A Gentle Introduction to Support Vector Machines in Biomedicine

The following sections are included:

• Contents

• Preface

• About the Authors

The following sections are included:

• Classes of Data-Analytic Problems Considered in This Book

• Basic Principles of Classification

• Main Ideas of the Support Vector Machine (SVM) Classification Algorithm

• History of SVMs and Their Use in the Literature

The following sections are included:

• Geometrical Representation of Objects

• Basic Operations on Vectors

• Hyperplanes as Decision Surfaces

• Basics of optimization

The following sections are included:

• Hard-Margin Linear SVM for Linearly Separable Data

• Soft-Margin Linear SVM for Data That is not Exactly Linearly Separable Due to Noise or Outliers

• Non-Linear SVM and Kernel Trick For Linearly Non-Separable Data

The following sections are included:

• Generalization and Overfitting

• “Loss + Penalty” Paradigm for Learning to Avoid Overfitting and Ensure Generalization

The following sections are included:

• Motivation of Model Selection Strategy

• Commonly Used Parameters/Kernels of SVM Classifiers

• Cross-Validation for Accuracy Estimation

• Cross-Validation for Accuracy Estimation and Model Selection

• Statistical Considerations

The following sections are included:

• One-Versus-Rest SVMs

• One-Versus-One SVMs

• Methods by Crammer and Singer and by Weston and Watkins

The following sections are included:

• Hard-Margin Linear ε-Insensitive SVR for Modeling Linear Relations

• Soft-Margin Linear ε-Insensitive SVR for Modeling Almost Linear Relations

• Non-Linear ε-Insensitive SVR for Modeling Non-Linear Relations

• Comparing ε-Insensitive SVR with Other Popular Regression Methods

• On Model Selection for ε-Insensitive SVR

The following sections are included:

• Hard-Margin Linear One-Class SVM

• Soft-Margin Linear One-Class SVM

• Non-Linear One-Class SVM

• On Model Selection for One-Class SVM

The following sections are included:

• The Minimal Enclosing Hyper-Sphere

• Cluster Assignment in SVC

• Dealing with Noise in the Data

• Relationship Between the Minimal Enclosing Hyper-Sphere and One-Class SVM

The following sections are included:

• Understanding the SVM Weight Vector

• Simple SVM-Based Variable Selection Algorithm

• SVM-RFE Variable Selection Algorithm

• Variable Selection and Estimation of Generalization Accuracy

The following sections are included:

• Simple Binning Method for Posterior Probability Estimation

• Platt's Method for Posterior Probability Estimation

So far we have covered how all major types of SVMs and related methods work. In the course of our exposition several important properties of SVMs became evident. We summarize these properties here…

The following sections are included:

• APPENDIX
  • Online Demonstrations
  • Software Implementations

• Bibliography
  • Additional Reading for Selected Chapters
  • List of References

• Index