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 between-groups and the within-groups sums of squares and cross-products 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:
|B1′B1 x - λ W1′W1 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 ni in each group:
|aprioriProbabilityi = ni / Σk=1..numberOfGroups nk|
© djmw, January 4, 1999