Statistical Discriminant Analysis

Canonical discriminant analysis (CDA) and linear discriminant analysis (LDA) are popular classification techniques. Likewise, practitioners, who are familiar with regularized discriminant analysis (RDA), soft modeling by class analogy (SIMCA), principal component analysis (PCA), and partial least squares (PLS) will often use them to perform classification. In this chapter, we will attempt to make some sense out of all of this. We will explain when CDA and LDA are the same and when they are not the same. We will also discuss the relative merits of the various stabilization and dimension reducing methods used, focusing on RDA for numerical stabilization of the inverse of the covariance matrix and PCA and PLS as part of a two-step process for classification when dimensionality reduction is an issue.