Stabilizing the PARAFAC decomposition of fluorescence spectra by insertion of zeros outside the data area

The use of fluorescence spectroscopy for recording multiple excitation and corresponding emission wavelengths and the subsequent technique of analyzing the resulting fluorescence landscapes is a rather new method as opposed to the use of just a single excitation wavelength. In a fluorescence landscape, several light-scatter effects are usually present, and often the part of the landscape containing information on the chemical and/or physical characteristics of the sample is surrounded by two Rayleigh scatter lines. When such landscapes are decomposed using parallel factor analysis (PARAFAC), the scatter effects may have detrimental effects on the resolved spectra, especially if the peaks from the analytes lie close to or on the Rayleigh scatter lines. Normally, all values close to and outside the Rayleigh scatter lines are set to missing values before decomposing the fluorescence landscapes by PARAFAC. In this paper, we introduce a novel pretreatment method applicable for two-dimensional fluorescence landscapes, where instead of inserting only missing values a mixture of zeros and missing values are inserted close to and outside the Rayleigh scatter lines. It is shown that, by the use of this technique, a physically and chemically meaningful decomposition is obtained, and furthermore the modeling converges faster. Constraining the PARAFAC solution to positive values in all modes gave results similar to those obtained for the unconstrained model, except that the loadings where less smooth and the number of iterations before convergence was smaller.