Statistical and Machine Learning Approaches for Network Analysis

11.5 Support Vector Machines and Kernels

A support vector machine [16] is a supervised machine learning method that distributes instances into two classes (extensions with more than two classes are also available). Using a set of training examples, a hyperplane is calculated that separates data of the two different classes from each other and maximizes the margin of the hyperplane. This margin is defined by the instances that are located closest to the hyperplane. Usually, a complete separation is not possible. Therefore, vectors on the wrong side of the hyperplane are allowed but penalized. The support vector optimization problem is given by [22]

(11.1)

with the constraints

(11.2)

where , vector, orthographic to the hyperplane; , parameter; , feature vectors; y_i { − 1, + 1}, class labels; ., ., the scalar product; ξ_i, slack variables; , a positive constant.

This optimization problem stated ...