Characterization of multi-way spectral data using Factorial Correspondence Regression

Abstract

The principal advantage in Factorial Correspondence Analysis, where rows and columns are processed symmetrically, is the possibility to have in the same factorial space observation (row) and variable (column) projections. For sequence of spectra, the joint plot is composed of projections of wavelengths and of spectra. In the reported study, the analyzed data set consisted in fluorescence emission spectra recorded on animal feed samples. Samples were composed of eight raw materials (4 cereals and 4 oilcakes) and 48 mixtures of one cereal and one oilcake. For each sample, several specific excitation wavelengths were used leading to a 3-dimensional or 3-way data set: one way for samples, one for emission wavelengths and one for excitation wavelengths. After reorganization of the data set, FCA was applied and the resulting joint plot allowed finding similarities between excitation-emission wavelength couples and samples. Furthermore, the association of the Partial Least- Squares regression (PLS) with the FCA method led to the selection of some wavelength couples characteristic of the eight raw materials. The mathematical procedure of this new regression technique, called Factorial Correspondence Partial Least Squares regression (FCR-PLS), is developed and the model validation, which is based on a cross-validation procedure to choose independent variables entering the regression equation, is reported. All computations were done with Matlab® and programming examples are given.