Regression analysis of spectroscopic process data using a combined architecture of linear and nonlinear artificial neural networks

The authors demonstrate that a combined architecture of linear and nonlinear artificial neural networks offers many advantages over the conventional multilayer feedforward networks and the conventional biased regression methods for the modeling of spectroscopic process data. This direct linear feedthrough (DLF) network is an especially useful tool for modeling process data when the true linear or nonlinear functionality of the system is not known. By just looking at the linear and nonlinear contributions of this DLF network, it is possible to tell if the data are purely linear or nonlinear. For the learning algorithm, sequential quadratic programming improves the training time of the neural network by 2-3 orders of magnitude compared to that of the back-propagation method. The authors also suggest that when the number of data samples is small compared to the size of the network, the risk of under-representing or overfitting the available data can be avoided by using the leave-one-out cross validation technique