Hierarchical excitation-emission matrix (EEM) decomposition: Relaxed implementation of Kasha’s rule to enhance resolution

Excitation-emission matrix (EEM) fluorescence spectroscopy is widely used for characterizing environmental samples and shows potential in water quality monitoring. Parallel factor analysis (PARAFAC) is currently the dominant method for EEM decomposition. However, it imposes strict adherence to Kasha's rule and is limited in resolving highly overlapping fluorophores, restricting its ability to interpret spectral shifts and sub-fluorophore level heterogeneity. Here, we propose a Hierarchical EEM Decomposition (HED) framework that relaxes Kasha's rule, enabling controlled spectral flexibility and improved decomposition resolution of chemically distinct components within the same fluorophore group. Applied to EEM datasets from wastewater and greywater treatment systems, HED revealed excitation-dependent emission behavior in long-wavelength DOM fluorescence consistent with charge transfer (CT) model assumptions, which PARAFAC cannot capture. HED also successfully deconvoluted signals with distinct chemical sources from overlapping tryptophan-like DOM fluorescence, as evidenced by the alignment of the deconvoluted signal pattern with the degree of treatment of wastewater and the improved estimation of bacterial and DOC concentrations for greywater. Furthermore, the integration of prior knowledge (e.g., target concentrations) as soft constraints enhanced model interpretability and predictive power. HED introduced in this work offers a physically grounded alternative to existing decomposition approaches, providing opportunities for high-resolution, interpretable EEM-based monitoring of complex water matrices.