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One of the more popular kernels\cite{Chang:2010:TTL:1756006.1859899} that can be used is the radial basis function (RBF) kernel, which is defined as:  $$K(\mathbf{x}, $K(\mathbf{x},  \mathbf{x'}) = \exp\left(-\frac{||\mathbf{x} - \mathbf{x'}||_2^2}{2\sigma^2}\right) $$ $  The value of the RBF value goes from zero (at infinity) to one (when $ x = x'$), so it can be viewed as a similarity measure. measure between the two samples.  \cite{Vert} Because sometimes there is noise in the data, so it may not be possible to separate the data linearly, not even in a high dimensional space or, even if possible, this may not be desirable, because it would overfit to the data and not generalize well. In such cases, it is prefered to have a decision surfaces that makes some mistakes on the training data, but generalizes better and represents the noisy data more accurately. SVMs can be used as soft margin classifiers, allowing examples to be classified wrongly at training time, but penalizing them according to their distance to the other side of the hyperplane. \cite{russell1995artificial}