Robust fitting by nonlinear neural units

Abstract A central problem in statistics is fitting a model which is linear in the parameters, to a set of observation points. Examples are regression, curve fitting, time series modeling, digital filtering, system theory, and automatic control. The usual approaches are least squares (LS) or total least squares (TLS) regression. In impulsive and colored noise environments, or in the presence of outliers, these methods are not optimal, however. Then robust fitting, based on a nonquadratic criterion, may give better results than the usual TLS. Neural network approaches to robust TLS regression are reviewed and a new learning algorithm is introduced, based on a robust TLS criterion involving a nonlinear function. The algorithm has the form of a nonlinear constrained anti-Hebbian learning rule. Instead of extracting the exact minor component, the algorithm extracts the robust minor component. Mathematical analysis of the algorithm and computer simulations are provided to illustrate that this neural fitting method outperforms the commonly used LS and TLS fitting methods in resisting both Gaussian noise and outliers.