering Electronics Engineering Pattern Recognition Systems Analysis & Design

Preface	p. xvii
Acknowledgments	p. xxi
About the Author	p. xxiii
From Data to Models: Complexity and Challenges in Understanding Biological, Ecological, and Natural Systems	p. 1
Introduction	p. 1
Layout of the Book	p. 4
References	p. 7
Fundamentals of Neural Networks and Models for Linear Data Analysis	p. 11
Introduction and Overview	p. 11
Neural Networks and Their Capabilities	p. 12
Inspirations from Biology	p. 16
Modeling Information Processing in Neurons	p. 18
Neuron Models and Learning Strategies	p. 19
Threshold Neuron as a Simple Classifier	p. 20
Learning Models for Neurons and Neural Assemblies	p. 23
Hebbian Learning	p. 23
Unsupervised or Competitive Learning	p. 26
Supervised Learning	p. 26
Perceptron with Supervised Learning as a Classifier	p. 27
Perceptron Learning Algorithm	p. 28
A Practical Example of Perceptron on a Larger Realistic Data Set: Identifying the Origin of Fish from the Growth-Ring Diameter of Scales	p. 35
Comparison of Perceptron with Linear Discriminant Function Analysis in Statistics	p. 38
Multi-Output Perceptron for Multicategory Classification	p. 40
Higher-Dimensional Classification Using Perceptron	p. 45
Perceptron Summary	p. 45
Linear Neuron for Linear Classification and Prediction	p. 46
Learning with the Delta Rule	p. 47
Linear Neuron as a Classifier	p. 51
Classification Properties of a Linear Neuron as a Subset of Predictive Capabilities	p. 53
Example: Linear Neuron as a Predictor	p. 54
A Practical Example of Linear Prediction: Predicting the Heat Influx in a Home	p. 61
Comparison of Linear Neuron Model with Linear Regression	p. 62
Example: Multiple Input Linear Neuron Model-Improving the Prediction Accuracy of Heat Influx in a Home	p. 63
Comparison of a Multiple-Input Linear Neuron with Multiple Linear Regression	p. 63
Multiple Linear Neuron Models	p. 64
Comparison of a Multiple Linear Neuron Network with Canonical Correlation Analysis	p. 65
Linear Neuron and Linear Network Summary	p. 65
Summary	p. 66
Problems	p. 66
References	p. 67
Neural Networks for Nonlinear Pattern Recognition	p. 69
Overview and Introduction	p. 69
Multilayer Perceptron	p. 71
Nonlinear Neurons	p. 72
Neuron Activation Functions	p. 73
Sigmoid Functions	p. 74
Gaussian Functions	p. 76
Example: Population Growth Modeling Using a Nonlinear Neuron	p. 77
Comparison of Nonlinear Neuron with Nonlinear Regression Analysis	p. 80
One-Input Multilayer Nonlinear Networks	p. 80
Processing with a Single Nonlinear Hidden Neuron	p. 80
Examples: Modeling Cyclical Phenomena with Multiple Nonlinear Neurons	p. 86
Example 1: Approximating a Square Wave	p. 86
Example 2: Modeling Seasonal Species Migration	p. 94
Two-Input Multilayer Perceptron Network	p. 98
Processing of Two-Dimensional Inputs by Nonlinear Neurons	p. 98
Network Output	p. 102
Examples: Two-Dimensional Prediction and Classification	p. 103
Example 1: Two-Dimensional Nonlinear Function Approximation	p. 103
Example 2: Two-Dimensional Nonlinear Classification Model	p. 105
Multidimensional Data Modeling with Nonlinear Multilayer Perceptron Networks	p. 109
Summary	p. 110
Problems	p. 110
References	p. 112
Learning of Nonlinear Patterns by Neural Networks	p. 113
Introduction and Overview	p. 113
Supervised Training of Networks for Nonlinear Pattern Recognition	p. 114
Gradient Descent and Error Minimization	p. 115
Backpropagation Learning	p. 116
Example: Backpropagation Training-A Hand Computation	p. 117
Error Gradient with Respect to Output Neuron Weights	p. 120
The Error Gradient with Respect to the Hidden-Neuron Weights	p. 123
Application of Gradient Descent in Backpropagation Learning	p. 127
Batch Learning	p. 128
Learning Rate and Weight Update	p. 130
Example-by-Example (Online) Learning	p. 134
Momentum	p. 134
Example: Backpropagation Learning Computer Experiment	p. 138
Single-Input Single-Output Network with Multiple Hidden Neurons	p. 141
Multiple-Input, Multiple-Hidden Neuron, and Single-Output Network	p. 142
Multiple-Input, Multiple-Hidden Neuron, Multiple-Output Network	p. 143
Example: Backpropagation Learning Case Study-Solving a Complex Classification Problem	p. 145
Delta-Bar-Delta Learning (Adaptive Learning Rate) Method	p. 152
Example: Network Training with Delta-Bar-Delta-A Hand Computation	p. 154
Example: Delta-Bar-Delta with Momentum-A Hand Computation	p. 157
Network Training with Delta-Bar Delta-A Computer Experiment	p. 158
Comparison of Delta-Bar-Delta Method with Backpropagation	p. 159
Example: Network Training with Delta-Bar-Delta-A Case Study	p. 160
Steepest Descent Method	p. 163
Example: Network Training with Steepest Descent-Hand Computation	p. 163
Example: Network Training with Steepest Descent-A Computer Experiment	p. 164
Second-Order Methods of Error Minimization and Weight Optimization	p. 166
QuickProp	p. 167
Example: Network Training with QuickProp-A Hand Computation	p. 168
Example: Network Training with QuickProp-A Computer Experiment	p. 170
Comparison of QuickProp with Steepest Descent, Delta-Bar-Delta, and Backpropagation	p. 170
General Concept of Second-Order Methods of Error Minimization	p. 172
Gauss-Newton Method	p. 174
Network Training with the Gauss-Newton Method-A Hand Computation	p. 176
Example: Network Training with Gauss-Newton Method-A Computer Experiment	p. 178
The Levenberg-Marquardt Method	p. 180
Example: Network Training with LM Method-A Hand Computation	p. 182
Network Training with the LM Method-A Computer Experiment	p. 183
Comparison of the Efficiency of the First-Order and Second-Order Methods in Minimizing Error	p. 184
Comparison of the Convergence Characteristics of First-Order and Second-Order Learning Methods	p. 185
Backpropagation	p. 187
Steepest Descent Method	p. 188
Gauss-Newton Method	p. 189
Levenberg-Marquardt Method	p. 190
Summary	p. 192
Problems	p. 192
References	p. 193
Implementation of Neural Network Models for Extracting Reliable Patterns from Data	p. 195
Introduction and Overview	p. 195
Bias-Variance Tradeoff	p. 196
Improving Generalization of Neural Networks	p. 197
Illustration of Early Stopping	p. 199
Effect of Initial Random Weights	p. 203
Weight Structure of the Trained Networks	p. 206
Effect of Random Sampling	p. 207
Effect of Model Complexity: Number of Hidden Neurons	p. 212
Summary on Early Stopping	p. 213
Regularization	p. 215
Reducing Structural Complexity of Networks by Pruning	p. 221
Optimal Brain Damage	p. 222
Example of Network Pruning with Optimal Brain Damage	p. 223
Network Pruning Based on Variance of Network Sensitivity	p. 229
Illustration of Application of Variance Nullity in Pruning Weights	p. 232
Pruning Hidden Neurons Based on Variance Nullity of Sensitivity	p. 235
Robustness of a Network to Perturbation of Weights	p. 237
Confidence Intervals for Weights	p. 239
Summary	p. 241
Problems	p. 242
References	p. 243
Data Exploration, Dimensionality Reduction, and Feature Extraction	p. 245
Introduction and Overview	p. 245
Example: Thermal Conductivity of Wood in Relation to Correlated Input Data	p. 247
Data Visualization	p. 248
Correlation Scatter Plots and Histograms	p. 248
Parallel Visualization	p. 249
Projecting Multidimensional Data onto Two-Dimensional Plane	p. 250
Correlation and Covariance between Variables	p. 251
Normalization of Data	p. 253
Standardization	p. 253
Simple Range Scaling	p. 254
Whitening-Normalization of Correlated Multivariate Data	p. 255
Selecting Relevant Inputs	p. 259
Statistical Tools for Variable Selection	p. 260
Partial Correlation	p. 260
Multiple Regression and Best-Subsets Regression	p. 261
Dimensionality Reduction and Feature Extraction	p. 262
Multicollinearity	p. 262
Principal Component Analysis (PCA)	p. 263
Partial Least-Squares Regression	p. 267
Outlier Detection	p. 268
Noise	p. 270
Case Study: Illustrating Input Selection and Dimensionality Reduction for a Practical Problem	p. 270
Data Preprocessing and Preliminary Modeling	p. 271
PCA-Based Neural Network Modeling	p. 275
Effect of Hidden Neurons for Non-PCA- and PCA-Based Approaches	p. 278
Case Study Summary	p. 279
Summary	p. 280
Problems	p. 281
References	p. 281
Assessment of Uncertainty of Neural Network Models Using Bayesian Statistics	p. 283
Introduction and Overview	p. 283
Estimating Weight Uncertainty Using Bayesian Statistics	p. 285
Quality Criterion	p. 285
Incorporating Bayesian Statistics to Estimate Weight Uncertainty	p. 288
Square Error	p. 289
Intrinsic Uncertainty of Targets for Multivariate Output	p. 292
Probability Density Function of Weights	p. 293
Example Illustrating Generation of Probability Distribution of Weights	p. 295
Estimation of Geophysical Parameters from Remote Sensing: A Case Study	p. 295
Assessing Uncertainty of Neural Network Outputs Using Bayesian Statistics	p. 300
Example Illustrating Uncertainty Assessment of Output Errors	p. 301
Total Network Output Errors	p. 301
Error Correlation and Covariance Matrices	p. 302
Statistical Analysis of Error Covariance	p. 302
Decomposition of Total Output Error into Model Error and Intrinsic Noise	p. 304
Assessing the Sensitivity of Network Outputs to Inputs	p. 311
Approaches to Determine the Influence of Inputs on Outputs in Feedforward Networks	p. 311
Methods Based on Magnitude of Weights	p. 311
Sensitivity Analysis	p. 312
Example: Comparison of Methods to Assess the Influence of Inputs on Outputs	p. 313
Uncertainty of Sensitivities	p. 314
Example Illustrating Uncertainty Assessment of Network Sensitivity to Inputs	p. 315
PCA Decomposition of Inputs and Outputs	p. 315
PCA-Based Neural Network Regression	p. 320
Neural Network Sensitivities	p. 323
Uncertainty of Input Sensitivity	p. 325
PCA-Regularized Jacobians	p. 328
Case Study Summary	p. 333
Summary	p. 333
Problems	p. 334
References	p. 335
Discovering Unknown Clusters in Data with Self-Organizing Maps	p. 337
Introduction and Overview	p. 337
Structure of Unsupervised Networks	p. 338
Learning in Unsupervised Networks	p. 339
Implementation of Competitive Learning	p. 340
Winner Selection Based on Neuron Activation	p. 340
Winner Selection Based on Distance to Input Vector	p. 341
Other Distance Measures	p. 342
Competitive Learning Example	p. 343
Recursive Versus Batch Learning	p. 344
Illustration of the Calculations Involved in Winner Selection	p. 344
Network Training	p. 346
Self-Organizing Feature Maps	p. 349
Learning in Self-Organizing Map Networks	p. 349
Selection of Neighborhood Geometry	p. 349
Training of Self-Organizing Maps	p. 350
Neighbor Strength	p. 350
Example: Training Self-Organizing Networks with a Neighbor Feature	p. 351
Neighbor Matrix and Distance to Neighbors from the Winner	p. 354
Shrinking Neighborhood Size with Iterations	p. 357
Learning Rate Decay	p. 358
Weight Update Incorporating Learning Rate and Neighborhood Decay	p. 359
Recursive and Batch Training and Relation to K-Means Clustering	p. 360
Two Phases of Self-Organizing Map Training	p. 360
Example: Illustrating Self-Organizing Map Learning with a Hand Calculation	p. 361
SOM Case Study: Determination of Mastitis Health Status of Dairy Herd from Combined Milk Traits	p. 368
Example of Two-Dimensional Self-Organizing Maps: Clustering Canadian and Alaskan Salmon Based on the Diameter of Growth Rings of the Scales	p. 371
Map Structure and Initialization	p. 372
Map Training	p. 373
U-Matrix	p. 380
Map Initialization	p. 382
Example: Training Two-Dimensional Maps on Multidimensional Data	p. 382
Data Visualization	p. 383
Map Structure and Training	p. 383
U-Matrix	p. 389
Point Estimates of Probability Density of Inputs Captured by the Map	p. 390
Quantization Error	p. 391
Accuracy of Retrieval of Input Data from the Map	p. 393
Forming Clusters on the Map	p. 395
Approaches to Clustering	p. 396
Example Illustrating Clustering on a Trained Map	p. 397
Finding Optimum Clusters on the Map with the Ward Method	p. 401
Finding Optimum Clusters by K-Means Clustering	p. 403
Validation of a Trained Map	p. 406
n-Fold Cross Validation	p. 406
Evolving Self-Organizing Maps	p. 411
Growing Cell Structure of Map	p. 413
Centroid Method for Mapping Input Data onto Positions between Neurons on the Map	p. 416
Dynamic Self-Organizing Maps with Controlled Growth (GSOM)	p. 419
Example: Application of Dynamic Self-Organizing Maps	p. 422
Evolving Tree	p. 427
Summary	p. 431
Problems	p. 432
References	p. 434
Neural Networks for Time-Series Forecasting	p. 437
Introduction and Overview	p. 437
Linear Forecasting of Time-Series with Statistical and Neural Network Models	p. 440
Example Case Study: Regulating Temperature of a Furnace	p. 442
Multistep-Ahead Linear Forecasting	p. 444
Neural Networks for Nonlinear Time-Series Forecasting	p. 446
Focused Time-Lagged and Dynamically Driven Recurrent Networks	p. 446
Focused Time-Lagged Feedforward Networks	p. 448
Spatio-Temporal Time-Lagged Networks	p. 450
Example: Spatio-Temporal Time-Lagged Network-Regulating Temperature in a Furnace	p. 452
Single-Step Forecasting with Neural NARx Model	p. 454
Multistep Forecasting with Neural NARx Model	p. 455
Case Study: River Flow Forecasting	p. 457
Linear Model for River Flow Forecasting	p. 460
Nonlinear Neural (NARx) Model for River Flow Forecasting	p. 463
Input Sensitivity	p. 467
Hybrid Linear (ARIMA) and Nonlinear Neural Network Models	p. 468
Case Study: Forecasting the Annual Number of Sunspots	p. 470
Automatic Generation of Network Structure Using Simplest Structure Concept	p. 471
Case Study: Forecasting Air Pollution with Automatic Neural Network Model Generation	p. 473
Generalized Neuron Network	p. 475
Case Study: Short-Term Load Forecasting with a Generalized Neuron Network	p. 482
Dynamically Driven Recurrent Networks	p. 485
Recurrent Networks with Hidden Neuron Feedback	p. 485
Encapsulating Long-Term Memory	p. 485
Structure and Operation of the Elman Network	p. 488
Training Recurrent Networks	p. 490
Network Training Example: Hand Calculation	p. 495
Recurrent Learning Network Application Case Study: Rainfall Runoff Modeling	p. 500
Two-Step-Ahead Forecasting with Recurrent Networks	p. 503
Real-Time Recurrent Learning Case Study: Two-Step-Ahead Stream Flow Forecasting	p. 505
Recurrent Networks with Output Feedback	p. 508
Encapsulating Long-Term Memory in Recurrent Networks with Output Feedback	p. 508
Application of a Recurrent Net with Output and Error Feedback and Exogenous Inputs: (NARIMAx) Case Study: Short-Term Temperature Forecasting	p. 510
Training of Recurrent Nets with Output Feedback	p. 513
Fully Recurrent Network	p. 515
Fully Recurrent Network Practical Application Case Study: Short-Term Electricity Load Forecasting	p. 517
Bias and Variance in Time-Series Forecasting	p. 519
Decomposition of Total Error into Bias and Variance Components	p. 521
Example Illustrating Bias-Variance Decomposition	p. 522
Long-Term Forecasting	p. 528
Case Study: Long-Term Forecasting with Multiple Neural Networks (MNNs)	p. 531
Input Selection for Time-Series Forecasting	p. 533
Input Selection from Nonlinearly Dependent Variables	p. 535
Partial Mutual Information Method	p. 535
Generalized Regression Neural Network	p. 538
Self-Organizing Maps for Input Selection	p. 539
Genetic Algorithms for Input Selection	p. 541
Practical Application of Input Selection Methods for Time-Series Forecasting	p. 543
Input Selection Case Study: Selecting Inputs for Forecasting River Salinity	p. 546
Summary	p. 549
Problems	p. 551
References	p. 552
Appendix	p. 555
Index	p. 561
Table of Contents provided by Ingram. All Rights Reserved.

Neural Networks for Applied Sciences and Engineering

From Fundamentals to Complex Pattern Recognition

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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