Support vector and kernel methods

Kernel Methods (KM) are a relatively new family of algorithms that presents a series of useful features for pattern analysis in datasets. In recent years, their simplicity, versatility and efficiency have made them a standard tool for practitioners, and a fundamental topic in many data analysis courses. We will outline some of their important features in this Chapter, referring the interested reader to more detailed articles and books for a deeper discussion (see for example [135] and references therein). KMs combine the simplicity and computational efficiency of linear algorithms, such as the perceptron algorithm or ridge regression, with the flexibility of non-linear systems, such as for example neural networks, and the rigour of statistical approaches such as regularization methods in multivariate statistics. As a result of the special way they represent functions, these algorithms typically reduce the learning step to a convex …