Study on Least Trimmed Absolute Deviations Artificial Neural Network

Abstract

In this paper, the least trimmed sum of absolute deviations (LTA) estimator, frequently used in robust linear parametric regression problems, will be generalized to nonparametric least trimmed sum of absolute deviations-artificial neural network (LTA-ANN) for nonlinear regression problems. In linear parametric regression problems, the LTA estimator usually have good robustness against outliers and can theoretically tolerate up to 50% of outlying data. Moreover, a nonderivative hybrid method mixing the simplex method of Nelder and Mead (NM) and particle swarm optimization algorithm (PSO), abbreviated as SNM-PSO, will be provided in this study for the training of the parameters of LTA-ANN. Some numerical examples will be provided to compare the robustness against outliers for usual artificial neural network (ANN) and the proposed LTA-ANN. Simulation results show that the LTA-ANN proposed in this paper have good robustness against outliers.