In numerous classification problems, the number of available samples to be used in the classifier training phase is small, and each sample is a vector whose dimension is large. This regime, called high-dimensional/low sample size is particularly challenging when classification tasks have to be performed. To overcome this shortcoming, several dimension reduction methods were proposed. This work investigates a greedy optimisation method that builds a low dimensional classifier input. Some numerical examples are proposed to illustrate the performances of the method and compare it to other dimension reduction strategies.