Taking advantage of the linear properties in high dimensional spaces, a general kind of kernel machines is formulated under a unified framework. These methods include KPCA, KFD and SVM. The theoretical framework will show a strong connection between KFD and SVM. The main practical result under the proposed framework is the solution of KFD for an arbitrary number of classes. The framework allows also the formulation of multiclass-SVM. The main goal of this article is focused in finding new solutions and not in the optimization of them.