## Support Vector Machines for Pattern ClassificationI was shocked to see a student’s report on performance comparisons between support vector machines (SVMs) and fuzzy classi?ers that we had developed withourbestendeavors.Classi?cationperformanceofourfuzzyclassi?erswas comparable, but in most cases inferior, to that of support vector machines. This tendency was especially evident when the numbers of class data were small. I shifted my research e?orts from developing fuzzy classi?ers with high generalization ability to developing support vector machine–based classi?ers. This book focuses on the application of support vector machines to p- tern classi?cation. Speci?cally, we discuss the properties of support vector machines that are useful for pattern classi?cation applications, several m- ticlass models, and variants of support vector machines. To clarify their - plicability to real-world problems, we compare performance of most models discussed in the book using real-world benchmark data. Readers interested in the theoretical aspect of support vector machines should refer to books such as [109, 215, 256, 257]. |

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### Contents

3 | |

TwoClass Support Vector Machines 15 | 14 |

Multiclass Support Vector Machines | 83 |

4 | 129 |

Training Methods | 155 |

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### Common terms and phrases

ability algorithm all-at-once Artificial Neural Networks belonging to class bias term blood cell data calculate class boundary classifier with ellipsoidal cluster convex hull cross-validation datum DDAG decision functions delete Di(x discuss dual problem ECOC exact KKT conditions feature space fuzzy classifier fuzzy support vector given Hessian matrix Hiragana-50 hyperplane hypersphere input space input variables KPCA L1 and L2 L2 support vector L2 SVM least squares linear kernels m-dimensional Mahalanobis distance Maximize maximum membership functions multiclass NRMSE number of support number of training objective function obtain one-against-all support vector optimal hyperplane optimal solution orthogonal outliers output performance polynomial kernels positive semidefinite quadratic programming RBF kernels recognition rates satisﬁed satisfy set of support shown in Fig singular value decomposition slack variables solve support vector machines support vector regressor Table test data Theorem thyroid data training data training data set unbounded support vectors unclassifiable regions