Inverse Least Squares (ILS) methods such as Principal Components Regression (PCR) and Partial Least Squares (PLS) are ubiquitous in data science and chemometrics. However, Classical Least Squares (CLS or forward least squares) techniques are seeing a resurgence in popularity. The two major reasons for this are 1) better interpretability due to their relationship with first principles models, and 2) the ability to more closely control aspects of the regression modeling. As with ILS, CLS methods can be used for exploratory analysis, detection, classification and quantification.
This half-day course will start by covering CLS regression methods including classical, extended, weighted and generalized least squares. It will be shown how these methods can be used to account for interferents (i.e. analytes other than the one of interest) in spectroscopic systems. CLS also provides a natural framework for the development of popular de-cluttering methods such as External Parameter Orthogonalization (EPO) and Generalized Least Squares (GLS) weighting. It will also be shown how constraints can be easily employed with these methods to allow greater control over the modeling. Hands-on exercises will be done using PLS_Toolbox/Solo.