Nonlinear PLS Modeling Using Neural Networks

Abstract This paper discusses the embedding of neural networks into the framework of the PLS (partial least squares) modeling method resulting in a neural net PLS modeling approach. By using the universal approximation property of neural networks, the PLS modeling method is genealized to a nonlinear framework. The resulting model uses neural networks to capture the nonlinearity and keeps the PLS projection to attain robust generalization property. In this paper, the standard PLS modeling method is briefly reviewed. Then a neural net PLS (NNPLS) modeling approach is proposed which incorporates feedforward networks into the PLS modeling. A multi-input-multi-output nonlinear modeling task is decomposed into linear outer relations and simple nonlinear inner relations which are performed by a number of single-input-single-output networks. Since only a small size network is trained at one time, the over-parametrized problem of the direct neural network approach is circumvented even when the training data are very sparse. A conjugate gradient learning method is employed to train the network. It is shown that, by analysing the NNPLS algorithm, the global NNPLS model is equivalent to a multilayer feedforward network. Finally, applications of the proposed NNPLS method are presented with comparison to the standard linear PLS method and the direct neural network approach. The proposed neural net PLS method gives better prediction results than the PLS modeling method and the direct neural network approach.