Linear feedforward neural network classifiers and reduced-rank approximation

This paper discusses the relationship between linear feedforward neural network classifiers (FNNC) and the reduced-rank approximation. From the viewpoint of linear algebra, it is shown that if the rank of the trained connection weight matrix of a two layered linear FNNC is greater than or equal to the rank of the between-class dispersion matrix of the input training samples, the two layered linear FNNC will be merged into a one layered linear FNNC. In addition, the condition of the null error cost function for a reduced rank approximation is also derived.