"circular" case, which corresponds to introducing only the sum of pure quadratic terms with no mixed products (), has been proven to be the optimal compromise between extending the classifier's representation power and controlling the risk of overfitting (Vapnik-Chervonenkis dimension). For linear classifiers based only on dot products, these expanded measurements do not have to be actually computed, since the dot product in the higher-dimensional space is simply related to that in the original space. This is an example of the so-called kernel trick, which can be applied to linear discriminant analysis as well as the support vector machine. References Sources: Classification algorithms Statistical classification