Geometrical Aspects of Discrimination by Multilayer Perceptrons

We investigate some geometrical aspects of the discriminant functions of the kindf_p(x)=∑^p_k=1 c_kτ(a′_kx) for suitable constantsa_k, c_kwhereτis a sigmoidal transformation. This function is realized by a multilayer perceptron with one hidden layer. These results are applied in the analysis of the discriminating power off_p. In particular, we prove that the class of finite populationsΩ₁andΩ₂that can be distinguished byf_pis monotonically increasing inpand we give a minimal sufficientpleading to a complete separation betweenΩ₁andΩ₂.