## A Gentle Introduction to Support Vector Machines in Biomedicine: 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 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. |

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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 border-line objects Chapter classiﬁcation accuracy cluster boundary Consider constraints cross-validation data points denotes dot product dual e-insensitive SVR example feature space ﬁgure ﬁnd ﬁr gene expression Gene X Figure GeneX GeneY Given objects e.g. hold-out cross-validation hyperplane independent variables kernel trick L2 norm linear decision surface linear function linear one-class SVM linear SVM formulation linearly separable Loss function machine learning minimal enclosing hyper-sphere model selection Negative objects y=-1 non-linear SVM number of objects optimization problem outliers overﬁtting patients/samples penalty points or vectors Positive objects y=+1 predict response variable samples shown in Figure slack variables soft-margin linear SVM soft-margin SVM Speciﬁcally Statnikov subset of variables support vector machines support vector regression SVM classiﬁer SVM output SVM weights SVM-based T-cell testing set train an SVM training data training set validation data validation set values Vapnik variable selection weight vector