
A command that creates a Discriminant object from every selected TableOfReal object. Row labels in the table indicate group membership.
We solve for directions x that are eigenvectors of the generalized eigenvalue equation:
B x  λ W x = 0, 
where B and W are the betweengroups and the withingroups sums of squares and crossproducts matrices, respectively. Both B and W are symmetric matrices. Standard formula show that both matrices can also be written as a matrix product. The formula above then transforms to:
B_{1}′B_{1} x  λ W_{1}′W_{1} x = 0 
The equation can be solved with the generalized singular value decomposition. This procedure is numerically very stable and can even cope with cases when both matrices are singular.
The a priori probabilities in the Discriminant will be calculated from the number of training vectors n_{i} in each group:
aprioriProbability_{i} = n_{i} / Σ_{k=1..numberOfGroups} n_{k} 
© djmw, January 4, 1999