## Advances in Kernel Methods: Support Vector LearningBernhard Schölkopf, Christopher J. C. Burges, Alexander J. Smola The Support Vector Machine is a powerful new learning algorithm for solving a variety of learning and function estimation problems, such as pattern recognition, regression estimation, and operator inversion. The impetus for this collection was a workshop on Support Vector Machines held at the 1997 NIPS conference. The contributors, both university researchers and engineers developing applications for the corporate world, form a Who's Who of this exciting new area. Contributors: Peter Bartlett, Kristin P. Bennett, Christopher J. C. Burges, Nello Cristianini, Alex Gammerman, Federico Girosi, Simon Haykin, Thorsten Joachims, Linda Kaufman, Jens Kohlmorgen, Ulrich Kressel, Davide Mattera, Klaus-Robert Muller, Manfred Opper, Edgar E. Osuna, John C. Platt, Gunnar Ratsch, Bernhard Scholkopf, John Shawe-Taylor, Alexander J. Smola, Mark O. Stitson, Vladimir Vapnik, Volodya Vovk, Grace Wahba, Chris Watkins, Jason Weston, Robert C. Williamson. |

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### Contents

Roadmap | 17 |

Three Remarks on the Support Vector Method of Function | 25 |

Generalization Performance of Support Vector Machines | 43 |

Bayesian Voting Schemes and Large Margin Classifiers | 55 |

Support Vector Machines Reproducing Kernel Hilbert Spaces | 69 |

Geometry and Invariance in Kernel Based Methods | 89 |

Entropy Numbers Operators and Support Vector Kernels | 127 |

Vector Classification | 147 |

Support Vector Machines for Dynamic Reconstruction of | 211 |

Using Support Vector Machines for Time Series Prediction | 243 |

Pairwise Classification and Support Vector Machines | 255 |

Reducing the Runtime Complexity in Support Vector Machines | 271 |

Support Vector Regression with ANOVA Decomposition Kernels | 285 |

Support Vector Density Estimation | 293 |

Combining Support Vector and Mathematical Programming | 307 |

Kernel Principal Component Analysis | 327 |

Making LargeScale Support Vector Machine Learning Practical | 169 |

Fast Training of Support Vector Machines Using Sequential | 185 |

### Common terms and phrases

algorithm ANOVA approach approximation approximation error benchmark bound chapter choice choose classifiers coefficients compute conjugate gradient consider constraints construct corresponding covering numbers CPU sec data set decision function decision tree decomposition defined density estimation dimensional distribution dot product e-insensitive eigenvalues eigenvectors entropy entropy numbers equation error fc(x feature space figure Gaussian given heuristic Hilbert space hyperplane input space invariant iteration kernel function kernel PCA Lagrange multipliers learning linear program loss function mapping margin matrix Mercer kernel method metric minimize multicategory nonlinear nonzero number of support obtained optimal hyperplane optimization problem parameters pattern recognition PCG chunking performance polynomial kernels principal components QP problem quadratic programming random reconstruction samples Scholkopf Smola solution solve sparse subset support vector machine SV machines SVM pairwise technique test set Theorem training data training examples training set Vapnik variables VC dimension Wahba zero

### Popular passages

Page 368 - Golowich, and A. Smola. Support Vector Method for Function Approximation, Regression Estimation and Signal Processing.

Page 360 - Application of the Karhunen-Loeve procedure for the characterization of human faces," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.

Page 354 - Proc. of the 4th Midwest Artificial Intelligence and Cognitive Science Society Conference, pages 97-101, 1992.

Page 355 - PS Bradley and OL Mangasarian. Feature selection via concave minimization and support vector machines. In J. Shavlik, editor, Machine Learning Proceedings of the Fifteenth International Conference(ICML '98), pages 82-90.