Hybridization of partial least squares and neural network models for quantifying lunar surface minerals

The goal of this study is to develop an efficient and accurate model for using visible–near infrared reflectance spectra to estimate the abundance of minerals on the lunar surface. Previous studies using partial least squares (PLS) and genetic algorithm–partial least squares (GA–PLS) models for this purpose revealed several drawbacks. PLS has two limitations: (1) redundant spectral bands cannot be removed effectively and (2) nonlinear spectral mixing (i.e., intimate mixtures) cannot be accommodated. Incorporating GA into the model is an effective way for selecting a set of spectral bands that are the most sensitive to variations in the presence/abundance of lunar minerals and to some extent overcomes the first limitation. Given the fact that GA–PLS is still subject to the effect of nonlinearity, here we develop and test a hybrid partial least squares–back propagation neural network (PLS–BPNN) model to determine the effectiveness of BPNN for overcoming the two limitations simultaneously. BPNN takes nonlinearity into account with sigmoid functions, and the weights of redundant spectral bands are significantly decreased through the back propagation learning process. PLS, GA–PLS and PLS–BPNN are tested with the Lunar Soil Characterization Consortium dataset (LSCC), which includes VIS–NIR reflectance spectra and mineralogy for various soil size fractions and the accuracy of the models are assessed based on R² and root mean square error values. The PLS–BPNN model is further tested with 12 additional Apollo soil samples. The results indicate that: (1) PLS–BPNN exhibits the best performance compared with PLS and GA–PLS for retrieving abundances of minerals that are dominant on the lunar surface; (2) PLS–BPNN can overcome the two limitations of PLS; (3) PLS–BPNN has the capability to accommodate spectral effects resulting from variations in particle size. By analyzing PLS beta coefficients, spectral bands selected by GA, and the loading curve of the latent variable with the largest weight in PLS–BPNN, we conclude that spectral information incorporated into the three models is directly derived from the diagnostic absorption bands associated with the individual minerals. It is concluded that the PLS–BPNN model should be applicable to both Clementine UV–VIS–NIRs and Moon Mineralogy Mapper (M³) data.