A Unified Approach to Support Vector Machines

Abstract

This chapter presents a unified introduction to support vector machine (SVM) methods for binary classification, one-class classification, and regression. The SVM method for binary classification (binary SVC) is introduced first, and then extended to encompass one-class classification (clustering). Next, using the regularized risk approach as a motivation, the SVM method for regression (SVR) is described. These methods are then combined to obtain a single unified SVM formulation that encompasses binary classification, one-class classification, and regression (as well as some extensions of these), and the dual formulation of this unified model is derived. A mechanical analogy for binary and one-class SVCs is given to give an intuitive explanation of the operation of these two formulations. Finally, the unified SVM is extended to implement general cost functions, and an application of SVM classifiers to the problem of spam e-mail detection is considered.