TableOfReal: To Discriminant

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:

B1B1 x - λ W1W1 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

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© djmw, January 4, 1999