Multi-Way Data Analysis Nowadays: Taking Advanced Chemometric Tools to Everyday Analytical Chemistry Applications

Multi-way analysis has become one of the most powerful and versatile chemometric approaches for dealing with the increasing complexity of data generated in modern analytical chemistry. Advances in instrumentation, the widespread use of hyphenated techniques, and the inherently multidimensional nature of many experimental designs require methods capable of preserving structural relationships within datasets. In this context, multi-way tools such as Tucker 3, PARAFAC, or other supervised variants provide rigorous and interpretable descriptions of variability across multiple modes (samples, variables, conditions), enabling the extraction of meaningful patterns, improved noise handling, and enhanced robustness, compared with traditional bilinear approaches. This review offers a critical overview of the most commonly applied multi-way algorithms and their practical use in fields such as environmental chemistry, food science, clinical diagnostics, industrial process monitoring, and pharmaceutical analysis. The essential steps of the workflow, from data acquisition and preprocessing to model selection and interpretation, are discussed, highlighting their impact on model reliability. A dedicated section summarizes the software environments available for performing multi-way analyses, guiding readers in selecting the most suitable tools for their needs. Overall, this review emphasizes how multi-way chemometrics is becoming increasingly crucial for converting complex, high-dimensional data into reliable and actionable chemical knowledge.