A procedure to facilitate the choice of the number of factors in multi-way data analysis applied to the natural samples: Application to monitoring the thermal degradation of oils using front-face fluorescence spectroscopy

Abstract Multi-way data analysis techniques are becoming ever more widely used to extract information from data, such as 3D excitation–emission fluorescence spectra, that are structured in (hyper-) cubic arrays. Parallel Factor Analysis (PARAFAC) is very commonly applied to resolve 3D-fluorescence data and to recover the signals corresponding to the various fluorescent constituents of the sample. The choice of the appropriate number of factors to use in PARAFAC is one of the crucial steps in the analysis. When the signals in the data come from a relatively small number of easily distinguished constituents, the choice of the appropriate number of factors is usually easy and the mathematical diagnostic tools such as the Core Consistency, in general give good results. However, when the data is from a set of natural samples, the core consistency may not be a good indicator for the choice of the appropriate number of factors. In this work, Multi-way Principal Component Analysis (MPCA) and the Durbin–Watson criterion (DW) are utilized to choose the number of factors to use in PARAFAC decomposition. This is demonstrated in a case where 3D-front-face fluorescence spectroscopy is used to monitor of the evolution of naturally occurring and neo-formed fluorescent components in oils during thermal treatment.