Statistical pattern recognition:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2011
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis Klappentext |
| Beschreibung: | XXIV, 642 S. Ill., graph. Darst. |
| ISBN: | 9780470682272 9780470682289 |
Internformat
MARC
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| 100 | 1 | |a Webb, Andrew R. |e Verfasser |0 (DE-588)140273085 |4 aut | |
| 245 | 1 | 0 | |a Statistical pattern recognition |c Andrew R. Webb ; Keith D. Copsey |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2011 | |
| 300 | |a XXIV, 642 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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| DE-BY-FWS_katkey | 450973 |
| DE-BY-FWS_media_number | 083101273400 |
| _version_ | 1806174029143343104 |
| adam_text | Contents
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
CONTENTS
34
34
35
35
35
37
39
40
40
40
41
41
42
44
45
46
46
46
48
49
51
52
55
60
62
63
63
66
66
67
Exercises
67
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
2.2
Estimating the Parameters of the Distributions
2.2.1
Estimative Approach
2.2.2
Predictive Approach
2.3
The Gaussian Classifier
2.3.1
Specification
2.3.2
Derivation of the Gaussian Classifier Plug-In Estimates
2.3.3
Example Application Study
2.4
Dealing with Singularities in the Gaussian Classifier
2.4.1
Introduction
2.4.2
Naïve Bayes
2.4.3
Projection onto a Subspace
2.4.4
Linear Discriminant Function
2.4.5
Regularised Discriminant Analysis
2.4.6
Example Application Study
2.4.7
Further Developments
2.4.8
Summary
2.5
Finite
Mixture Models
2.5.1
Introduction
2.5.2
Mixture Models for Discrimination
2.5.3
Parameter Estimation for Normal Mixture Models
2.5.4
Normal Mixture Model Covariance Matrix Constraints
2.5.5
How Many Components?
2.5.6
Maximum Likelihood Estimation via EM
2.5.7
Example Application Study
2.5.8
Further Developments
2.5.9
Summary
2.6
Application Studies
2.7
Summary and Discussion
2.8
Recommendations
2.9
Notes
and References
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
4.1
CONTENTS
ix
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
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
Bayesian Approaches to Discrimination
116
3.5.1
Labelled Training Data
116
3.5.2
Unlabelled Training Data
117
Sequential Monte Carlo Samplers
119
3.6.1
Introduction
119
3.6.2
Basic Methodology
121
3.6.3
Summary
125
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
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
Example Application Study
144
Application Studies
145
Summary and Discussion
146
Recommendations
147
Notes and References
147
ses
148
y
Estimation
-
Nonparametric
150
Introduction
150
4.1.1
Basic Prouerties of Density Estimators
150
CONTENTS
4.2 fc-Nearest-Neighbour
Method
152
4.2.1 Jfc-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
5.2.3
Fisher s Criterion
5.2.4
Least Mean-Squared-Error Procedures
5.2.5
Further Developments
5.2.6
Summary
5.3
Multiclass
Algorithms
5.3.1
General Ideas
5.3.2
Error-Correction Procedure
5.3.3
Fisher s Criterion
-
Linear Discriminant Analysis
5.3.4
Least Mean-Squared-Error Procedures
5.3.5
Régularisation
5.3.6
Example Application Study
5.3.7
Further Developments
5.3.8
Summary
5.4
Support
Vector
Machines
5.4.1
Introduction
5.4.2
Linearly Separable Two-Class Data
5.4.3
Linearly Nonseparable Two-Class Data
5.4.4
Multiclass SVMs
5.4.5
SVMs for Regression
5.4.6
Implementation
5.4.7
Example Application Study
5.4.8
Summary
5.5
Logistic
Discrimination
5.5.1
Two-Class Case
5.5.2
Maximum Likelihood Estimation
5.5.3
Multiclass Logistic Discrimination
5.5.4
Example Application Study
5.5.5
Further Developments
5.5.6
Summary
5.6
Application
Studies
5.7
Summary and Discussion
5.8
Recommendations
5.9
Notes
and References
Exercises
Nonlinear
Discriminant
Analysis
-
Kemel and Projection
Methods
6.1
Introduction
6.2
Radial
1
Basis Functions
6.2.1
Introduction
6.2.2
Specifying the Model
6.2.3
Specifying the Functional Form
6.2.4
The Positions of the Centres
6.2.5
Smoothing Parameters
6.2.6
Calculation of the Weights
6.2.7
Model Order Selection
6.2.8
Simple RBF
CONTENTS
xi
223
227
228
235
235
236
236
237
238
241
246
246
247
248
249
249
249
253
256
257
259
262
263
263
263
264
266
267
267
268
268
268
269
270
270
274
274
276
276
278
278
279
281
282
284
285
xii CONTENTS
6.2.9
Motivation
6.2.10
RBF Properties
6.2.11
Example Application Study
6.2.12
Further Developments
6.2.13
Summary
6.3
Nonlinear Support
Vector
Machines
6.3.1
Introduction
6.3.2
Binary Classification
6.3.3
Types of Kernel
6.3.4
Model Selection
6.3.5
Multiclass SVMs
6.3.6
Probability Estimates
6.3.7
Nonlinear Regression
6.3.8
Example Application Study
6.3.9
Further Developments
6.3.10
Summary
6.4
The Multilayer Perceptron
6.4.1
Introduction
6.4.2
Specifying the
MLP
Structure
6.4.3
Determining the
MLP
Weights
6.4.4
Modelling Capacity of the
MLP
6.4.5
Logistic Classification
6.4.6
Example Application Study
6.4.7
Bayesian
MLP
Networks
6.4.8
Projection Pursuit
6.4.9
Summary
6.5
Application Studies
6.6
Summary and Discussion
6.7
Recommendations
6.8
Notes
г
ind
References
Exercises
7 Ruh
;
and Decision Tree Induction
7.1
Introduction
7.2
Decision Trees
7.2.1
Introduction
7.2.2
Decision Tree Construction
7.2.3
Selection of the Splitting Rule
7.2.4
Terminating the Splitting Procedure
7.2.5
Assigning Class Labels to Terminal Nodes
7.2.6
Decision Tree Pruning
-
Worked Example
7.2.7
Decision Tree Construction Methods
7.2.8
Other Issues
7.2.9
Example Application Study
7.2.10
Further Developments
7.2.11
Summary
286
288
288
289
290
291
291
291
292
293
294
294
296
296
297
298
298
298
299
300
307
307
310
311
313
313
314
316
317
318
318
322
322
323
323
326
327
330
332
332
337
339
340
341
342
CONTENTS
7.3
Rule Induction
7.3.1
Introduction
7.3.2
Generating Rules from a Decision Tree
7.3.3
Rule Induction Using a Sequential Covering Algorithm
7.3.4
Example Application Study
7.3.5
Further Developments
7.3.6
Summary
7.4
Multivariate Adaptive Regression Splines
7.4.1
Introduction
7.4.2
Recursive Partitioning Model
7.4.3
Example Application Study
7.4.4
Further Developments
7.4.5
Summary
7.5
Application Studies
7.6
Summary and Discussion
7.7
Recommendations
7.8
Notes and References
Exercises
Ensemble
Methods
8.1
Introduction
8.2
Characterising a Classifier Combination Scheme
8.2.1
Feature Space
8.2.2
Level
8.2.3
Degree of Training
8.2.4
Form of Component Classifiers
8.2.5
Structure
8.2.6
Optimisation
8.3
Data Fusion
8.3.1
Architectures
8.3.2
Bayesian Approaches
8.3.3
Neyman-Pearson Formulation
8.3.4
Trainable Rules
8.3.5
Fixed Rules
8.4
Classifier Combination Methods
8.4.1
Product Rule
8.4.2
Sum Rule
8.4.3
Min,
Max and Median Combiners
8.4.4
Majority Vote
8.4.5
Borda
Count
8.4.6
Combiners Trained on Class Predictions
8.4.7
Stacked Generalisation
8.4.8
Mixture of Experts
8.4.9
Bagging
8.4.10
Boosting
8.4.11
Random Forests
8.4.12
Model Averaging
342
342
345
345
350
351
351
351
351
351
355
355
356
356
358
358
359
359
361
361
362
363
366
368
368
369
369
370
370
371
373
374
375
376
376
377
378
379
379
380
382
382
385
387
389
390
xiv CONTENTS
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
10.3.1
Principal Components Analysis
10.3.2
Karhunen-Loève
Transformation
10.3.3
Example Application Study
10.3.4
Further Developments
10.3.5
Summary
10.4
Multidimensional Scaling
10.4.1
Classical Scaling
10.4.2
Metric MDS
10.4.3
Ordinal Scaling
10.4.4
Algorithms
10.4.5
MDS for Feature Extraction
10.4.6
Example Application Study
10.4.7
Further Developments
10.4.8
Summary
10.5
Application Studies
10.6
Summary and Discussion
10.7
Recommendations
10.8
Notes and References
Exercises
CONTENTS
xv
463
464
475
481
482
483
484
484
486
487
490
491
492
493
493
493
495
495
496
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
xvi CONTENTS
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
CONTENTS xvii
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
Contents
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 B ook 29
1.9 Notes and References 29
Exercises 31
2 Density Estimation - Parametric 33
2.1 Introduction 33
CONTENTS
viii
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 Naïve 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
Density Estimation - Bayesian 70
3.1 Introduction 70
3.LI 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
CONTENTS
ix
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
Density Estimation - Nonparametric 150
4.1 Introduction 150
4.1.1 Basic Properties of Density Estimators 150
X
CONTENTS
4.2 ¿-Nearest-Neighbour Method 152
4.2.1 ¿-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
CONTENTS
xi
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 Régularisation 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
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
CONTENTS
xii
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
CONTENTS
xiii
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
8.1 Introduction
8.2 Characterising a Classifier Combination Scheme
8.2.1 Feature Space
8.2.2 Level
8.2.3 Degree of Training
8.2.4 Form of Component Classifiers
8.2.5 Structure
8.2.6 Optimisation
Data Fusion
8.3.1 Architectures
8.3.2 Bayesian Approaches
8.3.3 Neyman-Pearson Formulation
8.3.4 Trainable Rules
8.3.5 Fixed Rules
Classifier Combination Methods
8.4.1 Product Rule
8.4.2 Sum Rule
8.4.3 Min, Max and Median Combiners
8.4.4 Majority Vote
8.4.5 Borda Count
8.4.6 Combiners Trained on Class Predictions
8.4.7 Stacked Generalisation
8.4.8 Mixture of Experts
8.4.9 Bagging
8.4.10 Boosting
8.4.11 Random Forests
8.4.12 Model Averaging
361
361
362
363
366
368
368
369
369
370
370
371
373
374
375
376
376
377
378
379
379
380
382
382
385
387
389
390
396
398
399
399
400
401
401
402
404
404
405
405
406
413
415
419
421
422
423
424
424
425
426
428
429
429
429
430
430
430
431
433
433
435
435
439
440
449
450
454
458
459
460
462
462
463
CONTENTS
8.4.13 Summary of Methods
8.4.14 Example Application Study
8.4.15 Further Developments
8.5 Application Studies
8.6 Summary and Discussion
8.7 Recommendations
8.8 Notes and References
Exercises
Performance Assessment
9.1 Introduction
9.2 Performance Assessment
9.2.1 Performance Measures
9.2.2 Discriminability
9.2.3 Reliability
9.2.4 ROC Curves for Performance Assessment
9.2.5 Population and Sensor Drift
9.2.6 Example Application Study
9.2.7 Further Developments
9.2.8 Summary
9.3 Comparing Classifier Performance
9.3.1 Which Technique is Best?
9.3.2 Statistical Tests
9.3.3 Comparing Rules When Misclassification Costs are Uncertain
9.3.4 Example Application Study
9.3.5 Further Developments
9.3.6 Summary
9.4 Application Studies
9.5 Summary and Discussion
9.6 Recommendations
9.7 Notes and References
Exercises
Feature Selection and Extraction
10.1 Introduction
10.2 Feature Selection
10.2.1 Introduction
10.2.2 Characterisation of Feature Selection Approaches
10.2.3 Evaluation Measures
10.2.4 Search Algorithms for Feature Subset Selection
10.2.5 Complete Search - Branch and Bound
10.2.6 Sequential Search
10.2.7 Random Search
10.2.8 Markov Blanket
10.2.9 Stability of Feature Selection
10.2.10 Example Application Study
10.2.11 Further Developments
10.2.12 Summary
CONTENTS
xv
10.3 Linear Feature Extraction 463
10.3.1 Principal Components Analysis 464
10.3.2 Karhunen-Loeve 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
Clustering 501
îi.i 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
XVI
CONTENTS
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
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
CONTENTS xvii
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
Andrew R. Webb and Keith D. Copsey
Mathematics and Data Analysis Consultancy, Malvern, UK
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, Third 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 wifi 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 this 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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| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV039560527 |
| illustrated | Illustrated |
| indexdate | 2024-08-01T10:43:02Z |
| institution | BVB |
| isbn | 9780470682272 9780470682289 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024412203 |
| oclc_num | 751022720 |
| open_access_boolean | |
| owner | DE-M49 DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-824 DE-863 DE-BY-FWS DE-739 |
| owner_facet | DE-M49 DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-824 DE-863 DE-BY-FWS DE-739 |
| physical | XXIV, 642 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley |
| record_format | marc |
| spellingShingle | Webb, Andrew R. Copsey, Keith D. Statistical pattern recognition Statistische Analyse (DE-588)4116599-8 gnd Mustererkennung (DE-588)4040936-3 gnd Klassifikation (DE-588)4030958-7 gnd Bildauswertung (DE-588)4145394-3 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4116599-8 (DE-588)4040936-3 (DE-588)4030958-7 (DE-588)4145394-3 (DE-588)4056995-0 |
| title | Statistical pattern recognition |
| title_auth | Statistical pattern recognition |
| title_exact_search | Statistical pattern recognition |
| title_full | Statistical pattern recognition Andrew R. Webb ; Keith D. Copsey |
| title_fullStr | Statistical pattern recognition Andrew R. Webb ; Keith D. Copsey |
| title_full_unstemmed | Statistical pattern recognition Andrew R. Webb ; Keith D. Copsey |
| title_short | Statistical pattern recognition |
| title_sort | statistical pattern recognition |
| topic | Statistische Analyse (DE-588)4116599-8 gnd Mustererkennung (DE-588)4040936-3 gnd Klassifikation (DE-588)4030958-7 gnd Bildauswertung (DE-588)4145394-3 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistische Analyse Mustererkennung Klassifikation Bildauswertung Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024412203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024412203&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024412203&sequence=000006&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT webbandrewr statisticalpatternrecognition AT copseykeithd statisticalpatternrecognition |
Inhaltsverzeichnis
Inhaltsverzeichnis
Inhaltsverzeichnis
Würzburg Teilbibliothek SHL, Raum I.2.11
| Signatur: |
1340 ST 330 W365(3)st |
|---|---|
| Exemplar 1 | nicht ausleihbar Verfügbar |