A gentle introduction to support vector machines in biomedicine: 1 Theory and methods
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific Publ.
2011
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XV, 183 S. Ill., graph. Darst. |
| ISBN: | 9789814324380 9814324388 |
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MARC
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| 245 | 1 | 0 | |a A gentle introduction to support vector machines in biomedicine |n 1 |p Theory and methods |c Alexander Statnikov ... |
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Record in the Search Index
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| adam_text | Contents
Preface
........................................................................... ix
About the Authors
................................................................ xiii
1.
Introduction
.................................................................. 1
Classes of Data-Analytic Problems Considered in This Book
...................... 1
Basic Principles of Classification
................................................. 6
Main Ideas of the Support Vector Machine (SVM) Classification Algorithm
....... 12
History of SVMs and Their Use in the Literature
................................ 16
2.
Necessary Mathematical Concepts
............................................. 19
Geometrical Representation of Objects
.......................................... 19
Basic Operations on Vectors
..................................................... 24
Hyperplanes
as Decision Surfaces
................................................ 29
Basics of Optimization
.......................................................... 34
3.
Support Vector Machines (SVMs) for Binary Classification: Classical
Formulation
................................................................... 40
Hard-Margin Linear SVM for Linearly Separable Data
........................... 40
Soft-Margin Linear SVM for Data That is not Exactly Linearly Separable Due to
Noise or Outliers
............................................................ 49
Non-Linear SVM and Kernel Trick For Linearly Non-Separable Data
............. 57
4.
Basic Principles of Statistical Machine Learning
............................... 64
Generalization and Overfitting
.................................................. 64
Loss
+
Penalty Paradigm for Learning to Avoid Overfitting and Ensure
Generalization
............................................................... 68
vi A
Gentle Introduction to SVMs in
Biomedicine,
Volume
1:
Theory and Methods
5.
Model Selection for SVMs
.................................................... 73
Motivation of Model Selection Strategy
......................................... 74
Commonly Used Parameters/Kernels of SVM Classifiers
......................... 79
Cross-Validation for Accuracy Estimation
........................................ 81
Cross-Validation for Accuracy Estimation and Model Selection
................... 85
Statistical Considerations
........................................................ 90
6.
SVMs for
Multi-
Category Classification
....................................... 91
One-Versus-Rest SVMs
......................................................... 91
One-Versus-One SVMs
......................................................... 94
Methods by Crammer and Singer and by Weston and Watkins
.................... 96
7.
Support Vector Regression (SVR)
............................................. 97
Hard-Margin Linear
¿-Insensitive SVR
for Modeling Linear Relations
............ 97
Soft-Margin Linear e-Insensitive SVR for Modeling Almost Linear Relations
...... 106
Non-Linear
ε
-Insensitive SVR for Modeling Non-Linear Relations
................
Ill
Comparing «-Insensitive SVR with Other Popular Regression Methods
........... 113
On Model Selection for
е
-Insensitive SVR
....................................... 118
8.
Novelty Detection with SVM-Based Methods
................................. 119
Hard-Margin Linear One-Class SVM
............................................ 123
Soft-Margin Linear One-Class SVM
............................................. 125
Non-Linear One-Class SVM
.................................................... 129
On Model Selection for One-Class SVM
......................................... 135
9.
Support Vector Clustering (Contributed by Nikita I. Lytkin)
................. 136
The Minimal Enclosing Hyper-Sphere
........................................... 140
Cluster Assignment in SVC
..................................................... 144
Dealing with Noise in the Data
.................................................. 148
Relationship Between the Minimal Enclosing Hyper-Sphere and
One-Class SVM
............................................................. 153
10.
SVM-Based Variable Selection
............................................... 154
Understanding the SVM Weight Vector
........................................ 156
Simple SVM-Based Variable Selection Algorithm
............................... 161
Contents
vii
SVM-RFE Variable
Selection Algorithm
........................................ 164
Variable
Selection and Estimation of Generalization Accuracy
................... 166
11.
Computing Posterior Class Probabilities for SVM Classifiers
................ 168
Simple Binning Method for Posterior Probability Estimation
.................... 168
Platt s Method for Posterior Probability Estimation
............................. 171
12.
Conclusions
.................................................................. 174
Appendix
......................................................................... 176
Bibliography
..................................................................... 178
Index
............................................................................. 181
š
Support
Vector Machines (SVMs)
are among-î
fhe
[post
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in1!
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řnachineg:
IJeiarnirig.-Ťhey
häva
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ìn
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researchers
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ígrasping
both thV theory and
appiicaţionsîi
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;
(of^technical background. Th]e purpose
oí
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and
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і
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|
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| id | DE-604.BV040252486 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:20:02Z |
| institution | BVB |
| isbn | 9789814324380 9814324388 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025108425 |
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| physical | XV, 183 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | World Scientific Publ. |
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| spelling | A gentle introduction to support vector machines in biomedicine 1 Theory and methods Alexander Statnikov ... Singapore [u.a.] World Scientific Publ. 2011 XV, 183 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Support-Vektor-Maschine (DE-588)4505517-8 gnd rswk-swf Biomedizin (DE-588)4647152-2 gnd rswk-swf Support-Vektor-Maschine (DE-588)4505517-8 s Biomedizin (DE-588)4647152-2 s b DE-604 Statnikov, Alexander Sonstige oth (DE-604)BV040252468 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025108425&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025108425&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | A gentle introduction to support vector machines in biomedicine Support-Vektor-Maschine (DE-588)4505517-8 gnd Biomedizin (DE-588)4647152-2 gnd |
| subject_GND | (DE-588)4505517-8 (DE-588)4647152-2 |
| title | A gentle introduction to support vector machines in biomedicine |
| title_auth | A gentle introduction to support vector machines in biomedicine |
| title_exact_search | A gentle introduction to support vector machines in biomedicine |
| title_full | A gentle introduction to support vector machines in biomedicine 1 Theory and methods Alexander Statnikov ... |
| title_fullStr | A gentle introduction to support vector machines in biomedicine 1 Theory and methods Alexander Statnikov ... |
| title_full_unstemmed | A gentle introduction to support vector machines in biomedicine 1 Theory and methods Alexander Statnikov ... |
| title_short | A gentle introduction to support vector machines in biomedicine |
| title_sort | a gentle introduction to support vector machines in biomedicine theory and methods |
| topic | Support-Vektor-Maschine (DE-588)4505517-8 gnd Biomedizin (DE-588)4647152-2 gnd |
| topic_facet | Support-Vektor-Maschine Biomedizin |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025108425&sequence=000003&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=025108425&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040252468 |
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