Variable selection based on locally linear embedding mapping for near-infrared spectral analysis

• A method based on locally linear embedding is proposed for variable selection.
• A new criterion is developed for evaluation of variable importance.
• Several tens variables can be selected to build a parsimonious model.
• The method is applicable for different NIR datasets.

Locally linear embedding (LLE) is a nonlinear dimensionality reduction method that can preserve the relationship between samples in the mapping space. The neighbors in high dimensional space will keep their relative position in LLE space. A method based on the effect of the variables on the relative position of the samples in LLE space was proposed for variable selection in NIR spectral analysis. In the method, the spectra are mapped into LLE space with all variables at first, and then the mapping is repeated by removing a variable from the spectra. Therefore, the movement of the samples in LLE space caused by a variable can be used to evaluate the effect of the variable on the spectra. The variables that cause a large movement will be the important ones to affect the relationship of the spectra. For further selection of the informative variables specific to the target component, a forward stepwise selection is applied to the variables selected by LLE method. To validate the performance of the proposed method, it was applied to the partial least squares (PLS) modeling of three NIR spectral datasets of corn, pharmaceutical tablets and tobacco lamina samples. Results show that the proposed method can effectively select the informative variables from the NIR spectra, and build a parsimonious model by using several tens of selected variables.