Factorial correspondence regression applied to multi-way spectral data

Abstract

The principal advantage of factorial correspondence analysis, where rows and columns are processed symmetrically, is the possibility of having in the same factorial space observation (row) and variable (column) projections. This joint plot allows one to find similarities that may exist between variables and observations in term of distances. When dealing with picture sequences, this joint plot is composed of pixel and picture projections. For a sequence of spectra, the joint plot is composed of projections of the wavelengths or frequencies and of the spectra. In the reported study, 2D data sets were formed by outer product between mid- and near-infrared spectroscopic data recorded on edible oil samples with different levels of unsaturation. The association of a regression technique with factorial correspondence analysis gives a convenient way to detect interactions between wavenumbers and wavelengths as a function of the level of unsaturation. This new technique is called factorial correspondence regression. The mathematical procedure is developed and the validation method, which is based on a cross-validation procedure to choose independent variables entering the regression equation, is reported. The results obtained from the proposed method are presented in the form of maps for a graphical interpretation that allows much easier assignments of near-infrared peaks to combinations of mid-infrared peaks.