Overview of Canonical Discriminant Analysis

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Overview of Canonical Discriminant Analysis

*Canonical discriminant analysis*
is a dimension-reduction technique that is related to principal component analysis and canonical correlation. Given a nominal
classification variable and several interval variables, canonical discriminant analysis derives canonical variables (linear
combinations of the interval variables) that summarize between-class variation in much the same way that principal components
summarize total variation.

Canonical discriminant analysis is equivalent to canonical correlation analysis between the quantitative variables and a set
of dummy variables coded from the classification variable.

Given two or more groups of observations with measurements on several interval variables, canonical discriminant analysis
derives a linear combination of the variables that has the highest possible multiple correlation with the groups. This maximum
multiple correlation is called the first canonical correlation. The coefficients of the linear combination are the *canonical coefficients*. The variable defined by the linear combination is the first canonical variable. The second canonical correlation is obtained
by finding the linear combination uncorrelated with the first canonical variable that has the highest possible multiple correlation
with the groups. The process of extracting canonical variables can be repeated until the number of canonical variables equals
the number of original variables or the number of classes minus one, whichever is smaller. Canonical variables are also called
*canonical components*.

You can run the Canonical Discriminant analysis by selecting → → from the main menu. The analysis is implemented by calling the DISCRIM procedure with the CANONICAL option in SAS/STAT software.
See the documentation for the DISCRIM and CANDISC procedures in the
*SAS/STAT User's Guide* for additional details.

The analysis calls the DISCRIM procedure (rather than the CANDISC procedure)
because the DISCRIM procedure produces a discriminant function that can be used to classify current or future observations.

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