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Tables of Contents for Pattern Classification
Chapter/Section Title
Page #
Page Count
Preface
xv
Introduction
1
18
Recognition of Entities versus Model-Based Recognition
4
2
Statistical Approach
6
2
Neural Network Approach
8
3
Conceptual Framework
11
8
Classes
11
2
Measurements and Features
13
2
Observation Vector
15
1
Pattern Classification System
15
2
Learning
17
2
Statistical Decision Theory
19
12
The Pattern Source
20
1
Risk Minimization
21
3
Bayes Classifier
24
4
General Structure of Pattern Classifier
28
3
Need for Approximations: Fundamental Approaches
31
13
Least Mean-Square Functional Approximations
33
7
Hard and Soft Labeling
34
2
Regression Function
36
2
Comment
38
1
Relations between Minimum Distance and Maximum A Posteriori Decisions
39
1
Need for Approximations
39
1
Statistical Modeling of Class-Specific Distributions
40
2
Minimum-Distance Classification
42
2
Classification Based on Statistical Models Determined by First- and Second-Order Statistical Moments
44
53
Multidimensional Normal Distribution
45
8
Definiteness of Quadratic Form
47
3
Equidensity Ellipsoids
50
1
Orientation and Size of Ellipsoids
50
2
Some Further Properties of Normal Distribution
52
1
Bayes Classifier for Normally Distributed Classes
53
14
Example
55
3
Confidences
58
2
Quadratic Discriminant Functions
60
1
Class Regions and Borders
61
3
Forwarding Sets of Alternatives
64
1
Scatterplots in Measurement and in Decision Space
65
2
Simplification to Equal Covariance Matrices
67
5
White Covariance Matrix
69
1
Class Regions and Borders
69
3
Euclidean and Mahalanobis Distance Classifiers
72
3
Comments
74
1
Statistically Independent Binary Measurements
75
4
Impact of Variances of Binary Variables
77
2
Parameter Estimation
79
10
Statistical Moments
80
2
Augmented Measurement Vector
82
1
Parameter Estimation from Subsets
82
2
Visualization of Statistical Parameters
84
3
Interpretation
87
2
Recursive Parameter Estimation
89
8
Recursive Learning of Means
90
2
Recursive Learning of Moment Matrices
92
1
Recursive Learning of Inverse Convariance Matrix
93
2
Comments
95
2
Classification Based on Mean-Square Functional Approximations
97
5
Polynomial Regression
102
85
Adaptation of Coefficient Matrix
107
3
Comments
109
1
Properties of Solution
110
3
Residual Variance
110
1
Orthogonality of Estimation Error Δd
110
1
Unbiasedness of Estimation d(v)
111
1
Unity Sum of Components of d(v)
111
2
Functional Approximation with y versus p as Target Vectors
113
3
Comments
115
1
Mean and Covariance of Estimation Error
116
6
Class-Specific Means of Estimation Error
118
1
Row and Column Sums of Estimation Error Covariance Matrix
119
1
Error Bounds on Class-Specific Estimations
119
2
Comments
121
1
Covariance of Estimation Error and Residual Variance
122
1
Covariance and Class-Specific Means of Discriminant Vector d
122
2
Some Properties of Mapping V --> D from Measurement Space into Decision Space
124
3
Training Polynomial Classifier: Solving Matrix Equation
127
5
Linear Dependencies
128
1
Predictor and To-be-Predicted Variables
129
1
Solving Matrix Equation
130
2
Feature Selection and Pivot Strategies
132
8
Pivot Selection
133
4
Maximum Linear Independence (LU) Strategy
137
1
Minimum Residual Variance (MS) Strategy
138
2
Sequence of Intermediate Solutions and Feature Ranking
140
1
Establishing Moment Matrix M from Learning Set or from Statistical Models
140
2
Regularities of Moment Matrices for Complete Polynomials
141
1
Second-Degree Polynomial Classifier for Normally Distributed Classes
142
3
Deriving Up to Fourth-Order Moments for Normally Distributed Classes
143
2
Visualizations Based on Two-Dimensional Example of Chapter 4
145
6
Confidence Mapping
151
14
Motivation
152
2
Imperfect Estimations Used as Feature Variables for Subsequent Classifier
154
4
Computing Confidences from Eigen- and Fremd- Histograms
158
2
Smooth Approximations for Confidence Mapping Function
160
1
Generic Model for Confidence Mapping Function
161
1
Confidence Mapping Applied to Examples of Section 6.12
162
1
Comments
163
2
Recursive Learning
165
18
Recursive Learning Rule for Polynomial Classifier
173
1
Modifications by Use of Simplified Weight Matrices G
174
1
Why Changes in Weight Matrix G Do Not Disturb Convergence
175
1
Stability Limits for Learning Factor α
176
2
Role of Last Seen Sample in Recursive Learning
178
1
Visualizations Based on Example of Section 4
179
1
Comments
180
3
Classifier Iteration
183
4
Comments
186
1
Multilayer Perceptron Regression
187
44
Model Neuron
188
3
Sigmoidal Activation Function
191
2
Single Layer of Multilayer Perceptron
193
1
Multilayer Perceptron
194
3
Relations to Concept of Functional Approximation Based on Linear Combination of Basis Functions
196
1
Appearance of Perceptron Basis Functions
197
5
Linear Combination of Perceptron Basis Functions
198
3
Perceptron Basis Functions in Multilayer Case
201
1
Comments
202
1
Backpropagation Learning
202
8
Computing Gradient
204
1
Partial Derivatives for hth Layer
205
1
Partial Derivatives with Respect to Output Variables
206
1
Singular and Cumulative Learning
207
2
Comments
209
1
Visualizations Based on Two-Dimensional Example of Chapter 4
210
5
Constructive Design of Perceptron Basis Functions
215
8
Motivation
217
1
Pairwise Borders between Classes
218
3
Visualization
221
2
Properties of Multilayer Perceptron Regression
223
4
Modifications of Multilayer Perceptron
227
4
Incomplete Networks
227
1
Weight Sharing
228
1
Modified Optimization Criteria
229
1
Comment
230
1
Radial Basis Functions
231
22
Relations to Nearest-Neighbor and Restricted-Neighborhood Techniques
233
9
Euclidean One-Nearest-Neighbor Classifier
234
3
Comments
237
1
Restricted-Neighborhood Classifier
238
3
Euclidean k-Nearest-Neighbor Classifier
241
1
Clustering
242
6
Vector Quantization Approach
244
4
Radial Basis Function Approximations to prob(v/k)
248
2
Radial Basis Function Approximations to prob(k/v)
250
3
Outlook
251
2
Measurements, Features, and Feature Selection
253
36
Evaluation of Features Individually
256
6
Mutual Information
257
1
Correlation
258
2
Relations to Minimum Residual Variance Strategy of Section 6.9
260
1
Comments
261
1
Rank-Order-Based Feature Selection
262
2
Collective Evaluation of Feature Sets
264
6
Relations to Class-Specific, Pooled, and Common Covariance Matrices
266
1
Interpretations
267
2
Relations to Minimum-Distance Classification
269
1
Fisher Criterion
269
1
Principal-Axis Transform and Its Neural Counterpart
270
19
Translation and Rotation of Coordinate System
271
3
Projections Based on New Coordinate System
274
1
Flat-Galaxy Interpretation
275
2
Whitening Transformation
277
1
Two- and Three-Dimensional Views of High-Dimensional Spaces
277
3
Reconstruction versus Classification
280
3
Reduction to Basic Constituents
283
1
Neural Principal-Axis Transform
284
5
Reject Criteria and Classifier Performance
289
41
Garbage Pattern Problem
290
3
Reject Criteria
293
5
Ambiguous Patterns and Sets of Alternatives
298
3
Relations between Reject and Forming Sets of Alternatives
301
1
Controlling Number of Alternatives
301
6
Introduction to Multiple-Class Target Points in Decision Space
301
4
Weighing Out Confidences
305
2
Performance Measuring and Operating Characteristics
307
23
Reclassification and Generalization
308
1
Learning and Test Set Sizes
309
1
Statistical Measures Describing Deterministic System
310
1
Jackknifing and Leave One Out
310
1
Variability of Error Rate Measurements
311
3
Error and Reject Rates Depending on Reject Threshold
314
7
Optimizing Reject Threshold
321
3
Residual Error Rate and Mean Number of Alternatives Depending on Confidence Threshold
324
6
Combining Classifiers
330
27
Concatenating Classifiers
331
3
Classifier Tuning
333
1
Classifiers Working in Parallel
334
7
Combination of Fast Low-Performance with Slow High-Performance Classifiers
334
1
Voting
334
2
Classifier Combination Following Dempster's Rule
336
2
Combining Classifiers as Classification Task
338
3
Hierarchical Classifiers
341
9
Operations of Individual Node Classifier
342
2
Confidence Distribution Network
344
1
Pruning Classifier Tree
345
1
Design of Tree Structure
346
2
Adaptation of Node Classifiers
348
1
Comments
349
1
Classifier Networks
350
7
Combination of Pairwise Estimations Viewed as Combination of Experts' Votes
352
1
Combination Network
353
2
Special Advantages
355
1
Relations to Multilayer Perceptron
356
1
Conclusion
357
3
STATMOD Program: Description of ftp Package
360
4
References
364
5
Index
369