Review of Variable Selection Methods for Discriminant-Type Problems in Chemometrics - Sorochan Armstrong, Michael D.; de la Mata, A. Paulina; Harynuk, James J. (Frontiers in Analytical Science, 2022)
Discriminant-type analyses arise from the need to classify samples based on their measured characteristics (variables), usually with respect to some observable property. In the case of samples that are difficult to obtain, or using advanced instrumentation, it is very common to encounter situations with many more measured characteristics than samples. The method of Partial Least Squares Regression (PLS-R), and its variant for discriminant-type analyses (PLS-DA) are among the most ubiquitous of these tools. PLS utilises a rank-deficient method to solve the inverse least-squares problem in a way that maximises the co-variance between the known properties of the samples (commonly referred to as the $Y$-Block), and their measured characteristics (the $X$-block). A relatively small subset of highly co-variate variables are weighted more strongly than those that are poorly co-variate, in such a way that an ill-posed matrix inverse problem is circumvented. Methods based on PLS are widely used, but suffer from a tendency to over-fit the data and may poorly indicate external samples. Feature selection is a common way of reducing the dimensionality of the data to a relatively small but robust subset of variables for use in subsequent modelling. The utility of these features can be inferred and tested any number of ways; this is the subject of this review.