Multivariate curve resolution-soft independent modelling of class analogy (MCR-SIMCA)

Various classification, class modeling, and clustering techniques operate within abstract spaces, utilizing Principal Components (e.g., Linear Discriminant Analysis (LDA), Principal Component Analysis (PCA)) or latent variable spaces (e.g., Partial Least Squares Discriminant Analysis (PLS-DA)). It's important to note that PCA, despite being a mathematical tool, defines its Principal Components under certain mathematical constraints, it has a wide range of applications in the analysis of real-world systems. In this research, we assess the viability of employing the Multivariate Curve Resolution (MCR) subspace within class modeling techniques, as an alternative to the PC subspace. (92).

This study evaluates the use of the MCR subspace in class modeling methods, specifically in tandem with soft independent modeling of class analogy (SIMCA), to investigate the advantages of employing the meaningful physico-chemical subspace of MCR over the mathematical subspace of PCA. In the MCR-SIMCA strategy, the model is constructed by applying MCR to training samples from a target class. The MCR model effectively partitions the data into two smaller sub-matrices: the contribution matrix and the corresponding response matrix. In the next step, the contribution matrix resulting from the decomposition of the training set develops a distance plot (DP). First, the theory of the MCR-SIMCA model is discussed in detail. Next, two real experimental datasets were analyzed, and their performance was compared with the DD-SIMCA model. In most cases, the results were as good as or even more satisfactory than those obtained with the DD-SIMCA model. (146).

The suggested class modeling method presents a promising avenue for the analysis of real-world natural systems. The study's results emphasize the practical utility of the MCR approach, underscoring the significance of the MCR subspace advantages over the PCA subspace. (39).