Nonlinear partial least squares regressions for spectral quantitative analysis

Abstract

As a traditional linear regression model, the partial least squares (PLS) could not handle the nonlinearities in spectral quantitative analysis. This paper focuses on four types of nonlinear partial least square (NPLS) models: the internal NPLS model, the external NPLS model, the nonlinear components extracted NPLS model and the kernel NPLS model. The internal NPLS model adopts the neural network as the nonlinear function to describe the inner relation. For the external NPLS model, the PLS regression is performed on the extended input matrix which contains the nonlinear terms of the independent variables. The nonlinear components extracted NPLS model extracts the nonlinear principal components by selecting the weight vectors with PLS, and then the nonlinear relationship between the nonlinear principal components and the dependent variables is established. For the kernel NPLS model, the original input is transformed into a high-dimensional space by the nonlinear kernel functions and the PLS regression model is built in the new feature space. The 10-fold root–mean–squares error of cross validation is the criterion to decide the optimal parameters of these models. The performance of the different regressions is demonstrated by three real spectral datasets: the meat dataset, the flue gas dataset of gas-fired plant and the flue gas dataset of coal-fired plant. The results suggest that the internal NPLS model with the radial basis function neural network, the external NPLS model with the radial basis function neural network and the kernel NPLS model with polynomial kernel function have a higher predictive ability for spectral quantitative analysis in most cases.