
A command to use the selected Discriminant to classify each row from the selected TableOfReal. The newly created ClassificationTable will then contain the posterior probabilities of group membership.
The posterior probabilities of group membership p_{j} for a vector x are defined as:
p_{j} = p(jx) = exp (–d_{j}^{2}(x) / 2) / ∑_{k=1..numberOfGroups} exp (–d_{k}^{2}(x) / 2), 
where d_{i}^{2} is the generalized squared distance function:
d_{i}^{2}(x) = ((x–μ_{i})′ Σ_{i}^{1} (x–μ_{i}) + ln determinant (Σ_{i})) / 2 – ln aprioriProbability_{i} 
that depends on the individual covariance matrix Σ_{i} and the mean μ_{i} for group i.
When the covariances matrices are pooled, the squared distance function can be reduced to:
d_{i}^{2}(x) = ((x–μ_{i})′ Σ^{1} (x–μ_{i}) – ln aprioriProbability_{i}, 
and Σ is now the pooled covariance matrix.
The a priori probabilities normally will have values that are related to the number of training vectors n_{i} in each group:
aprioriProbability_{i} = n_{i} / Σ_{k=1..numberOfGroups} n_{k} 
© djmw 20040407