Canonical discriminant analysis is a dimension-reduction technique related to principal component analysis and canonical correlation called canonical discriminant analysis. It derives the canonical coefficients parallels that of one-way MANOVA and it finds linear combinations of the quantitative variables that provide maximal separation between the classes or groups in much the same way that principal components summarize total variation.

The output produced are the canonical coefficients and the scored canonical variables. The canonical coefficients are rotated. The ellipse confidence bounds. Also, it proceeds with a Bartlett's approximate chi-squared statistic for testing the canonical correlation coefficients.

In summary, the canonical discriminant analysis:
- Transform the variables so that the pooled within-group covariance matrix is
an identity matrix.
- Compute group means on the transformed variables.
- Performs a principal component analysis on the means, weighting each mean by the number of observations in the group. The eigenvalues are equal to the ratio of between-group variation to the within-group variation in the direction of each principal component. Here, the principal component analysis is runned by the singular value decomposition.
- Back-transform the principal components into the space of the original variables, obtaining the canonical variables.

File gives you the option to get an unbiased or maximum-likelihood parameter estimation.