Learning with kernels: support vector machines, regularization, optimization, and beyond
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge, Mass. [u.a.]
MIT Press
2002
|
| Schriftenreihe: | Adaptive computation and machine learning
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009886274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XVIII, 626 S. Ill., graph. Darst. |
| ISBN: | 0262194759 9780262194754 9780262536578 |
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| 245 | 1 | 0 | |a Learning with kernels |b support vector machines, regularization, optimization, and beyond |c Bernhard Schölkopf ; Alexander J. Smola |
| 264 | 1 | |a Cambridge, Mass. [u.a.] |b MIT Press |c 2002 | |
| 300 | |a XVIII, 626 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Adaptive computation and machine learning | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Algorithme |2 rasuqam | |
| 650 | 4 | |a Algorithmes | |
| 650 | 4 | |a Algoritmalar | |
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| 650 | 4 | |a Apprentissage automatique | |
| 650 | 7 | |a Apprentissage automatique |2 rasuqam | |
| 650 | 7 | |a Aprendizado computacional |2 larpcal | |
| 650 | 4 | |a Kernel fonksiyonları | |
| 650 | 7 | |a Machine à vecteurs de support |2 rasuqam | |
| 650 | 7 | |a Machine-learning |2 gtt | |
| 650 | 4 | |a Makine öğrenme | |
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| 650 | 4 | |a Noyaux (Mathématiques) | |
| 650 | 7 | |a Otimização matemática |2 larpcal | |
| 650 | 7 | |a Vectorcomputers |2 gtt | |
| 650 | 4 | |a Kernel functions | |
| 650 | 4 | |a Support vector machines | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009886274 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001 08.2002 B 12 0048 DAT 708f 2001 B 1739 0102 DAT 708 2001 B 1739 0102 DAT 708f 2001 B 1739 0104 DAT 708 2001 B 1739 |
|---|---|
| DE-BY-TUM_katkey | 1312536 |
| DE-BY-TUM_location | Mag LSB 01 |
| DE-BY-TUM_media_number | 040004455221 040071403026 040010192908 040010192975 040020115382 040010085500 |
| _version_ | 1821932640049037312 |
| adam_text | Contents
Series
Foreword
xiii
Preface
xv
1
A Tutorial Introduction
1
1.1
Data Representation and Similarity
................... 1
1.2
A Simple Pattern Recognition Algorithm
............... 4
1.3
Some Insights From Statistical Learning Theory
........... 6
1.4 Hyperplane
Classifiers
.......................... 11
1.5
Support Vector Classification
...................... 15
1.6
Support Vector Regression
........................ 17
1.7
Kernel Principal Component Analysis
................. 19
1.8
Empirical Results and Implementations
................ 21
1 CONCEPTS AND TOOLS
23
2
Kernels
25
2.1
Product Features
............................. 26
2.2
The Representation of Similarities in Linear Spaces
.......... 29
2.3
Examples and Properties of Kernels
.................. 45
2.4
The Representation of Dissimilarities in Linear Spaces
........ 48
2.5
Summary
.................................. 55
2.6
Problems
.................................. 55
3
Risk and Loss Functions
61
3.1
Loss Functions
............................... 62
3.2
Test Error and Expected Risk
...................... 65
3.3
A Statistical Perspective
......................... 68
3.4
Robust Estimators
............................. 75
3.5
Summary
.................................. 83
3.6
Problems
.................................. 84
4
Regularization
87
4.1
The Regularized Risk Functional
.................... 88
viii Contents
4.2
The
Représenter
Theorem
........................ 89
4.3
Regularization Operators
........................ 92
4.4
Translation Invariant Kernels
...................... 96
4.5
Translation Invariant Kernels in Higher Dimensions
......... 105
4.6
Dot Product Kernels
........................... 110
4.7
Multi-Output Regularization
...................... 113
4.8
Semiparametric Regularization
..................... 115
4.9
Coefficient Based Regularization
.................... 118
4.10
Summary
.................................. 121
4.11
Problems
.................................. 122
Elements of Statistical Learning Theory
125
5.1
Introduction
................................ 125
5.2
The Law of Large Numbers
....................... 128
5.3
When Does Learning Work: the Question of Consistency
...... 131
5.4
Uniform Convergence and Consistency
................ 131
5.5
How to Derive a VC Bound
....................... 134
5.6
A Model Selection Example
....................... 144
5.7
Summary
.................................. 146
5.8
Problems
.................................. 146
Optimization
149
6.1
Convex Optimization
........................... 150
6.2
Unconstrained Problems
......................... 154
6.3
Constrained Problems
.......................... 165
6.4
Interior Point Methods
.......................... 175
6.5
Maximum Search Problems
....................... 179
6.6
Summary
.................................. 183
6.7
Problems
.................................. 184
II SUPPORT VECTOR MACHINES
187
7
Pattern Recognition
189
7.1
Separating
Hyperplanes......................... 189
7.2
The Role of the Margin
.......................... 192
7.3
Optimal Margin
Hyperplanes...................... 196
7.4
Nonlinear Support Vector Classifiers
.................. 200
7.5
Soft Margin
Hyperplanes ........................ 204
7.6
Multi-Class Classification
........................ 211
7.7
Variations on a Theme
.......................... 214
7.8
Experiments
................................ 215
7.9
Summary
.................................. 222
7.10
Problems
.................................. 222
Contents ix
8
Single-Class
Problems: Quantile
Estimation and Novelty Detection
227
8.1
Introduction
................................ 228
8.2
A Distribution s Support and Quantiles
................ 229
8.3
Algorithms
................................. 230
8.4
Optimization
................................ 234
8.5
Theory
................................... 236
8.6
Discussion
................................. 241
8.7
Experiments
................................ 243
8.8
Summary
.................................. 247
8.9
Problems
.................................. 248
9
Regression Estimation
251
9.1
Linear Regression with Insensitive Loss Function
........... 251
9.2
Dual Problems
............................... 254
9.3
v-SV Regression
.............................. 260
9.4
Convex Combinations and i -Norms
.................. 266
9.5
Parametric Insensitivity Models
..................... 269
9.6
Applications
................................ 272
9.7
Summary
.................................. 273
9.8
Problems
.................................. 274
10
Implementation
279
10.1
Tricks of the Trade
............................. 281
10.2
Sparse Greedy Matrix Approximation
................. 288
10.3
Interior Point Algorithms
........................ 295
10.4
Subset Selection Methods
........................ 300
10.5
Sequential Minimal Optimization
.................... 305
10.6
Iterative Methods
............................. 312
10.7
Summary
.................................. 327
10.8
Problems
.................................. 329
11
Incorporating
Invariances
333
11.1
Prior Knowledge
............................. 333
11.2
Transformation
Invariance
........................ 335
11.3
The Virtual
SV
Method
.......................... 337
11.4
Constructing
Invariance
Kernels
.................... 343
11.5
The Jittered SV Method
.......................... 354
11.6
Summary
.................................. 356
11.7
Problems
.................................. 357
12
Learning Theory Revisited
359
12.1
Concentration of Measure Inequalities
................. 360
12.2
Leave-One-Out Estimates
........................ 366
12.3
PAC-Bayesian Bounds
.......................... 381
12.4
Operator-Theoretic Methods in Learning Theory
........... 391
Contents
12.5
Summary
.................................. 403
12.6 Problems.................................. 404
III
KERNEL
METHODS
405
13
Designing
Kernels 407
13.1
Tricks for Constructing Kernels
..................... 408
13.2
String Kernels
............................... 412
13.3
Locality-Improved Kernels
........................ 414
13.4
Natural Kernels
.............................. 418
13.5
Summary
.................................. 423
13.6
Problems
.................................. 423
14
Kernel Feature Extraction
427
14.1
Introduction
................................ 427
14.2
Kernel PCA
................................ 429
14.3
Kernel PCA Experiments
......................... 437
14.4
A Framework for Feature Extraction
.................. 442
14.5
Algorithms for Sparse KFA
....................... 447
14.6
KFA Experiments
............................. 450
14.7
Summary
.................................. 451
14.8
Problems
.................................. 452
15
Kernel Fisher Discriminant
457
15.1
Introduction
................................ 457
15.2
Fisher s Discriminant in Feature Space
................. 458
15.3
Efficient Training of Kernel Fisher Discriminants
........... 460
15.4
Probabilistic Outputs
........................... 464
15.5
Experiments
................................ 466
15.6
Summary
.................................. 467
15.7
Problems
.................................. 468
16
Bayesian Kernel Methods
469
16.1
Bayesics
.................................. 470
16.2
Inference Methods
............................ 475
16.3
Gaussian Processes
............................ 480
16.4
Implementation of Gaussian Processes
................. 488
16.5
Laplacian Processes
............................ 499
16.6
Relevance Vector Machines
....................... 506
16.7
Summary
.................................. 511
16.8
Problems
.................................. 513
17
Regularized Principal Manifolds
517
17.1
A Coding Framework
.......................... 518
Contents xi
17.2
A Regularized Quantization Functional
................ 522
17.3
An Algorithm for Minimizing Rreg[/]
................. 526
17.4
Connections to Other Algorithms
.................... 529
17.5
Uniform Convergence Bounds
..................... 533
17.6
Experiments
................................ 537
17.7
Summary
.................................. 539
17.8
Problems
.................................. 540
18
Pre-Images and Reduced Set Methods
543
18.1
The Pre-Image Problem
......................... 544
18.2
Finding Approximate Pre-Images
.................... 547
18.3
Reduced Set Methods
........................... 552
18.4
Reduced Set Selection Methods
..................... 554
18.5
Reduced Set Construction Methods
................... 561
18.6
Sequential Evaluation of Reduced Set Expansions
.......... 564
18.7
Summary
................................. 566
18.8
Problems
.................................. 567
A Addenda
569
A.I Data Sets
.................................. 569
A.2 Proofs
.................................... 572
В
Mathematical Prerequisites
575
B.I Probability
................................. 575
B.2 Linear Algebra
............................... 580
B.3 Functional Analysis
............................ 586
References
591
Index
617
Notation and Symbols
625
|
| any_adam_object | 1 |
| author | Schölkopf, Bernhard 1968- Smola, Alexander J. |
| author_GND | (DE-588)14184633X |
| author_facet | Schölkopf, Bernhard 1968- Smola, Alexander J. |
| author_role | aut aut |
| author_sort | Schölkopf, Bernhard 1968- |
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| building | Verbundindex |
| bvnumber | BV014515165 |
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| callnumber-sort | Q 3325.5 |
| callnumber-subject | Q - General Science |
| classification_rvk | ST 278 ST 300 ST 304 |
| classification_tum | DAT 708f |
| ctrlnum | (OCoLC)48970254 (DE-599)BVBBV014515165 |
| dewey-full | 006.31 006.3/1 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.31 006.3/1 |
| dewey-search | 006.31 006.3/1 |
| dewey-sort | 16.31 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV014515165 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:04:40Z |
| institution | BVB |
| isbn | 0262194759 9780262194754 9780262536578 |
| language | English |
| lccn | 2001095750 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009886274 |
| oclc_num | 48970254 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-20 DE-19 DE-BY-UBM DE-703 DE-91 DE-BY-TUM DE-706 DE-83 DE-473 DE-BY-UBG DE-11 DE-188 DE-863 DE-BY-FWS DE-739 DE-384 DE-634 DE-29T DE-898 DE-BY-UBR DE-M347 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-20 DE-19 DE-BY-UBM DE-703 DE-91 DE-BY-TUM DE-706 DE-83 DE-473 DE-BY-UBG DE-11 DE-188 DE-863 DE-BY-FWS DE-739 DE-384 DE-634 DE-29T DE-898 DE-BY-UBR DE-M347 |
| physical | XVIII, 626 S. Ill., graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | MIT Press |
| record_format | marc |
| series2 | Adaptive computation and machine learning |
| spellingShingle | Schölkopf, Bernhard 1968- Smola, Alexander J. Learning with kernels support vector machines, regularization, optimization, and beyond Algorithme rasuqam Algorithmes Algoritmalar Algoritmos larpcal Apprentissage automatique Apprentissage automatique rasuqam Aprendizado computacional larpcal Kernel fonksiyonları Machine à vecteurs de support rasuqam Machine-learning gtt Makine öğrenme Noyau (Mathématiques) rasuqam Noyaux (Mathématiques) Otimização matemática larpcal Vectorcomputers gtt Kernel functions Support vector machines Maschinelles Lernen (DE-588)4193754-5 gnd Support-Vektor-Maschine (DE-588)4505517-8 gnd Kernel Informatik (DE-588)4338679-9 gnd |
| subject_GND | (DE-588)4193754-5 (DE-588)4505517-8 (DE-588)4338679-9 |
| title | Learning with kernels support vector machines, regularization, optimization, and beyond |
| title_auth | Learning with kernels support vector machines, regularization, optimization, and beyond |
| title_exact_search | Learning with kernels support vector machines, regularization, optimization, and beyond |
| title_full | Learning with kernels support vector machines, regularization, optimization, and beyond Bernhard Schölkopf ; Alexander J. Smola |
| title_fullStr | Learning with kernels support vector machines, regularization, optimization, and beyond Bernhard Schölkopf ; Alexander J. Smola |
| title_full_unstemmed | Learning with kernels support vector machines, regularization, optimization, and beyond Bernhard Schölkopf ; Alexander J. Smola |
| title_short | Learning with kernels |
| title_sort | learning with kernels support vector machines regularization optimization and beyond |
| title_sub | support vector machines, regularization, optimization, and beyond |
| topic | Algorithme rasuqam Algorithmes Algoritmalar Algoritmos larpcal Apprentissage automatique Apprentissage automatique rasuqam Aprendizado computacional larpcal Kernel fonksiyonları Machine à vecteurs de support rasuqam Machine-learning gtt Makine öğrenme Noyau (Mathématiques) rasuqam Noyaux (Mathématiques) Otimização matemática larpcal Vectorcomputers gtt Kernel functions Support vector machines Maschinelles Lernen (DE-588)4193754-5 gnd Support-Vektor-Maschine (DE-588)4505517-8 gnd Kernel Informatik (DE-588)4338679-9 gnd |
| topic_facet | Algorithme Algorithmes Algoritmalar Algoritmos Apprentissage automatique Aprendizado computacional Kernel fonksiyonları Machine à vecteurs de support Machine-learning Makine öğrenme Noyau (Mathématiques) Noyaux (Mathématiques) Otimização matemática Vectorcomputers Kernel functions Support vector machines Maschinelles Lernen Support-Vektor-Maschine Kernel Informatik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009886274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT scholkopfbernhard learningwithkernelssupportvectormachinesregularizationoptimizationandbeyond AT smolaalexanderj learningwithkernelssupportvectormachinesregularizationoptimizationandbeyond |
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Teilbibliothek Mathematik & Informatik
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