Support vector machines for pattern classification:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Springer
2010
|
| Edition: | 2nd. ed. |
| Series: | Advances in Pattern Recognition
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIX, 471 S. Ill., graph. Darst. |
| ISBN: | 9781849960977 |
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MARC
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| 100 | 1 | |a Abe, Shigeo |d 1947- |e Verfasser |0 (DE-588)122089545 |4 aut | |
| 245 | 1 | 0 | |a Support vector machines for pattern classification |c Shigeo Abe |
| 250 | |a 2nd. ed. | ||
| 264 | 1 | |a London |b Springer |c 2010 | |
| 300 | |a XIX, 471 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Advances in Pattern Recognition | |
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Record in the Search Index
| _version_ | 1805093898808197120 |
|---|---|
| adam_text |
Contents
Preface
.
v
Acknowledgments
. xi
Symbols
. xix
Introduction
. 1
1.1
Decision Functions
. 2
1.1.1
Decision Functions for Two-Class Problems
. 2
1.1.2
Decision Functions for Multiclass Problems
. 4
1.2
Determination of Decision Functions
. 8
1.3
Data Sets Used in the Book
. 9
1.4
Classifier Evaluation
. 13
References
. 16
Two-Class Support Vector Machines
. 21
2.1
Hard-Margin Support Vector Machines
. 21
2.2
Ll Soft-Margin Support Vector Machines
. 28
2.3
Mapping to a High-Dimensional Space
. 31
2.3.1
Kernel Tricks
. 31
2.3.2
Kerneb
. 33
2.3.3
Normalizing Kernels
. 43
2.3.4
Properties of Mapping Functions Associated with
Kerneb
. 44
2.3.5
Implicit Bias Terms
. 47
2.3.6
Empirical Feature Space
. 50
2.4
L2 Soft-Margin Support Vector Machines
. 56
2.5
Advantages and Disadvantages
. 58
2.5.1
Advantages
. 58
2.5.2
Disadvantages
. 59
2.6
Characteristics of Solutions
. 60
2.6.1
Hessian Matrix
. 60
2.6.2
Dependence of Solutions on
С
. 62
xffi
xiv
Contents
2.6.3
Equivalence of LI and L2 Support Vector Machines
. 67
2.6.4
Nonunique Solutions
. 70
2.6.5
Reducing the Number of Support Vectors
. 78
2.6.6
Degenerate Solutions
. 81
2.6.7
Duplicate Copies of Data
. 83
2.6.8
unbalanced Data
. 85
2.6.9
Classification for the Blood Cell Data
. 85
2.7
Class Boundaries for Different Kernels
. 88
2.8
Developing Classifiers
. 93
2.8.1
Model Selection
. 93
2.8.2
Estimating Generalization Errors
. 93
2.8.3
Sophistication of Model Selection
. 97
2.8.4
Effect of Model Selection by Cross-Validation
. 98
2.9
Invariance
for Linear Transformation
. 102
References
. 106
3
Multiclass Support Vector Machines
.113
3.1
One-Against-All Support Vector Machines
.114
3.1.1
Conventional Support Vector Machines
.114
3.1.2
Fuzzy Support Vector Machines
.116
3.1.3
Equivalence of Fuzzy Support Vector Machines and
Support Vector Machines with Continuous Decision
Functions
.119
3.1.4
Decision-Tree-Based Support Vector Machines
.122
3.2
Pairwise Support Vector Machines
.127
3.2.1
Conventional Support Vector Machines
.127
3.2.2
Fuzzy Support Vector Machines
.128
3.2.3
Performance Comparison of Fuzzy Support Vector
Machines
.129
3.2.4
Cluster-Based Support Vector Machines
.132
3.2.5
Decision-Tree-Based Support Vector Machines
.133
3.2.6
Pairwise Classification with Correcting Classifiers
.143
3.3
Error-Correcting Output Codes
.144
3.3.1
Output Coding by Error-Correcting Codes
.145
3.3.2
Unified Scheme for Output Coding
.146
3.3.3
Equivalence of ECOC with Membership Functions
_147
3.3.4
Performance Evaluation
.147
3.4
All-at-Once Support Vector Machines
.149
3.5
Comparisons of Architectures
.152
3.5.1
One-Against-AH Support Vector Machines
.152
3.5.2
Pairwise Support Vector Machines
.152
3.5.3
ECOC Support Vector Machines
.153
3.5.4
All-at-Once Support Vector Machines
.153
3.5.5
Training Difficulty
.153
3.5.6
Training Time Comparison
.157
References
.158
Contents
Variants
of Support Vector Machines
.163
4.1
Least-Squares Support Vector Machines
.163
4.1.1
Two-Class Least-Squares Support Vector Machines
. 164
4.1.2
One-Against-All Least-Squares Support Vector
Machines
.166
4.1.3
Pairwise Least-Squares Support Vector Machines
.168
4.1.4
Alł-at-Once
Least-Squares Support Vector Machines
. 169
4.1.5
Performance Comparison
.170
4.2
Linear Programming Support Vector Machines
.174
4.2.1
Architecture
.175
4.2.2
Performance Evaluation
.178
4.3
Sparse Support Vector Machines
.180
4.3.1
Several Approaches for Sparse Support
Vector Machines
.181
4.3.2
Idea
.183
4.3.3
Support Vector Machines Trained in the Empirical
Feature Space
.184
4.3.4
Selection of Linearly Independent Data
.187
4.3.5
Performance Evaluation
.189
4.4
Performance Comparison of Different Classifiers
.192
4.5
Robust Support Vector Machines
.196
4.6
Bayesian Support Vector Machines
.197
4.6.1
One-Dimensional Bayesian Decision Functions
.199
4.6.2
Parallel Displacement of
a
Hyperplane.200
4.6.3
Normal Test
.201
4.7
Incremental Training
.201
4.7.1
Overview
.201
4.7.2
Incremental Training Using Hyperspheres
.204
4.8
Learning Using Privileged Information
.213
4.9
Semi-Supervised Learning
.216
4.10
Multiple Classifier Systems
.217
4.11
Multiple Kernel Learning
.218
4.12
Confidence Level
.219
4.13
Visualization
.220
References
.220
Iraining Methods
.227
5.1
Preselecting Support Vector Candidates
.227
5.1.1
Approximation of Boundary Data
.228
5.1.2
Performance Evaluation
.230
5.2
Decomposition Techniques
.231
5.3
KKT Conditions Revisited
.234
5.4
Overview of Training Methods
.239
5.5
Primal-Dual Interior-Point Methods
.242
Contents
5.5.1
Primal-Dual Interior-Point Methods for Linear
Programming
.242
5.5.2
Primal-Dual Interior-Point Methods for Quadratic
Programming
.246
5.5.3
Performance Evaluation
.248
5.6
Steepest Ascent Methods and Newton's Methods
.252
5.6.1
Solving Quadratic Programming Problems Without
Constraints
.252
5.6.2
Training of LI Soft-Margin Support Vector Machines
. 254
5.6.3
Sequential Minimal Optimization
.259
5.6.4
Training of L2 Soft-Margin Support Vector Machines
. 260
5.6.5
Performance Evaluation
.261
5.7
Batch Training by Exact Incremental Training
.262
5.7.1
KKT Conditions
.263
5.7.2
Training by Solving a Set of Linear Equations
.264
5.7.3
Performance Evaluation
.272
5.8
Active Set Training in Primal and Dual
.273
5.8.1
Training Support Vector Machines in the Primal
.273
5.8.2
Comparison of Training Support Vector Machines in
the Primal and the Dual
.276
5.8.3
Performance Evaluation
.279
5.9
Training of Linear Programming Support Vector Machines
. 281
5.9.1
Decomposition Techniques
.282
5.9.2
Decomposition Techniques for Linear Programming
Support Vector Machines
.289
5.9.3
Computer Experiments
.297
References
.299
Kernel-Based Methods
.305
6.1
Kernel Least Squares
.305
6.1.1
Algorithm
.305
6.1.2
Performance Evaluation
.308
6.2
Kernel Principal Component Analysis
.311
6.3
Kernel Mahalanobis Distance
.314
6.3.1
SVD-Based Kernel Mahalanobis Distance
.315
6.3.2
KPCA-Based Mahalanobis Distance
.318
6.4
Principal Component Analysis in the Empirical
Feature Space
.319
6.5
Kernel Discriminant Analysis
.320
6.5.1
Kernel Discriminant Analysis for Two-Class Problems
. 321
6.5.2
Linear Discriminant Analysis for Two-Class Problems
in the Empirical Feature Space
.324
6.5.3
Kernel Discriminant Analysis for Multiclass Problems
. 325
References
.327
Contents xvii
7 Feature
Selection and Extraction
.331
7.1
Selecting an Initial Set of Features
.331
7.2
Procedure for Feature Selection
.332
7.3
Feature Selection Using Support Vector Machines
.333
7.3.1
Backward or Forward Feature Selection
.333
7.3.2
Support Vector Machine-Based Feature Selection
.336
7.3.3
Feature Selection by Cross-Validation
.337
7.4
Feature Extraction
.339
References
.340
8
Clustering
.343
8.1
Domain Description
.343
8.2
Extension to Clustering
.349
References
.351
9
Maximum-Margin Multilayer Neural Networks
.353
9.1
Approach
.353
9.2
Three-Layer Neural Networks
.354
9.3
CARVE Algorithm
.357
9.4
Determination of Hidden-Layer
Hyperplanes.358
9.4.1
Rotation of
Hyperplanes .359
9.4.2
Training Algorithm
.362
9.5
Determination of Output-Layer
Hyperplanes.363
9.6
Determination of Parameter Values
.363
9.7
Performance Evaluation
.364
References
.365
10
Maximum-Margin Fuzzy Classifiers
.367
10.1
Kernel Fuzzy Classifiers with Ellipsoidal Regions
.368
10.1.1
Conventional Fuzzy Classifiers with
Ellipsoidal Regions
.368
10.1.2
Extension to a Feature Space
.369
10.1.3
Transductive Training
.370
10.1.4
Maximizing Margins
.375
10.1.5
Performance Evaluation
.378
10.2
Fuzzy Classifiers with Polyhedral Regions
.382
10.2.1
Training Methods
.383
10.2.2
Performance Evaluation
.391
References
.393
11
Function Approximation
.395
11.1
Optimal
Hyperplanes.395
11.2
LI Soft-Margin Support Vector Regressors
.399
11.3
L2 Soft-Margin Support Vector Regressors
.401
11.4
Model Selection
.403
11.5
Training Methods
.403
xviii Contents
11.5.1
Overview
.403
11.5.2
Newton's Methods
.405
11.5.3
Active Set Training
.422
11.6
Variants of Support Vector Regressors
.429
11.6.1
Linear Programming Support Vector Regressors
.430
11.6.2
zz-Support Vector Regressors
.431
11.6.3
Least-Squares Support Vector Regressors
.432
11.7
Variable Selection
.435
11.7.1
Overview
.435
11.7.2
Variable Selection by Block Deletion
.436
11.7.3
Performance Evaluation
.437
References
.438
A Conventional Classifiers
.443
A.I Bayesian Classifiers
.443
A.2 Nearest-Neighbor Classifiers
.444
References
.445
В
Matrices
.447
B.I Matrix Properties
.447
B.2 Least-Squares Methods and Singular Value Decomposition
. 449
B.3 Covariance Matrices
.452
References
.454
С
Quadratic Programming
.455
C.I Optimality Conditions
.455
C.2 Properties of Solutions
.456
D
Positive
Semidefinite
Kernels and Reproducing Kernel
Hilbert Space
.459
D.I Positive
Semidefinite
Kernels
.459
D.2 Reproducing Kernel Hilbert Space
.463
References
.465
Index
.467 |
| any_adam_object | 1 |
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| author_GND | (DE-588)122089545 |
| author_facet | Abe, Shigeo 1947- |
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| indexdate | 2024-07-20T10:34:48Z |
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| isbn | 9781849960977 |
| language | English |
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| owner_facet | DE-11 DE-355 DE-BY-UBR |
| physical | XIX, 471 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Advances in Pattern Recognition |
| spelling | Abe, Shigeo 1947- Verfasser (DE-588)122089545 aut Support vector machines for pattern classification Shigeo Abe 2nd. ed. London Springer 2010 XIX, 471 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advances in Pattern Recognition Mustererkennung (DE-588)4040936-3 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf Mustererkennung (DE-588)4040936-3 s Maschinelles Lernen (DE-588)4193754-5 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3374918&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abe, Shigeo 1947- Support vector machines for pattern classification Mustererkennung (DE-588)4040936-3 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| subject_GND | (DE-588)4040936-3 (DE-588)4193754-5 |
| title | Support vector machines for pattern classification |
| title_auth | Support vector machines for pattern classification |
| title_exact_search | Support vector machines for pattern classification |
| title_full | Support vector machines for pattern classification Shigeo Abe |
| title_fullStr | Support vector machines for pattern classification Shigeo Abe |
| title_full_unstemmed | Support vector machines for pattern classification Shigeo Abe |
| title_short | Support vector machines for pattern classification |
| title_sort | support vector machines for pattern classification |
| topic | Mustererkennung (DE-588)4040936-3 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | Mustererkennung Maschinelles Lernen |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3374918&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195543&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT abeshigeo supportvectormachinesforpatternclassification |