Handle Matrix Rank Deficiency, Noise, and Interferences in 3D Emission-Excitation Matrices: Effective Truncated Singular-Value Decomposition in Chemometrics Applied to the Analysis of Polycyclic Aromatic Compounds.

The characterization of organic compounds in polluted matrices by eco-friendly three-dimensional (3D) fluorescence spectroscopy coupled with chemometric algorithms constitutes a powerful alternative to the separation techniques conventionally used. However, the systematic presence of Rayleigh and Raman scattering signals in the excitation-emission matrices (EEMs) complicates the spectral decomposition via PARAllel FACtor analysis (PARAFAC) due to the nontrilinear structure of these signals. Likewise, the specific problem of selectivity in spectroscopy for unexpected chemical components in a complex sample may render its chemical interpretation difficult at first glance. The relevant chemical information can then be complicated to extract, especially if the raw data is noisy. There are several strategies to overcome these drawbacks, but weaknesses remain. As a consequence, a new alternative method is proposed to handle these interferences, the noise, and the rank deficiencies in the data and applied for the characterization of polycyclic aromatic compound (PAC) mixtures. It is based on effective truncated singular-value decomposition (MT-SVD) that does not require any prior knowledge of the raw data. The algorithm provides a valuable estimation of the global rank to choose on complex samples where selectivity problems are observed. It is a real alternative compared to other existing methods applied to the fluorescence matrix to filter the signal from noise or light scattering effects. The first exploratory results of the proposed algorithm are promising to handle matrix rank deficiencies as well as the effects of noise and light scattering on complex PAC mixtures.