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5.10 Support Vector Machines
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Case 1 Case 101 Case 201 Case 301 Case 401
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Figure 5.43. Prediction of foetal weight using an RBF4:4:1 network with
Gaussian kernel and k-means centroid adjustment (compare with Figure 5.40).
5.10 Support Vector Machines
Support vector machines (SVM) is a distinctive approach to pattern classification
and regression, since it tackles the principle of structural risk minimization,
described in section 5.6.5, in a special way. As a consequence, support vector
machines can provide a good generalization performance independent of the
distributions of the patterns.
The central idea of SVM is the adjustment of a discriminating function so that it
optimally uses the separability information of the boundary patterns. Let us first
assume a linear discriminating function and two linearly separable classes with
target values +1 and -1. A discriminating hyperplane will satisfy:
or (perceptron rule),
Taking into account the hyperplane properties mentioned in section 2.1, the
distance of any point x; to a hyperplane is precisely Iwlx,-twollllwII, as shown in
Figure 5.44. In particular, the distance to the origin is simply Iwol/llwII.
Given a hyperplane, the distance of the closest pattern to it is called the margin
of separation. The SVM approach, in its simplest linear version, consists of