Discriminating between classes from spectra deals with an ill-conditioned problem, which is generally solved by means of dimension reduction, using principal component analysis or partial least squares regression. In this paper, a new method is presented, which aims at finding a parcimonious set of discriminant vectors, without reducing the dimension of the space. It acts by scanning a restricted number of scalar functions, called Focal Eigen Functions. These functions are theoretically defined and some of their interesting properties are proven. Three scanning algorithms, based on these properties, are given as examples. An application to real spectroscopic data shows the efficiency of that new method, compared to the Partial Least Squares Discriminant Analysis.