Efficient tools for multivariate curve resolution: Outlier detection and estimation of the optimal number of...

Multivariate Curve Resolution (MCR) encompasses a wide range of algorithms widely used in solving analytical problems such as second-order calibration, where the well-known second-order advantage can be achieved. Another key application of these methods is the analysis of first-order data for analyte quantification using correlation constraints. In recent decades, MCR methods have also been successfully extended to classification and class modeling problems. This article discusses several critical aspects of exploratory analysis using MCR, including the estimation of appropriate model complexity and the influence of outliers. New tools are introduced to assess the complexity of MCR models, such as degrees-of-freedom plots developed for between-space distances, as well as the Extreme and Distance plots, which provide new insights into the behavior of both calibration and test data. The practical use of these tools is first demonstrated with a simulated dataset. Additionally, three real-world datasets from diverse application domains are used to showcase their capabilities: NIR corn data, wine classification by geographical origin, and the well-known Marzipan dataset; each widely used for demonstration and benchmarking purposes in chemometrics. The proposed methodology is intended as a complementary framework for assessing model complexity and model adequacy in MCR analyses. The presented calibration and class-modeling examples are used as illustrative case studies, while the proposed diagnostic tools are not intended to replace the chemical interpretation of resolved profiles, which remains a central aspect of MCR-based investigations.