Evaluation of Classical Least Squares Discriminant Analysis (CLS-DA) as a Novel Supervised Pattern Recognition Technique

Multivariate calibration techniques and machine learning algorithms are inextricably linked within the realm of chemometrics and data analysis. Classical least squares (CLS) modeling, a fundamental multivariate regression approach, has traditionally been utilized for quantitative analysis tasks, establishing relationships between predictor variables (e.g., spectroscopic data) and response variables (e.g., chemical concentrations). However, a unique feature of CLS is its ability to handle scenarios with partial knowledge of the independent variable matrix, making it an intriguing candidate for qualitative pattern recognition and discriminant analysis applications. This study proposes a novel approach, Classical Least Squares Discriminant Analysis (CLS-DA), which combines the principles of CLS modeling with discriminant analysis objectives. The performance of CLS-DA is comprehensively evaluated using two real-world datasets: chemical analysis of three wine cultivars and mid-infrared spectroscopy of minced meat samples (pork, chicken, and turkey). The results are compared against the well-established Partial Least Squares Discriminant Analysis (PLS-DA) method, a widely adopted technique for classification tasks in chemometrics. For both sets of experimental data, CLS-DA and PLS-DA showed comparable efficiency. For the classification of three types of wine, the accuracy of the proposed method was 94.3%, while the accuracy of the reference method was 98.1%. For the classification of minced meat samples, the accuracies of CLS-DA and PLS-DA were 97.2% and 94%, respectively for all three groups. The findings demonstrate the potential of CLS-DA as a straightforward and interpretable supervised pattern recognition technique, exhibiting comparable classification performance to PLS-DA. The study highlights the advantages of CLS-DA, including its ability to operate within the original data space and its flexibility in accommodating partial knowledge scenarios. The proposed CLS-DA approach presents a promising alternative for discriminant analysis, offering new perspectives on the applications of classical least squares modeling in chemometrics.