Multiclass partial least squares discriminant analysis: Taking the right way—A critical tutorial

Abstract

AbstractHere, the theory of the multi‐class partial least squares discriminant analysis (PLS‐DA) is presented. A distinct feature of this theory is that it does not utilize PLS scores but is entirely based on the predicted dummy responses. It is shown that the results of the multi‐class PLS‐DA can be presented in a straightforward way by projecting the response matrix on the “super‐score” space by means of principal component analysis. Two approaches to discrimination are considered: the hard and the soft way of allocation. Correspondingly, 2 versions of PLS‐DA are presented: the conventional hard PLS‐DA, and the newly introduced soft PLS‐DA that seems to be a novel approach in chemometrics. The quality of classification is assessed using the figures of merit (sensitivity, specificity, and efficiency). It is shown how these characteristics are used for the selection of the model complexity. A number of practical problems are investigated, such as unbalanced sizes of classes, comparison of the discriminant and the class‐modeling methods and authentication by the “one against all” strategy. The paper is illustrated by real‐world and simulated examples.