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Statistical Pattern Recognition, 3rd Edition

ISBN: 978-0-470-68227-2
666 pages
November 2011, ©2011
Statistical Pattern Recognition, 3rd Edition (0470682272) cover image
Statistical pattern recognition relates to the use of statistical techniques for analysing data measurements in order to extract information and make justified decisions.  It is a very active area of study and research, which has seen many advances in recent years. Applications such as data mining, web searching, multimedia data retrieval, face recognition, and cursive handwriting recognition, all require robust and efficient pattern recognition techniques.

This third edition provides an introduction to statistical pattern theory and techniques, with material drawn from a wide range of fields, including the areas of engineering, statistics, computer science and the social sciences. The book has been updated to cover new methods and applications, and includes a wide range of techniques such as Bayesian methods, neural networks, support vector machines, feature selection and feature reduction techniques.Technical descriptions and motivations are provided, and the techniques are illustrated using real examples.

Statistical Pattern Recognition, 3rd Edition:

  • Provides a self-contained introduction to statistical pattern recognition.
  • Includes new material presenting the analysis of complex networks.
  • Introduces readers to methods for Bayesian density estimation.
  • Presents descriptions of new applications in biometrics, security, finance and condition monitoring.
  • Provides descriptions and guidance for implementing techniques, which will be invaluable to software engineers and developers seeking to develop real applications
  • Describes mathematically the range of statistical pattern recognition techniques.
  • Presents a variety of exercises including more extensive computer projects.

The in-depth technical descriptions make the book suitable for senior undergraduate and graduate students in statistics, computer science and engineering.  Statistical Pattern Recognition is also an excellent reference source for technical professionals.  Chapters have been arranged to facilitate implementation of the techniques by software engineers and developers in non-statistical engineering fields.

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Preface xix

Notation xxiii

1 Introduction to Statistical Pattern Recognition 1

1.1 Statistical Pattern Recognition 1

1.1.1 Introduction 1

1.1.2 The Basic Model 2

1.2 Stages in a Pattern Recognition Problem 4

1.3 Issues 6

1.4 Approaches to Statistical Pattern Recognition 7

1.5 Elementary Decision Theory 8

1.5.1 Bayes’ Decision Rule for Minimum Error 8

1.5.2 Bayes’ Decision Rule for Minimum Error – Reject Option 12

1.5.3 Bayes’ Decision Rule for Minimum Risk 13

1.5.4 Bayes’ Decision Rule for Minimum Risk – Reject Option 15

1.5.5 Neyman–Pearson Decision Rule 15

1.5.6 Minimax Criterion 18

1.5.7 Discussion 19

1.6 Discriminant Functions 20

1.6.1 Introduction 20

1.6.2 Linear Discriminant Functions 21

1.6.3 Piecewise Linear Discriminant Functions 23

1.6.4 Generalised Linear Discriminant Function 24

1.6.5 Summary 26

1.7 Multiple Regression 27

1.8 Outline of Book 29

1.9 Notes and References 29

Exercises 31

2 Density Estimation – Parametric 33

2.1 Introduction 33

2.2 Estimating the Parameters of the Distributions 34

2.2.1 Estimative Approach 34

2.2.2 Predictive Approach 35

2.3 The Gaussian Classifier 35

2.3.1 Specification 35

2.3.2 Derivation of the Gaussian Classifier Plug-In Estimates 37

2.3.3 Example Application Study 39

2.4 Dealing with Singularities in the Gaussian Classifier 40

2.4.1 Introduction 40

2.4.2 Na¨ive Bayes 40

2.4.3 Projection onto a Subspace 41

2.4.4 Linear Discriminant Function 41

2.4.5 Regularised Discriminant Analysis 42

2.4.6 Example Application Study 44

2.4.7 Further Developments 45

2.4.8 Summary 46

2.5 Finite Mixture Models 46

2.5.1 Introduction 46

2.5.2 Mixture Models for Discrimination 48

2.5.3 Parameter Estimation for Normal Mixture Models 49

2.5.4 Normal Mixture Model Covariance Matrix Constraints 51

2.5.5 How Many Components? 52

2.5.6 Maximum Likelihood Estimation via EM 55

2.5.7 Example Application Study 60

2.5.8 Further Developments 62

2.5.9 Summary 63

2.6 Application Studies 63

2.7 Summary and Discussion 66

2.8 Recommendations 66

2.9 Notes and References 67

Exercises 67

3 Density Estimation – Bayesian 70

3.1 Introduction 70

3.1.1 Basics 72

3.1.2 Recursive Calculation 72

3.1.3 Proportionality 73

3.2 Analytic Solutions 73

3.2.1 Conjugate Priors 73

3.2.2 Estimating the Mean of a Normal Distribution with Known Variance 75

3.2.3 Estimating the Mean and the Covariance Matrix of a Multivariate Normal Distribution 79

3.2.4 Unknown Prior Class Probabilities 85

3.2.5 Summary 87

3.3 Bayesian Sampling Schemes 87

3.3.1 Introduction 87

3.3.2 Summarisation 87

3.3.3 Sampling Version of the Bayesian Classifier 89

3.3.4 Rejection Sampling 89

3.3.5 Ratio of Uniforms 90

3.3.6 Importance Sampling 92

3.4 Markov Chain Monte Carlo Methods 95

3.4.1 Introduction 95

3.4.2 The Gibbs Sampler 95

3.4.3 Metropolis–Hastings Algorithm 103

3.4.4 Data Augmentation 107

3.4.5 Reversible Jump Markov Chain Monte Carlo 108

3.4.6 Slice Sampling 109

3.4.7 MCMC Example – Estimation of Noisy Sinusoids 111

3.4.8 Summary 115

3.4.9 Notes and References 116

3.5 Bayesian Approaches to Discrimination 116

3.5.1 Labelled Training Data 116

3.5.2 Unlabelled Training Data 117

3.6 Sequential Monte Carlo Samplers 119

3.6.1 Introduction 119

3.6.2 Basic Methodology 121

3.6.3 Summary 125

3.7 Variational Bayes 126

3.7.1 Introduction 126

3.7.2 Description 126

3.7.3 Factorised Variational Approximation 129

3.7.4 Simple Example 131

3.7.5 Use of the Procedure for Model Selection 135

3.7.6 Further Developments and Applications 136

3.7.7 Summary 137

3.8 Approximate Bayesian Computation 137

3.8.1 Introduction 137

3.8.2 ABC Rejection Sampling 138

3.8.3 ABC MCMC Sampling 140

3.8.4 ABC Population Monte Carlo Sampling 141

3.8.5 Model Selection 142

3.8.6 Summary 143

3.9 Example Application Study 144

3.10 Application Studies 145

3.11 Summary and Discussion 146

3.12 Recommendations 147

3.13 Notes and References 147

Exercises 148

4 Density Estimation – Nonparametric 150

4.1 Introduction 150

4.1.1 Basic Properties of Density Estimators 150

4.2 k-Nearest-Neighbour Method 152

4.2.1 k-Nearest-Neighbour Classifier 152

4.2.2 Derivation 154

4.2.3 Choice of Distance Metric 157

4.2.4 Properties of the Nearest-Neighbour Rule 159

4.2.5 Linear Approximating and Eliminating Search Algorithm 159

4.2.6 Branch and Bound Search Algorithms: kd-Trees 163

4.2.7 Branch and Bound Search Algorithms: Ball-Trees 170

4.2.8 Editing Techniques 174

4.2.9 Example Application Study 177

4.2.10 Further Developments 178

4.2.11 Summary 179

4.3 Histogram Method 180

4.3.1 Data Adaptive Histograms 181

4.3.2 Independence Assumption (Naïve Bayes) 181

4.3.3 Lancaster Models 182

4.3.4 Maximum Weight Dependence Trees 183

4.3.5 Bayesian Networks 186

4.3.6 Example Application Study – Naïve Bayes Text Classification 190

4.3.7 Summary 193

4.4 Kernel Methods 194

4.4.1 Biasedness 197

4.4.2 Multivariate Extension 198

4.4.3 Choice of Smoothing Parameter 199

4.4.4 Choice of Kernel 201

4.4.5 Example Application Study 202

4.4.6 Further Developments 203

4.4.7 Summary 203

4.5 Expansion by Basis Functions 204

4.6 Copulas 207

4.6.1 Introduction 207

4.6.2 Mathematical Basis 207

4.6.3 Copula Functions 208

4.6.4 Estimating Copula Probability Density Functions 209

4.6.5 Simple Example 211

4.6.6 Summary 212

4.7 Application Studies 213

4.7.1 Comparative Studies 216

4.8 Summary and Discussion 216

4.9 Recommendations 217

4.10 Notes and References 217

Exercises 218

5 Linear Discriminant Analysis 221

5.1 Introduction 221

5.2 Two-Class Algorithms 222

5.2.1 General Ideas 222

5.2.2 Perceptron Criterion 223

5.2.3 Fisher’s Criterion 227

5.2.4 Least Mean-Squared-Error Procedures 228

5.2.5 Further Developments 235

5.2.6 Summary 235

5.3 Multiclass Algorithms 236

5.3.1 General Ideas 236

5.3.2 Error-Correction Procedure 237

5.3.3 Fisher’s Criterion – Linear Discriminant Analysis 238

5.3.4 Least Mean-Squared-Error Procedures 241

5.3.5 Regularisation 246

5.3.6 Example Application Study 246

5.3.7 Further Developments 247

5.3.8 Summary 248

5.4 Support Vector Machines 249

5.4.1 Introduction 249

5.4.2 Linearly Separable Two-Class Data 249

5.4.3 Linearly Nonseparable Two-Class Data 253

5.4.4 Multiclass SVMs 256

5.4.5 SVMs for Regression 257

5.4.6 Implementation 259

5.4.7 Example Application Study 262

5.4.8 Summary 263

5.5 Logistic Discrimination 263

5.5.1 Two-Class Case 263

5.5.2 Maximum Likelihood Estimation 264

5.5.3 Multiclass Logistic Discrimination 266

5.5.4 Example Application Study 267

5.5.5 Further Developments 267

5.5.6 Summary 268

5.6 Application Studies 268

5.7 Summary and Discussion 268

5.8 Recommendations 269

5.9 Notes and References 270

Exercises 270

6 Nonlinear Discriminant Analysis – Kernel and Projection Methods 274

6.1 Introduction 274

6.2 Radial Basis Functions 276

6.2.1 Introduction 276

6.2.2 Specifying the Model 278

6.2.3 Specifying the Functional Form 278

6.2.4 The Positions of the Centres 279

6.2.5 Smoothing Parameters 281

6.2.6 Calculation of the Weights 282

6.2.7 Model Order Selection 284

6.2.8 Simple RBF 285

6.2.9 Motivation 286

6.2.10 RBF Properties 288

6.2.11 Example Application Study 288

6.2.12 Further Developments 289

6.2.13 Summary 290

6.3 Nonlinear Support Vector Machines 291

6.3.1 Introduction 291

6.3.2 Binary Classification 291

6.3.3 Types of Kernel 292

6.3.4 Model Selection 293

6.3.5 Multiclass SVMs 294

6.3.6 Probability Estimates 294

6.3.7 Nonlinear Regression 296

6.3.8 Example Application Study 296

6.3.9 Further Developments 297

6.3.10 Summary 298

6.4 The Multilayer Perceptron 298

6.4.1 Introduction 298

6.4.2 Specifying the MLP Structure 299

6.4.3 Determining the MLP Weights 300

6.4.4 Modelling Capacity of the MLP 307

6.4.5 Logistic Classification 307

6.4.6 Example Application Study 310

6.4.7 Bayesian MLP Networks 311

6.4.8 Projection Pursuit 313

6.4.9 Summary 313

6.5 Application Studies 314

6.6 Summary and Discussion 316

6.7 Recommendations 317

6.8 Notes and References 318

Exercises 318

7 Rule and Decision Tree Induction 322

7.1 Introduction 322

7.2 Decision Trees 323

7.2.1 Introduction 323

7.2.2 Decision Tree Construction 326

7.2.3 Selection of the Splitting Rule 327

7.2.4 Terminating the Splitting Procedure 330

7.2.5 Assigning Class Labels to Terminal Nodes 332

7.2.6 Decision Tree Pruning – Worked Example 332

7.2.7 Decision Tree Construction Methods 337

7.2.8 Other Issues 339

7.2.9 Example Application Study 340

7.2.10 Further Developments 341

7.2.11 Summary 342

7.3 Rule Induction 342

7.3.1 Introduction 342

7.3.2 Generating Rules from a Decision Tree 345

7.3.3 Rule Induction Using a Sequential Covering Algorithm 345

7.3.4 Example Application Study 350

7.3.5 Further Developments 351

7.3.6 Summary 351

7.4 Multivariate Adaptive Regression Splines 351

7.4.1 Introduction 351

7.4.2 Recursive Partitioning Model 351

7.4.3 Example Application Study 355

7.4.4 Further Developments 355

7.4.5 Summary 356

7.5 Application Studies 356

7.6 Summary and Discussion 358

7.7 Recommendations 358

7.8 Notes and References 359

Exercises 359

8 Ensemble Methods 361

8.1 Introduction 361

8.2 Characterising a Classifier Combination Scheme 362

8.2.1 Feature Space 363

8.2.2 Level 366

8.2.3 Degree of Training 368

8.2.4 Form of Component Classifiers 368

8.2.5 Structure 369

8.2.6 Optimisation 369

8.3 Data Fusion 370

8.3.1 Architectures 370

8.3.2 Bayesian Approaches 371

8.3.3 Neyman–Pearson Formulation 373

8.3.4 Trainable Rules 374

8.3.5 Fixed Rules 375

8.4 Classifier Combination Methods 376

8.4.1 Product Rule 376

8.4.2 Sum Rule 377

8.4.3 Min, Max and Median Combiners 378

8.4.4 Majority Vote 379

8.4.5 Borda Count 379

8.4.6 Combiners Trained on Class Predictions 380

8.4.7 Stacked Generalisation 382

8.4.8 Mixture of Experts 382

8.4.9 Bagging 385

8.4.10 Boosting 387

8.4.11 Random Forests 389

8.4.12 Model Averaging 390

8.4.13 Summary of Methods 396

8.4.14 Example Application Study 398

8.4.15 Further Developments 399

8.5 Application Studies 399

8.6 Summary and Discussion 400

8.7 Recommendations 401

8.8 Notes and References 401

Exercises 402

9 Performance Assessment 404

9.1 Introduction 404

9.2 Performance Assessment 405

9.2.1 Performance Measures 405

9.2.2 Discriminability 406

9.2.3 Reliability 413

9.2.4 ROC Curves for Performance Assessment 415

9.2.5 Population and Sensor Drift 419

9.2.6 Example Application Study 421

9.2.7 Further Developments 422

9.2.8 Summary 423

9.3 Comparing Classifier Performance 424

9.3.1 Which Technique is Best? 424

9.3.2 Statistical Tests 425

9.3.3 Comparing Rules When Misclassification Costs are Uncertain 426

9.3.4 Example Application Study 428

9.3.5 Further Developments 429

9.3.6 Summary 429

9.4 Application Studies 429

9.5 Summary and Discussion 430

9.6 Recommendations 430

9.7 Notes and References 430

Exercises 431

10 Feature Selection and Extraction 433

10.1 Introduction 433

10.2 Feature Selection 435

10.2.1 Introduction 435

10.2.2 Characterisation of Feature Selection Approaches 439

10.2.3 Evaluation Measures 440

10.2.4 Search Algorithms for Feature Subset Selection 449

10.2.5 Complete Search – Branch and Bound 450

10.2.6 Sequential Search 454

10.2.7 Random Search 458

10.2.8 Markov Blanket 459

10.2.9 Stability of Feature Selection 460

10.2.10 Example Application Study 462

10.2.11 Further Developments 462

10.2.12 Summary 463

10.3 Linear Feature Extraction 463

10.3.1 Principal Components Analysis 464

10.3.2 Karhunen–Lo`eve Transformation 475

10.3.3 Example Application Study 481

10.3.4 Further Developments 482

10.3.5 Summary 483

10.4 Multidimensional Scaling 484

10.4.1 Classical Scaling 484

10.4.2 Metric MDS 486

10.4.3 Ordinal Scaling 487

10.4.4 Algorithms 490

10.4.5 MDS for Feature Extraction 491

10.4.6 Example Application Study 492

10.4.7 Further Developments 493

10.4.8 Summary 493

10.5 Application Studies 493

10.6 Summary and Discussion 495

10.7 Recommendations 495

10.8 Notes and References 496

Exercises 497

11 Clustering 501

11.1 Introduction 501

11.2 Hierarchical Methods 502

11.2.1 Single-Link Method 503

11.2.2 Complete-Link Method 506

11.2.3 Sum-of-Squares Method 507

11.2.4 General Agglomerative Algorithm 508

11.2.5 Properties of a Hierarchical Classification 508

11.2.6 Example Application Study 509

11.2.7 Summary 509

11.3 Quick Partitions 510

11.4 Mixture Models 511

11.4.1 Model Description 511

11.4.2 Example Application Study 512

11.5 Sum-of-Squares Methods 513

11.5.1 Clustering Criteria 514

11.5.2 Clustering Algorithms 515

11.5.3 Vector Quantisation 520

11.5.4 Example Application Study 530

11.5.5 Further Developments 530

11.5.6 Summary 531

11.6 Spectral Clustering 531

11.6.1 Elementary Graph Theory 531

11.6.2 Similarity Matrices 534

11.6.3 Application to Clustering 534

11.6.4 Spectral Clustering Algorithm 535

11.6.5 Forms of Graph Laplacian 535

11.6.6 Example Application Study 536

11.6.7 Further Developments 538

11.6.8 Summary 538

11.7 Cluster Validity 538

11.7.1 Introduction 538

11.7.2 Statistical Tests 539

11.7.3 Absence of Class Structure 540

11.7.4 Validity of Individual Clusters 541

11.7.5 Hierarchical Clustering 542

11.7.6 Validation of Individual Clusterings 542

11.7.7 Partitions 543

11.7.8 Relative Criteria 543

11.7.9 Choosing the Number of Clusters 545

11.8 Application Studies 546

11.9 Summary and Discussion 549

11.10 Recommendations 551

11.11 Notes and References 552

Exercises 553

12 Complex Networks 555

12.1 Introduction 555

12.1.1 Characteristics 557

12.1.2 Properties 557

12.1.3 Questions to Address 559

12.1.4 Descriptive Features 560

12.1.5 Outline 560

12.2 Mathematics of Networks 561

12.2.1 Graph Matrices 561

12.2.2 Connectivity 562

12.2.3 Distance Measures 562

12.2.4 Weighted Networks 563

12.2.5 Centrality Measures 563

12.2.6 Random Graphs 564

12.3 Community Detection 565

12.3.1 Clustering Methods 565

12.3.2 Girvan–Newman Algorithm 568

12.3.3 Modularity Approaches 570

12.3.4 Local Modularity 571

12.3.5 Clique Percolation 573

12.3.6 Example Application Study 574

12.3.7 Further Developments 575

12.3.8 Summary 575

12.4 Link Prediction 575

12.4.1 Approaches to Link Prediction 576

12.4.2 Example Application Study 578

12.4.3 Further Developments 578

12.5 Application Studies 579

12.6 Summary and Discussion 579

12.7 Recommendations 580

12.8 Notes and References 580

Exercises 580

13 Additional Topics 581

13.1 Model Selection 581

13.1.1 Separate Training and Test Sets 582

13.1.2 Cross-Validation 582

13.1.3 The Bayesian Viewpoint 583

13.1.4 Akaike’s Information Criterion 583

13.1.5 Minimum Description Length 584

13.2 Missing Data 585

13.3 Outlier Detection and Robust Procedures 586

13.4 Mixed Continuous and Discrete Variables 587

13.5 Structural Risk Minimisation and the Vapnik–Chervonenkis Dimension 588

13.5.1 Bounds on the Expected Risk 588

13.5.2 The VC Dimension 589

References 591

Index 637

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“In the end I must add that this book is so appealing that I often found myself lost in the reading, pausing the overview of the manuscript in order to look more into some presented subject, and not being able to continue until I had finished seeing all about it.”  (Zentralblatt MATH, 1 December 2012)

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