A statistical analysis of Fukunaga-Koontz transform

The Fukunaga-Koontz transform (FKT) has been proposed as a feature selection methodology for nearly 32 years. There are a huge number of citations. We have not seen a direct analysis between FKT, and a well established statistical method: Fisher quadratic discriminant analysis (QDA). In this letter, under certain assumptions, we establish such a connection. We speculate that a link in a more general situation is hard to find.