The Fisher linear discriminant is a linear transformation to one dimension used to separate two classes of multivariate
observations. Let the class sample means be 
and 
, and let 
be the sum of the two within-class scatter matrices.
A Fisher linear discriminant is obtained by choosing a nonzero vector 
that maximizes Fisher's criterion.
When 
is a nonsingular matrix, every maximizing direction is proportional to
 |
The resulting scalar 
can then be compared with a threshold to classify an observation.
This construction forms the two-class basis of linear discriminant analysis.
