## A Gentle Introduction to Support Vector Machines in Biomedicine: Volume 1: Theory and MethodsSupport 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 case studies (Volume 2). |

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### Contents

1 Introduction | 1 |

2 Necessary Mathematical Concepts | 19 |

Classical Formulation | 40 |

4 Basic Principles of Statistical Machine Learning | 64 |

5 Model Selection for SVMs | 73 |

6 SVMs for MultiCategory Classification | 91 |

7 Support Vector Regression SVR | 97 |

8 Novelty Detection with SVMBased Methods | 119 |

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### Common terms and phrases

accuracy estimates algorithm Aliferis Answer apply B-cell border-line objects Chapter classes of objects classification accuracy cluster boundary Consider constraints data points denotes dot product example feature space formulation Given objects gene expression Gene X Figure Gene X Gene Given objects e.g. hold-out cross-validation hyperplane input space kernel trick L2 norm linear function linear one-class SVM linear SVM formulation LOSS function machine learning microarray minimal enclosing hyper-sphere model selection Negative objects y=-1 non-linear one-class SVMs non-linear SVM number of objects number of variables one-class SVM formulation optimization problem Overfitting patients/samples points or vectors Positive objects y=+1 posterior probabilities primal hard-margin response variable samples shown in Figure slack variables soft-margin linear SVM soft-margin SVM subset of variables support vector machines support vector regression SVM classifier SVM output SVM weights SVM-based SVM-RFE testing set train an SVM training data training set validation data validation set values Vapnik variable selection