## An Introduction to Support Vector Machines and Other Kernel-based Learning MethodsThis is the first comprehensive introduction to Support Vector Machines (SVMs), a new generation learning system based on recent advances in statistical learning theory. SVMs deliver state-of-the-art performance in real-world applications such as text categorisation, hand-written character recognition, image classification, biosequences analysis, etc., and are now established as one of the standard tools for machine learning and data mining. Students will find the book both stimulating and accessible, while practitioners will be guided smoothly through the material required for a good grasp of the theory and its applications. |

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### Contents

The Learning Methodology | 1 |

Linear Learning Machines | 9 |

KernelInduced Feature Spaces | 26 |

Generalisation Theory | 52 |

Optimisation Theory | 79 |

Support Vector Machines | 93 |

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### Common terms and phrases

1-norm soft margin algorithm analysis applications approach Bayesian bound Chapter choice classification computational consider constraints convergence convex corresponding datasets Definition described dual problem dual representation e-insensitive loss fat-shattering dimension feasibility gap feature mapping feature space finite Gaussian processes generalisation error geometric margin given Hence heuristics high dimensional Hilbert space hyperplane hypothesis inequality inner product space input space introduced iterative Karush-Kuhn-Tucker Karush-Kuhn-Tucker conditions kernel function kernel matrix Lagrange multipliers Lagrangian learning algorithm linear functions linear learning machines loss function machine learning margin distribution margin slack vector maximal margin hyperplane maximise minimise neural networks norm objective function obtained on-line optimal optimisation problem parameters perceptron perceptron algorithm performance positive semi-definite quantity real-valued function Remark result ridge regression Section sequence slack variables soft margin optimisation solution solve subset Support Vector Machines SVMs techniques Theorem training data training examples training points training set update Vapnik VC dimension weight vector zero