Pattern Recognition, 4th Edition

3.7. Support Vector Machines

3.7.1. Separable Classes

In this section, an alternative rationale for designing linear classifiers will be adopted. We will start with the two-class linearly separable task, and then we will extend the method to more general cases where data are not separable.

Let xⁱ, i = 1, 2,…, N, be the feature vectors of the training set, X. These belong to either of two classes, ω¹, ω², which are assumed to be linearly separable. The goal, once more, is to design a hyperplane(3.71)that classifies correctly all the training vectors. As we have already discussed in Section 3.3, such a hyperplane is not unique. The perceptron ...