Chapter 1 Introduction Support vector machines and their variants and extensions, often called kernel-based methods(or simply kernel methods), have been studied exten- sively and applied to various pattern classification and function approxima- tion problems. Pattern classification is to classify some object into one of the given categories called classes. For a specific pattern classification problem fier, which is computer software, is developed so that objects are clas- correctly with reasonably good accuracy. Inputs to the classifier are called features, because they are determined so that they represent each class well or so that data belonging to different classes are well separated in the In general there are two approaches to develop classifiers: a parametric approach [ 1, in which a priori knowledge of data distributions is assumed and a nonparametric approach, in which no a priori knowledge is assumed Neural networks 2-4, fuzzy systems 5-7, and support vector machines 8, 9 are typical nonparametric classifiers. Through training using input output pairs, classifiers acquire decision functions that classify an input int one of the given classes In this chapter we first classify decision functions for a two-class prob- lem into direct and indirect decision functions. The class boundary given by a direct decision function corresponds to the curve where the function vanishes, while the class boundary given by two indirect decision functions responds to the curve where the two functions give the same values. Then we discuss how to define and determine the direct decision functions for mul- ticlass problems and list up benchmark data sets used in the book. Finally we discuss some measures to evaluate performance of classifiers and function approximators for a given data set Advances in Pattern Recognition, DOI 10.1007 /978-1-84996-098-41 C Springer-Verlag London Limited 2010Chapter 1 Introduction Support vector machines and their variants and extensions, often called kernel-based methods (or simply kernel methods), have been studied exten￾sively and applied to various pattern classification and function approxima￾tion problems. Pattern classification is to classify some object into one of the given categories called classes. For a specific pattern classification problem, a classifier, which is computer software, is developed so that objects are clas￾sified correctly with reasonably good accuracy. Inputs to the classifier are called features, because they are determined so that they represent each class well or so that data belonging to different classes are well separated in the input space. In general there are two approaches to develop classifiers: a parametric approach [1], in which a priori knowledge of data distributions is assumed, and a nonparametric approach, in which no a priori knowledge is assumed. Neural networks [2–4], fuzzy systems [5–7], and support vector machines [8, 9] are typical nonparametric classifiers. Through training using input– output pairs, classifiers acquire decision functions that classify an input into one of the given classes. In this chapter we first classify decision functions for a two-class prob￾lem into direct and indirect decision functions. The class boundary given by a direct decision function corresponds to the curve where the function vanishes, while the class boundary given by two indirect decision functions corresponds to the curve where the two functions give the same values. Then we discuss how to define and determine the direct decision functions for mul￾ticlass problems and list up benchmark data sets used in the book. Finally we discuss some measures to evaluate performance of classifiers and function approximators for a given data set. S. Abe, Support Vector Machines for Pattern Classification, 1 Advances in Pattern Recognition, DOI 10.1007/978-1-84996-098-4_1, c Springer-Verlag London Limited 2010