# PLS Discriminant Analysis

PLS Discriminant Analysis (PLS-DA) is a discrimination method based on PLS regression. At some point the idea of PLS-DA is similar to logistic regression — we use PLS for a dummy response variable, y, which is equal to +1 for objects belonging to a class, and -1 for those that do not (in some implementations it can also be 1 and 0 correspondingly). Then a conventional PLS regression model is calibrated and validated, which means that all methods and plots, you already used in PLS, can be used for PLS-DA models and results as well.

The extra step in PLS-DA is, actually, classification, which is based on thresholding of predicted y-values. If the predicted value is above 0, a corresponding object is considered as a member of a class and if not — as a stranger. In mdatools this is done automatically using methods plsda() and plsdares(), which inhertit all pls() and plsres() methods. Plus they have something extra to represent classification results, which you have already read about in the chapter devoted to SIMCA. If you have not, it makes sense to do this first, to make the understanding of PLS-DA implementation easier.

In this chapter we will describe shortly how PLS-DA implementation works. All examples are based on the well-known Iris dataset, which will be split into two subsets — calibration (75 objects, 25 for each class) and validation (another 75 objects). Two PLS-DA models will be built — one only for virginica class and one for all three classes.