A Summary of Support Vector Machine

The Support Vector Machine(SVM) has achieved a lot of attention since it is developed. It is widely used in many areas because of its powerful ability of classification and regression, such as textual classification, face recognition, image processing, hand-written recognition and so forth. In this article I try to give a summary of SVM. Because of its plentiful contents, This article has to mainly focus on one aspect—Support Vector Classifier(SVC). All of the techniques mentioned here are realized in a new SVM software package—PKSVM. Presently PKSVM can handle two-class and multi-class classification problems using C-SVC and ν-SVC (omitted here). The earliest pattern recognition systems were Linear Classifiers(Nilsson,1965). We will point out the differences between SVC and LC in the following sections. Suppose n training data(sometimes called examples or observations) (xi, yi) are given, where xi ∈ Rp(p features or variables) and yi ∈ R. Without loss of generality, the whole article is limited to two-class problems, that is to say, yi’s only have two values, which can be +1 and −1 for simplicity.