On the relationship between the Support Vector Machine for classification and sparsified Fisher's Linear Discriminant

We show that the orientation and location of the separating hyperplane for 2-class supervised pattern classification obtained by the Support Vector Machine (SVM) proposed by Vapnik and his colleagues, is equivalent to the solution obtained by Fisher's Linear Discriminant on the set of Support Vectors. In other words, SVM can be seen as a way to `sparsify' Fisher's Linear Discriminant in order to obtain the most generalizing classification from the training set.