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E-raamat: Gentle Introduction To Support Vector Machines In Biomedicine, A - Volume 1: Theory And Methods

(Clopinet, Usa), (New York Univ, Usa), (New York Univ, Usa), (Vanderbilt Univ, Usa)
  • Formaat: 200 pages
  • Ilmumisaeg: 22-Feb-2011
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789813107991
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Gentle Introduction To Support Vector Machines In Biomedicine, A - Volume 1: Theory And MethodsSuurem pilt
  • Formaat: 200 pages
  • Ilmumisaeg: 22-Feb-2011
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789813107991
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Support Vector Machines (SVMs) are among the most important recent developments in pattern recognition and statistical machine learning. They have found a great range of applications in various fields including biology and medicine. However, biomedical researchers often experience difficulties grasping both the theory and applications of these important methods because of lack of technical background. The purpose of this book is to introduce SVMs and their extensions and allow biomedical researchers to understand and apply them in real-life research in a very easy manner. The book is to consist of two volumes: theory and methods (Volume 1) and cases studies (Volume 2).The proposed book follows the approach of “programmed learning” whereby material is presented in short sections called “frames”. Each frame consists of a very small amount of information to be learned, a multiple choice quiz, and answers to the quiz. The reader can proceed to the next frame only after verifying the correct answers to the current frame.
Preface ix
About the Authors xiii
1 Introduction
1(18)
Classes of Data-Analytic Problems Considered in This Book
1(5)
Basic Principles of Classification
6(6)
Main Ideas of the Support Vector Machine (SVM) Classification Algorithm
12(4)
History of SVMs and Their Use in the Literature
16(3)
2 Necessary Mathematical Concepts
19(21)
Geometrical Representation of Objects
19(5)
Basic Operations on Vectors
24(5)
Hyperplanes as Decision Surfaces
29(5)
Basics of Optimization
34(6)
3 Support Vector Machines (SVMs) for Binary Classification: Classical Formulation
40(24)
Hard-Margin Linear SVM for Linearly Separable Data
40(9)
Soft-Margin Linear SVM for Data That is not Exactly Linearly Separable Due to Noise or Outliers
49(8)
Non-Linear SVM and Kernel Trick For Linearly Non-Separable Data
57(7)
4 Basic Principles of Statistical Machine Learning
64(9)
Generalization and Overfitting
64(4)
"Loss + Penalty" Paradigm for Learning to Avoid Overfitting and Ensure Generalization
68(5)
5 Model Selection for SVMs
73(18)
Motivation of Model Selection Strategy
74(5)
Commonly Used Parameters/Kernels of SVM Classifiers
79(2)
Cross-Validation for Accuracy Estimation
81(4)
Cross-Validation for Accuracy Estimation and Model Selection
85(5)
Statistical Considerations
90(1)
6 SVMs for Multi-Category Classification
91(6)
One-Versus-Rest SVMs
91(3)
One-Versus-One SVMs
94(2)
Methods by Crammer and Singer and by Weston and Watkins
96(1)
7 Support Vector Regression (SVR)
97(22)
Hard-Margin Linear ε-Insensitive SVR for Modeling Linear Relations
97(9)
Soft-Margin Linear ε-Insensitive SVR for Modeling Almost Linear Relations
106(5)
Non-Linear ε-Insensitive SVR for Modeling Non-Linear Relations
111(2)
Comparing ε-Insensitive SVR with Other Popular Regression Methods
113(5)
On Model Selection for ε-Insensitive SVR
118(1)
8 Novelty Detection with SVM-Based Methods
119(17)
Hard-Margin Linear One-Class SVM
123(2)
Soft-Margin Linear One-Class SVM
125(4)
Non-Linear One-Class SVM
129(6)
On Model Selection for One-Class SVM
135(1)
9 Support Vector Clustering
136(18)
Nikita I. Lytkin
The Minimal Enclosing Hyper-Sphere
140(4)
Cluster Assignment in SVC
144(4)
Dealing with Noise in the Data
148(5)
Relationship Between the Minimal Enclosing Hyper-Sphere and One-Class SVM
153(1)
10 SVM-Based Variable Selection
154(14)
Understanding the SVM Weight Vector
156(5)
Simple SVM-Based Variable Selection Algorithm
161(3)
SVM-RFE Variable Selection Algorithm
164(2)
Variable Selection and Estimation of Generalization Accuracy
166(2)
11 Computing Posterior Class Probabilities for SVM Classifiers
168(6)
Simple Binning Method for Posterior Probability Estimation
168(3)
Platt's Method for Posterior Probability Estimation
171(3)
12 Conclusions
174(2)
Appendix 176(2)
Bibliography 178(3)
Index 181
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