Support vector machines nonlinear classifiers

Support Vector Machines (SVMs) generate either linear or nonlinear classifiers depending on the so-called kernel [149]. The kernel is a matrix that performs a transformation of the data into an arbitrarily high-dimensional feature-space, where linear classification relates to nonlinear classifiers in the original space the input data lives in. SVMs are quite a recent Machine Learning method that received a lot of attention because of their superiority on a number of hard problems [150]. 

In Figure 39, we present the network structure of a support vector machine classifier. The input layer is represented by the support vectors xi,. .x and the test (prediction) pattern Xt, which are transformed by the feature function cj) and mapped into the feature space. The next layer performs the dot product between the test pattern (( (x ) and each support vector ( > xi). The dot product of feature functions is then multiplied with the Lagrangian multipliers, and the output is the nonlinear classifier from Eq. [53] in which the dot product of feature functions was substituted with a kernel function. 

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