Multi-way data modelling for enhancing classification performance: Fluorescence data as a case of study

The exploitation of multidimensional information represents a key challenge in analytical chemistry, particularly for classification tasks involving complex systems. This study systematically investigates the influence of data structure-ranging from first-to third-order-on classification performance using simulated and experimental fluorescence datasets. Chemometric models based on partial least squares-discriminant analysis (PLS-DA), multi-way PLS-DA (N-PLS-DA), and parallel factor analysis combined with discriminant analysis (PARAFAC-DA) were evaluated under varying conditions of class balance, noise, and sample size. Simulated and experimental datasets based on excitation-emission fluorescence spectroscopy were used.

Simulated results demonstrated that increasing data dimensionality markedly enhanced discrimination ability, yielding higher accuracy and reduced error rates. Third-order models achieved average accuracies above 93 %, improving by up to 20 % and 10 % compared to the first- and second-order models, respectively. The methodology was further validated using excitation-emission fluorescence data from extra virgin and virgin olive oils subjected to infrared heating. Both N-PLS-DA and PARAFAC-DA provided successful discrimination, with PARAFAC-DA offering superior interpretability through chemically meaningful component profiles describing degradation and oxidation processes. Overall, the findings confirm that third-order chemometric models effectively integrate structural, spectral, and kinetic information, thereby improving classification reliability and interpretability. Even under conditions of class imbalance and limited sample availability, third-order models maintained low error rates and consistently high accuracy values, confirming their robustness and generalizability.

This study provides a comprehensive evaluation of how data structure influences multivariate classification performance. The proposed approach highlights the analytical potential of higher-order data modelling as a powerful and versatile strategy for classifying complex matrices. The findings firmly establish third-order modelling as a versatile and compelling tool for analytical applications where data complexity and real-world variability are unavoidable.