ORTHOGONAL CANONICAL VARIATES FOR DISCRIMINATION AND CLASSIFICATION

A new set of derived variables is proposed for exhibiting group separation in multivariate data or for preprocessing such data prior to discriminant analysis. The technique combines optimal features of canonical variate analysis and principal component analysis: the derived variables are linear combinations of the original variables that optimize the canonical variate criterion (ratio of between-group to within-group variance) but subject to the orthogonality constraints of principal components. In this formulation the canonical variates can be derived even when the within-group matrix is singular (i.e. when there are more variables than objects in the data matrix). A simple computational algorithm for extraction of these variables is proposed. The methods are illustrated on several data sets and compared with alternative techniques such as principal component analysis and partial least squares.