PREFACE
1 INTRODUCTION, 1
1.1 Machine Perception, 1
1.2 An Example, 1
1.2.1 Related Fields, 8
1.3 Pattern Recognition Systems, 9
1.3.1 Sensing, 9
1.3.2 Segmentation and Grouping, 9
1.3.3 Feature Extraction, 11
1.3.4 Classification, 12
1.3.5 Post Processing, 13
1.4 The Design Cycle, 14
1.4.1 Data Collection, 14
1.4.2 Feature Choice, 14
1.4.3 Model Choice, 15
1.4.4 Training, 15
1.4.5 Evaluation, 15
1.4.6 Computational Complexity, 16
1.5 Learning and Adaptation, 16
1.5.1 Supervised Learning, 16
1.5.2 Unsupervised Learning, 17
1.5.3 Reinforcement Learning, 17
1.6 Conclusion, 17
Summary by Chapters, 17
Bibliographical and Historical Remarks, 18
Bibliography, 19
2 BAYESIAN DECISION THEORY, 20
2.1 Introduction, 20
2.2 Bayesian Decision Theory--Continuous Features, 24
2.2.1 Two-Category Classification, 25
2.3 Minimum-Error-Rate Classification, 26
2.3.1 Minimax Criterion, 27
*2.3.2 Neyman-Pearson Criterion, 28
2.4 Classifiers, Discriminant Functions, and Decision Surfaces, 29
2.4.1 The Multicategory Case, 29
2.4.2 The Two-Category Case, 30
2.5 The Normal Density, 31
2.5.1 Univariate Density, 32
2.5.2 Multivariate Density, 33
2.6 Discriminant Functions for the Normal Density, 36
*2.7 Error Probabilities and Integrals, 45
*2.8 Error Bounds for Normal Densities, 46
2.8.1 ChernoffBound, 46
2.8.2 BhattacharyyaBound, 47
Example 2 Error Bounds for Gaussian Distributions, 48
2.8.3 Signal Detection Theory and Operating Characteristics, 48
2.9 Bayes Decision Theory--Discrete Features, 51
2.9.1 Independent Binary Features, 52
Example 3 Bayesian Decisions for Three-Dimensional
Binary Data, 53
'2.10 Missing and Noisy Features, 54
2.10.1 Missing Features, 54
2.10.2 Noisy Features, 55
*2.11 Bayesian Belief Networks, 56
Example 4 Belief Network for Fish, 59
2.12 Compound Bayesian Decision Theory and Context, 62
Summary, 63
Bibliographical and Historical Remarks, 64
Problems, 65
Computer exercises, 80
Bibliography, 82
MAXIMUM-LIKELIHOOD AND BAYESIAN
3 PARAMETER ESTIMATION, 34
3.1 Introduction, 84
3.2 Maximum-Likelihood Estimation, 85
3.2.1 The General Principle, 85
3.2.2 The Gaussian Case: Unknown , 88
3.2.3 The Gaussian Case: Unknown and , 88
3.2.4 Bias, 89
3.3 Bayesian Estimation, 90
3.3.1 The Class-Conditional Densities, 91
3.3.2 The Parameter Distribution, 91
3.4 Bayesian Parameter Estimation: Gaussian Case, 92
3.4.1 The Univariate Case: p(D), 92
3.4.2 The Univariate Case: p(x|D), 95
3.4.3 The Multivariate Case, 95
3.5 Bayesian Parameter Estimation: General Theory, 97
Example 1 RecursiveBayes'Leaming, 98
3.5.1 When Do Maximum-Likelihood and Bayes Methods Differ?, 100
3.5.2 Noninformative Priors and Invariance, 101
3.5.3 Gibbs Algorithm, 102
*3.6 Sufficient Statistics, 102
3.6.1 Sufficient Statistics and the Exponential Family, 106
3.7 Problems of Dimensionality, 107
3.7.1 Accuracy, Dimension, and Training Sample Size, 107
3.7.2 Computational Complexity, 111
3.7.30verfitting, 113
*3.8 Component Analysis and Discriminants, 114
3.8.1 Principal ComponentAnalysis (PCA), 115
3.8.2 Fisher Linear Discriminant, 117
3.8.3 Multiple Discriminant Analysis, 121
*3.9 Expectation-Maximization (EM), 124
Example 2 Expectation-Maximization for a 2D Normal Model, 126
3.10 Hidden Markov Models, 128
3.10.1 First-Order Markov Models, 128
3.10.2 First-Order Hidden Markov Models, 129
3.10.3 Hidden Markov Model Computation, 129
3.10.4 Evaluation, 131
Example 3 Hidden Markov Model, 133
3.10.5 Decoding, 135
Example 4 HMM Decoding, 136
3.10.6 Learning, 137
Summary, 139
Bibliographical and Historical Remarks, 139
Problems, 140
Computer exercises, 155
Bibliography, 159
4 NONPARAMETRIC TECHNIQUES, 161
4.1 Introduction, 161
4.2 Density Estimation, 161
4.3 Parzen Windows, 164
4.3.1 Convergence of the Mean, 167
4.3.2 Convergence of the Variance, 167
4.3.3 Illustrations, 168
4.3.4 Classification Example, 168
4.3.5 Probabilistic Neural Networks (PNNs), 172
4.3.6 Choosing the Window Function, 174
4.4 kn-Nearest-Neighbor Estimation, 174
4.4.1 kn-Nearest-Neighbor and Parzen-Window Estimation, 176
4.4.2 Estimation ofA Posteriori Probabilities, 177
4.5 The Nearest-Neighbor Rule, 177
4.5.1 Convergence of the Nearest Neighbor, 179
4.5.2 Error Rate for the Nearest-Neighbor Rule, 180
4.5.3 Error Bounds, 180
4.5.4 The k-Nearest-Neighbor Rule, 182
4.5.5 Computational Complexity of the k-Nearest-Neighbor Rule, 184
4.6 Metrics and Nearest-Neighbor Classification, 187
4.6.1 Properties of Metrics, 187
4.6.2 Tangent Distance, 188
*4.7 Fuzzy Classification, 192
*4.8 Reduced Coulomb Energy Networks, 195
4.9 Approximations by Series Expansions, 197
Summary, 199
Bibliographical and Historical Remarks, 200
Problems, 201
Computer exercises, 209
Bibliography, 213
5 LINEAR DISCRIMINANT FUNCTIONS, 215
5.1 Introduction, 215
5.2 Linear Discriminant Functions and Decision Surfaces, 216
5.2.1 The Two-Category Case, 216
5.2.2 The Multicategory Case, 218
5.3 Generalized Linear Discriminant Functions, 219
5.4 The Two-Category Linearly Separable Case, 223
5.4.1 Geometry and Terminology, 224
5.4.2 Gradient Descent Procedures, 224
5.5 Minimizing the Perceptron Criterion Function, 227
5.5.1 The Perceptron Criterion Function, 227
5.5.2 Convergence Proof for Single-Sample Correction, 229
5.5.3 Some Direct Generalizations, 232
5.6 Relaxation Procedures, 235
5.6.1 The Descent Algorithm, 235
5.6.2 Convergence Proof, 237
5.7 Nonseparable Behavior, 238
5.8 Minimum Squared-Error Procedures, 239
5.8.1 Minimum Squared-Error and the Pseudoinverse, 240
Example 1 Constructing a Linear Classifier by Matrix
Pseudoinverse, 241
5.8.2 Relation to Fisher's Linear Discriminant, 242
5.8.3 Asymptotic Approximation to an Optimal Discriminant, 243
5.8.4 The Widrow-Hoffor LMS Procedure, 245
5.8.5 Stochastic Approximation Methods, 246
5.9 The Ho-Kashyap Procedures, 249
5.9.1 The Descent Procedure, 250
5.9.2 Convergence Proof, 251
5.9.3 Nonseparable Behavior, 253
5.9.4 Some Related Procedures, 253
'5.10 Linear Programming Algorithms, 256
5.10.1 Linear Programming, 256
5.10.2 The Linearly Separable Case, 257
5.10.3 Minimizing the Perceptron Criterion Function, 258
*5.11 Support Vector Machines, 259
5.11.1 SVM Training, 263
Example 2 SVM for the XOR Problem, 264
5.12 Multicategory Generalizations, 265
5.12.1 Kesler's Construction, 266
5.12.2 Convergence of the Fixed-Increment Rule, 266
5.12.3 Generalizations for MSE Procedures, 268
Summary, 269
Bibliographical and Historical Remarks, 270
Problems, 271
Computer exercises, 278
Bibliography, 281
6 MULTILAYER NEURAL NETWORKS, 282
6.1 Introduction, 282
6.2 Feedforward Operation and Classification, 284
6.2.1 General Feedforward Operation, 286
6.2.2 Expressive Power of Multilayer Networks, 287
6.3 Backpropagation Algorithm, 288
6.3.1 Network Learning, 289
6.3.2 Training Protocols, 293
6.3.3 Learning Curves, 295
6.4 Error Surfaces, 296
6.4.1 Some Small Networks, 296
6.4.2 The Exclusive-OR (XOR), 298
6.4.3 Larger Networks, 298
6.4.4 How Important Are Multiple Minima?, 299
6.5 Backpropagation as Feature Mapping, 299
6.5.1 Representations at the Hidden Layer Weights, 302
6.6 Backpropagation, Bayes Theory and Probability, 303
6.6.1 Bayes Discriminants and Neural Networks, 303
6.6.2 Outputs as Probabilities, 304
*6.7 Related Statistical Techniques, 305
6.8 Practical Techniques for Improving Backpropagation, 306
6.8.1 Activation Function, 307
6.8.2 Parameters for the Sigmoid, 308
6.8.3 Scaling Input, 308
6.8.4 Target Values, 309
6.8.5 Training with Noise, 310
6.8.6 Manufacturing Data, 310
6.8.7 Number of Hidden Units, 310
6.8.8 Initializing Weights, 311
6.8.9 Learning Rates, 312
6.8.10 Momentum, 313
6.8.11 Weight Decay, 314
6.8.12 Hints, 315
6.8.13 On-Line, Stochastic or Batch Training?, 316
6.8.14 Stopped Training, 316
6.8.15 Number of Hidden Layers, 317
6.8.16 Criterion Function, 318
*6.9 Second-Order Methods, 318
6.9.1 Hessian Matrix, 318
6.9.2 Newton's Method, 319
6.9.3 Quickprop, 320
6.9.4 Conjugate Gradient Descent, 321
Example 1 Conjugate Gradient Descent, 322
*6.10 Additional Networks and Training Methods, 324
6.10.1 Radial Basis Function Networks (RBFs), 324
6.10.2 Special Bases, 325
6.10.3 Matched Filters, 325
6.10.4 Convolutional Networks, 326
6.10.5 Recurrent Networks, 328
6.10.6 Cascade-Correlation, 329
6.11 Regularization, Complexity Adjustment and Pruning, 330
Summary, 333
Bibliographical and Historical Remarks, 333
Problems, 335
Computer exercises, 343
Bibliography, 347
7 STOCHASTIC METHODS, 350
7.1 Introduction, 350
7.2 Stochastic Search, 351
7.2.1 Simulated Annealing, 351
7.2.2 The Boltzmann Factor, 352
7.2.3 Deterministic Simulated Annealing, 357
7.3 Boltzmann Learning, 360
7.3.1 Stochastic Boltzmann Learning of Visible States, 360
7.3.2 Missing Features and Category Constraints, 365
7.3.3 Deterministic Boltzmann Learning, 366
7.3.4 Initialization and Setting Parameters, 367
*7.4 Boltzmann Networks and Graphical Models, 370
7.4.1 Other Graphical Models, 372
*7.5 Evolutionary Methods, 373
7.5.1 Genetic Algorithms, 373
7.5.2 Further Heuristics, 377
7.5.3 Why Do They Work?, 378
*7.6 Genetic Programming, 378
Summary, 381
Bibliographical and Historical Remarks, 381
Problems, 383
Computer exercises, 388
Bibliography, 391
8 NONMETRIC METHODS, 394
8.1 Introduction, 394
8.2 Decision Trees, 395
8.3 CART, 396
8.3.1 Number of Splits, 397
8.3.2 Query Selection and Node Impurity, 398
8.3.3 When to Stop Splitting, 402
8.3.4 Pruning, 403
8.3.5 Assignment of Leaf Node Labels, 404
Example 1 A Simple Tree, 404
8.3.6 Computational Complexity, 406
8.3.7 Feature Choice, 407
8.3.8 Multivariate Decision Trees, 408
8.3.9 Priors and Costs, 409
8.3.10 Missing Attributes, 409
Example 2 Surrogate Splits and Missing Attributes, 410
8.4 Other Tree Methods, 411
8.4.1 ID3, 411
8.4.2 C4.5, 411
8.4.3 Which Tree Classifier Is Best?, 412
*8.5 Recognition with Strings, 413
8.5.1 String Matching, 4i5
8.5.2 Edit Distance, 418
8.5.3 Computational Complexity, 420
8.5.4 String Matching with Errors, 420
8.5.5 String Matching with the "Don't-Care" Symbol, 421
8.6 Grammatical Methods, 421
8.6.1 Grammars, 422
8.6.2 Types of String Grammars, 424
Example 3 A Grammar for Pronouncing Numbers, 425
8.6.3 Recognition Using Grammars, 426
8.7 Grammatical Inference, 429
Example 4 Grammatical Inference, 431
*8.8 Rule-Based Methods, 431
8.8.1 Learning Rules, 433
Summary, 434
Bibliographical and Historical Remarks, 435
Problems, 437
Computer exercises, 446
Bibliography, 450
9 ALGORITHM-INDEPENDENT MACHINE LEARNING, 453
9.1 Introduction, 453
9.2 Lack of Inherent Superiority of Any Classifier, 454
9.2.1 No Free Lunch Theorem, 454
Example 1 No Free Lunch for Binary Data, 457
*9.2.2 Ugly Duckling Theorem, 458
9.2.3 Minimum Description Length (MDL), 461
9.2.4 Minimum Description Length Principle, 463
9.2.50verfitting Avoidance and Occam's Razor, 464
9.3 Bias and Variance, 465
9.3.1 Bias and Variance for Regression, 466
9.3.2 Bias and Variance for Classification, 468
9.4 Resampling for Estimating Statistics, 471
9.4.1 Jackknife, 472
Example 2 Jackknife Estimate of Bias and Variance of the Mode, 473
9.4.2 Bootstrap, 474
9.5 Resampling for Classifier Design, 475
9.5.1 Bagging, 475
9.5.2 Boosting, 476
9.5.3 Learning with Queries, 480
9.5.4 Arcing, Learning with Queries, Bias and Variance, 482
9.6 Estimating and Comparing Classifiers, 482
9.6.1 Parametric Models, 483
9.6.2 Cross-Validation, 483
9.6.3 Jackknife and Bootstrap Estimation of Classification Accuracy, 485
9.6.4 Maximum-Likelihood Model Comparison, 486
9.6.5 Bayesian Model Comparison, 487
9.6.6 The Problem-Average Error Rate, 489
9.6.7 Predicting Final Performance from Learning Curves, 492
9.6.8 The Capacity of a Separating Plane, 494
9.7 Combining Classifiers, 495
9.7.1 Component Classifiers with Discriminant Functions, 496
9.7.2 Component Classifiers without Discriminant Functions, 498
Summary, 499
Bibliographical and Historical Remarks, 500
Problems, 502
Computer exercises, 508
Bibliography, 513
10 UNSUPERVISED LEARNING AND CLUSTERING, 517
10.1 Introduction, 517
10.2 Mixture Densities and Identifiability, 518
10.3 Maximum-Likelihood Estimates, 519
10.4 Application to Normal Mixtures, 521
10.4.1 Case 1: Unknown Mean Vectors, 522
10.4.2 Case 2: All Parameters Unknown, 524
10.4.3 k-Means Clustering, 526
* 10.4.4 Fuzzy k-Means Clustering, 528
10.5 Unsupervised Bayesian Learning, 530
10.5.1 The Bayes Classifier, 530
10.5.2 Learning the Parameter Vector, 531
Example 1 Unsupervised Learning of Gaussian Data, 534
10.5.3 Decision-Directed Approximation, 536
10.6 Data Description and Clustering, 537
10.6.1 Similarity Measures, 538
10.7 Criterion Functions for Clustering, 542
10.7.1 The Sum-of-Squared-Error Criterion, 542
10.7.2 Related Minimum Variance Criteria, 543
10.7.3 Scatter Criteria, 544
Example 2 Clustering Criteria, 546
10.8 Iterative Optimization, 548
10.9 Hierarchical Clustering, 550
10.9.1 Definitions, 551
10.9.2 Agglomerative Hierarchical Clustering, 552
10.9.3 Stepwise-Optimal Hierarchical Clustering, 555
10.9.4 Hierarchical Clustering and Induced Metrics, 556
* 10.10 The Problem of Validity, 557
*10.11 On-line clustering, 559
10.11.1 Unknown Number of Clusters, 561
10.11.2 Adaptive Resonance, 563
10.11.3 Learning with a Critic, 565
'10.12 Graph-Theoretic Methods, 566
10.13 Component Analysis, 568
10.13.1 Principal Component Analysis (PCA), 568
10.13.2 Nonlinear Component Analysis (NLCA), 569
* 10.13.3 Independent Component Analysis (ICA), 570
10.14 Low-Dimensional Representations and Multidimensional Scaling (MDS), 573
10.14.1 Self-Organizing Feature Maps, 576
10.14.2 Clustering and Dimensionality Reduction, 580
Summary, 581
Bibliographical and Historical Remarks, 582
Problems, 583
Computer exercises, 593
Bibliography, 598
A MATHEMATICAL FOUNDATIONS, 601
A.1 Notation, 601
A.2 Linear Algebra, 604
A.2.1 Notation and Preliminaries, 604
A.2.2 Inner Product, 605
A.2.3 Outer Product, 606
A.2.4 Derivatives of Matrices, 606
A.2.5 Determinant and Trace, 608
A.2.6 Matrix Inversion, 609
A.2.7 Eigenvectors and Eigenvalues, 609
A.3 LagrangeOptimization, 610
A.4 Probability Theory, 611
A.4.1 Discrete Random Variables, 611
A.4.2 Expected Values, 611
A.4.3 Pairs of Discrete Random Variables, 612
A.4.4 Statistical Independence, 613
A.4.5 Expected Values of Functions of Two Variables, 613
A.4.6 Conditional Probability, 614
A.4.7 The Law of Total Probability and Bayes Rule, 615
A.4.8 Vector Random Variables, 616
A.4.9 Expectations, Mean Vectors and Covariance Matrices, 617
A.4.10 Continuous Random Variables, 618
A.4.11 Distributions of Sums of Independent Random Variables, 620
A.4.12 Normal Distributions, 621
A.5 Gaussian Derivatives and Integrals, 623
A.5.1 Multivariate Normal Densities, 624
A.5.2 Bivariate Normal Densities, 626
A.6 Hypothesis Testing, 628
A.6.1 Chi-SquaredTest, 629
A.7 Information Theory, 630
A.7.1 Entropy and Information, 630
A.7.2 Relative Entropy, 632
A.7.3 Mutual Information, 632
A.8 Computational Complexity, 633
Bibliography, 635
INDEX
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