Nonlinear data analysis and multilayer perceptrons

The correspondence between multilayer perceptrons (MLPs) with linear processing elements and classical data analysis methods (principal component analysis, discriminant analysis) was shown by P. Galinari et al. (see Proc. IEEE ICNN-88, p.I-391-9, 1988). The authors extend their results to the nonlinear case and show that MLP with nonlinear elements approximates the nonlinear data analysis methods. The classical linear data analysis methods are first formulated and solved from the viewpoint of least mean squared error approximation. Nonlinear data analysis methods are then formulated and solved from the same viewpoint. The close relationship between the nonlinear MLP and backpropagation as well as the nonlinear data analysis methods are discussed, and some simulation results are given.<>