On the equivalence of Kernel Fisher discriminant analysis and Kernel Quadratic Programming Feature Selection

We reformulate the Quadratic Programming Feature Selection (QPFS) method in a Kernel space to obtain a vector which maximizes the quadratic objective function of QPFS. We demonstrate that the vector obtained by Kernel Quadratic Programming Feature Selection is equivalent to the Kernel Fisher vector and, therefore, a new interpretation of the Kernel Fisher discriminant analysis is given which provides some computational advantages for highly unbalanced datasets.

► Kernelization of the quadratic programming feature selection (QPFS) algorithm.
► Proof of the equivalence with Kernel Fisher discriminant (KFD).
► New solution and interpretation of the KFD direction.
► More efficient computation of KFD vector when the classes are highly unbalanced.