Support Vector Machines – An Introduction

Abstract

Abstract This is a book about learning from empirical data (i.e., examples, samples, measurements, records, patterns or observations) by applying support vector machines (SVMs) a.k.a. kernel machines. The basic aim of this introduction1 is to give, as far as possible, a condensed (but systematic) presentation of a novel learning paradigm embodied in SVMs. Our focus will be on the constructive learning algorithms for both the classification (pattern recognition) and regression (function approximation) problems. Consequently, we will not go into all the subtleties and details of the statistical learning theory (SLT) and structural risk minimization (SRM) which are theoretical foundations for the learning algorithms presented below. Instead, a quadratic programming based learning leading to parsimonious SVMs will be presented in a gentle way - starting with linear separable problems, through the classification tasks having overlapped classes but still a linear separation boundary, beyond the linearity assumptions to the nonlinear separation boundary, and finally to the linear and nonlinear regression problems. The adjective “parsimonious” denotes an SVM with a small number of support vectors. The scarcity of the model results from a sophisticated learning that matches the model capacity to the data complexity ensuring a good performance on the future, previously unseen, data.