Hyperspectral image classification by means of Deep Learning techniques is now a widespread practice. Its success comes from the abstract features learned by the deep architecture that are ultimately well separated in the feature space. The great amount of parameters to be learned requires the training data set to be very large, otherwise the risk of overfitting appears. Alternatively, one can resort to features selection in order to decrease the architecture's number of parameters to be learnt. For that purpose, this work proposes a simple feature selection method, based on single-layer neural networks, which select the most distinguishing features for each class. Then, the data will be classified by a deep neural network. The accuracy results for the testing data are higher for the lower dimensional data set when compared to the full data set, indicating less over-fitting for the reduced data. Besides, a metric based on scatter matrices shows that the classes are better separated in the reduced feature space.